case study based questions on fractions class 6

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Case Study Questions for Class 6 Maths

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Here in this article, we are providing case study questions for class 6 maths.

Maths Class 6 Chapter List

Latest chapter list (2023-24).

Chapter 1 Knowing Our Numbers Case Study Questions Chapter 2 Whole Numbers Case Study Questions Chapter 3 Playing with Numbers Case Study Questions Chapter 4 Basic Geometrical Ideas Case Study Questions Chapter 5 Understanding Elementary Shape Case Study Questions Chapter 6 Integers Case Study Questions Chapter 7 Fractions Case Study Questions Chapter 8 Decimals Case Study Questions Chapter 9 Data Handling Case Study Questions Chapter 10 Mensuration Case Study Questions Chapter 11 Algebra Case Study Questions Chapter 12 Ratio and Proportion Case Study Questions

Old Chapter List

Chapter 1 Knowing Our Numbers Chapter 2 Whole Numbers Chapter 3 Playing with Numbers Chapter 4 Basic Geometrical Ideas Chapter 5 Understanding Elementary Shape Chapter 6 Integers Chapter 7 Fractions Chapter 8 Decimals Chapter 9 Data Handling Chapter 10 Mensuration Chapter 11 Algebra Chapter 12 Ratio and Proportion Chapter 13 Symmetry Chapter 14 Practical Geometry

Deleted Chapter:

Tips for Answering Case Study Questions for Class 6 Maths in Exam

1. Comprehensive Reading for Context: Prioritize a thorough understanding of the provided case study. Absorb the contextual details and data meticulously to establish a strong foundation for your solution.

2. Relevance Identification: Pinpoint pertinent mathematical concepts applicable to the case study. By doing so, you can streamline your thinking process and apply appropriate methods with precision.

3. Deconstruction of the Problem: Break down the complex problem into manageable components or steps. This approach enhances clarity and facilitates organized problem-solving.

4. Highlighting Key Data: Emphasize critical information and data supplied within the case study. This practice aids quick referencing during the problem-solving process.

5. Application of Formulas: Leverage pertinent mathematical formulas, theorems, and principles to solve the case study. Accuracy in formula selection and unit usage is paramount.

6. Transparent Workflow Display: Document your solution with transparency, showcasing intermediate calculations and steps taken. This not only helps track progress but also offers insight into your analytical process.

7. Variable Labeling and Definition: For introduced variables or unknowns, offer clear labels and definitions. This eliminates ambiguity and reinforces a structured solution approach.

8. Step Explanation: Accompany each step with an explanatory note. This reinforces your grasp of concepts and demonstrates effective application.

9. Realistic Application: When the case study pertains to real-world scenarios, infuse practical reasoning and logic into your solution. This ensures alignment with real-life implications.

10. Thorough Answer Review: Post-solving, meticulously review your answer for accuracy and coherence. Assess its compatibility with the case study’s context.

11. Solution Recap: Before submission, revisit your solution to guarantee comprehensive coverage of the problem and a well-organized response.

12. Previous Case Study Practice: Boost your confidence by practicing with past case study questions from exams or textbooks. This familiarity enhances your readiness for the question format.

13. Efficient Time Management: Strategically allocate time for each case study question based on its complexity and the overall exam duration.

14. Maintain Composure and Confidence: Approach questions with poise and self-assurance. Your preparation equips you to conquer the challenges presented.

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CBSE Important Questions Class 6 Maths Chapter 7

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Important Questions Class 6 Maths Chapter 7 – Fractions

Maths is a major subject taught in school, but it is a subject that is needed in our everyday life too.

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Chapter 7 of Class 6 Maths is about fractions. Students are familiar with fractions. In simple words, a fraction represents a part of the whole. It has a numerator and denominator. Generally, the numerator is smaller than the denominator, but the opposite happens too. Students must practise questions from the chapter to clarify their understanding of these concepts.

Extramarks is a leading company that provides unlimited study materials to students. Our experts have prepared the Important Questions Class 6 Maths Chapter 7 to help students practise. They have collected several questions and provided the solutions here. Thus, it will help students clear any doubts that they have.

You can register on the official website of Extramarks to download various study materials. We provide CBSE syllabus, CBSE sample papers, CBSE extra questions, CBSE past years’ question papers, CBSE revision notes, NCERT books, NCERT solutions, NCERT important questions, vital formulas and many more.

Fraction Questions for Class 6 – With Solutions

The experts of Extramarks have collected the following questions from different sources. They have taken help from the textbook exercises, NCERT exemplar and important reference books. Apart from this, they have also included some questions from CBSE past years’ question papers and CBSE sample papers so that students may know which types of questions generally come in exams. Thus, students may follow the Important Questions Class 6 Maths Chapter 7 to boost their exam preparation. The questions are-

Question 1. Write the fraction representing the shaded portion: Answer 1. Total number of parts = 4

Shaded parts = 2

Fraction of shaded parts = 2/4

Question 2. Write the fraction representing the shaded portion:

Answer 2. Total number of parts = 9

Shaded parts = 4

Fraction of shaded parts = 4/9

Question 3. Write the fraction representing the shaded portion:

Answer 3. Total number of parts = 8

Fraction of shaded parts = 4/8

Question 4. What fraction of a day are eight hours? 

Answer 4. Total number of hours in a day = 24

Therefore, the fraction of 8 hours = 8/24 or 1/3

Question 5. What fraction of an hour are 40 minutes? 

Answer 5. Minutes in an hour = 60

Therefore, a fraction of 40 minutes = 40/60 or 2/3.

Question 6. Arya, Abhimanyu and Vivek shared lunch today. Arya had brought two sandwiches, one made of vegetables and one of jam. The other two students Abhimanyu and Vivek forgot to bring their lunch today. Arya agreed to share his two sandwiches so that all three would have an equal share of each sandwich. 

How can Arya divide his two sandwiches so that each person has an equal share? 

Answer 6. He will have to divide each of the sandwiches into three equal parts.

What part of a sandwich will each student receive? 

Each boy will receive 1×1/3 or 1/3 sandwiches of each type.

Question 7. Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished? 

Answer 7. Total number of dresses = 30

Number of dresses finished by Kanchan = 20

Fraction of dresses finished = 20/30 or 2/3

Question 8. The two consecutive integers in between which the fraction 5/7 lies are

(A) 5 and 7 

(B) 0 and 1 

(C) 5 and 6 

(D) 6 and 7

(B) 0 and 1

A fraction whose numerator(N) is less than the denominator(D) is called a proper fraction.

So, 5/7 = 0.715

Therefore, 5/7 lies between 0 and 1.

Question 9.

Write down the 11 natural numbers from 2 to 12. What fraction of them are prime numbers?

Natural numbers from 2 to 12 are – 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.

Prime numbers from among these numbers are 2, 3, 5, 7, and 11.

Therefore, out of the 11 numbers, 5 are prime numbers. It represents a fraction of 5/11.

Question 10.

Write the 12 natural numbers from 102 to 113. What fraction of them are prime numbers?

Natural numbers from 102 to 113 are – 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113

Among these 12 numbers, the 4 prime numbers are 103, 107, 109, and 113.

Therefore, out of the 12 numbers, 4 are prime numbers. It represents a fraction of 4/12.

Question 11. When ¼ is written with the denominator as 12, its numerator is

(1 × 3)/(4 × 3) = 3/12

Consider, 3/12

Divide both numerator and denominator by 3.

Question 12. Which of the following fraction is not equal to the others?

(ii) 12/16 

(iii) 15/25 

(iii) 15/25

All the options given in the question are further simplified as follows,

Divide both numerator and denominator by 2.

Divide both numerator and denominator by 4.

Divide both numerator and denominator by 5.

Divide both numerator and denominator by 6.

Comparing all results, (¾ = ¾ = ¾) ≠ 3/5

Therefore, (6/8 = 12/16 = 18/24) ≠ 15/25

Question 13. Which of the following given fractions is the greatest?

We know that among all fractions with the same numerator, the one having a smaller denominator will be the highest fraction.

5/9 < 5/8 < 5/7 < 5/6

Therefore, among four options, (ii) 5/6 has a small denominator. So, it is the greatest fraction.

Question 14. The mixed fraction 5(4/7) can also be expressed as –

(iii) 33/4 

The mixed fraction 5(4/7) can be expressed as = 5 + (4/7)

= (35 + 4)/7

Question 15. Is 7/19 a fraction?

7/19 is a proper fraction.

Question 16. Are 5/8 and 3/8 proper fractions or not?

5/8 and 3/8 are like proper fractions.

Fractions with the same denominators are called fractions.

Question 17. What type of fractions are 18/135 and 90/675. Are they proper, unlike fractions? 

18/135 and 90/675 are proper, unlike and equivalent fractions.

Consider the two given fractions, 18/135 and 90/675

So, (18/135) = (90/675)

By cross multiplication, we get

(18 × 675) = (90 × 135)

12,150 = 12,150

Therefore, 18/135 and 90/675 are proper, unlike and equivalent fractions.

Question 18. The following fractions below are represented by just three different numbers. Now, separate them into three groups of all equivalent fractions by changing each one of them to its simplest form.

(i) 2/12 (ii) 3/15 (iii) 8/50 (iv) 16/100 (v) 10/60 (vi) 15/75

(vii) 12/60 (viii) 16 / 96 (ix) 12 / 75 (x) 12 / 72 (xi) 3 / 18 (xii) 4/25

(i) 2 / 12 = (1 × 2) / (6 × 2)

(ii) 3 / 15 = (1 × 3) / (5 × 3)

(iii) 8 / 50 = (4 × 2) / (25 × 2)

(iv) 16 / 100 = (4 × 4) / (25 × 4)

(v) 10 / 60 = (1 × 10) / (6 × 10)

(vi) 15 / 75 = (1 × 15) / (5 × 15)

(vii) 12 / 60 = (1 × 12) / (5 × 12)

(viii) 16 / 96

= (1 × 16) / (6 × 16)

(ix) 12 / 75 = (4 × 3) / (25 × 3)

(x) 12 / 72 = (1 × 12) / 6 × 12)

(xi) 3 / 18 = (1 × 3) / (6 × 3)

(xii) 4 / 25

Totally there are three groups of equivalent fractions.

1 / 6 = (a), (e), (h), (j), (k)

1 / 5 = (b), (f), (g)

4 / 25 = (c), (d), (i), (l)

Question 19. Find the answers to the following. Write and indicate how to solve the following:

(a) Is 5 / 9 equals(=) to 4 / 5

(b) Is 9 / 16 equals(=) to 5 / 9

(c) Is 4 /5 equals(=) to 16 / 20

(d) Is 1 / 15 equals(=) to 4 / 30

(a) 5 / 9 and 4 / 5

Now, convert all these fractions into like fractions:

5 / 9 = (5 / 9) × (5 / 5)

4 / 5 = (4 / 5) × (9 / 9)

∴ 25 / 45 ≠ 36 / 45

Therefore, 5 / 9 is not equal to 4 / 5

(b) 9 / 16, 5 / 9

Convert all these fractions into like fractions:

9 / 16 = (9 / 16) × (9 / 9)

5 / 9 = (5 / 9) × (16 / 16)

∴ 81 / 144 ≠ 80 / 144

Therefore, 9 / 16 is not equal to 5 / 9

(c) 4 / 5, 16 / 20

16 / 20 = (4 × 4) / (5 × 4)

∴ 4 / 5 = 16 / 20

Therefore, 4 / 5 is equal to 16 / 20

(d) 1 / 15, 4 / 30

4 / 30 = (2 × 2) / (15 × 2)

∴ 1 / 15 ≠ 4 / 30

Therefore, 1 / 15 is not equal to 4 / 30.

Question 20. Rafiq had exercised for 3 / 6 of an hour today, while Rohit exercised for 3 / 4 of an hour today. Who exercised for a longer ime today?

Rafiq exercised = 3 / 6 of an hour

Rohit exercised = 3 / 4 of an hour.

3 / 6 and 3 / 4

Convert both of these into like fractions:

(1) 3 / 6 = (3 × 2) / (6 × 2) = 6 / 12

(2) 3 / 4 = (3 × 3) / (4 × 3) = 9 / 12

So clearly, 9 / 12 is greater than 6 / 12.

∴ 3 / 4 > 3 / 6

Hence, Rohit exercised for a longer time than Rafiq.

Question 21 . In class A of total 25 students, 20 passed with 60% or more marks; in class B, of total 30 students, 24 passed with 60% or re marks. Calculate in which class was a greater fraction of students getting 60% or more marks.

The total number of students in Class A = 25

Students passed in the first class in Class A = 20

Therefore, fraction = 20 / 25

The total number of students in Class B = 30

Students passed in the first class in Class B = 24

Therefore, fraction = 24 / 30

∴ An equal fraction of the students passed in first class in both classes

Question 22.  

Write all these fractions appropriately as additions or subtractions:

(a) The total number of parts each rectangle has = 5

No. of all shaded parts in first rectangle = 1 i.e 1 / 5

No. of all shaded parts in second rectangle = 2 i.e 2 / 5

No. of all shaded parts in third rectangle = 3, i.e. 3 / 5

Clearly, the fraction which is represented by the third rectangle = the sum of the fractions represented by the first and the second rectangle.

Therefore, 1 / 5 + 2 / 5 = 3 / 5

(b) The total number of all parts each circle has is = 5

We have observed that the first, second and third circles represent 5, 3 and 2 shaded parts out of total 5 equal parts, respectively. Clearly, the Fraction represented above by the third circle is the difference between the fractions represented by the first and second circles.

Hence, 5 / 5 – 3 / 5 = 2 / 5

(c) Here, we may observe that the first, second and third rectangles represent 2, 3 and 5 shaded parts out of 6 equal parts, respectively. Clearly, the fraction represented by the third rectangle is the sum of fractions represented by the first and second rectangles.

Hence, 2 / 6 + 3 / 6 = 5 / 6

Question 23.

Kristin had received a CD player for her birthday. She bought 3 CDs and received five others as a gift. What fraction of the total CDs did she buy, and what fraction did she receive as gifts?

Answer 23. Total number of CDs with Kristin = 3 + 5

Total number of CDs she bought = 3

CDs she received as gift = 5

fraction of CDs she bought = 3/8 

fraction of CDs she received as gift = 5/8

Question 24.

Ramesh had 20 pencils, whereas Sheelu had 50 pencils, and Jamaal had 80 pencils. After four months, Ramesh used up ten pencils, Sheelu also used up 25 pencils, and Jamaal also used up 40 pencils. What fraction did each of them use up? Check if each of them has used up an equal fraction of her/his pencils.

Fraction used by Ramesh = 10/20 =1/2

Fraction used by Sheelu = 25/50 = 1/2

Fraction used by Jamaal = 40/80 = 1/2

Yes, all of them used an equal fraction of pencils, i.e., 1/2.

Question 25.

Write the fractions and pair up with the equivalent fractions from each row.

(a) Here, 1 part is shaded out of total of 2 equal parts (i.e., rectangle). Hence, this figure represents a fraction 1/2.

(b) Here, four parts are shaded out of 6 equal parts (i.e., rectangle). Hence, this figure represents a fraction of 4/6 = 2/3.

(c) Here, three parts are shaded out of 9 equal parts (i.e., squares). Hence, this figure represents a fraction of 3/9 = 1/3.

(d) Here, two parts are shaded out of 8 equal parts (i.e., rectangle). Hence, this figure represents a fraction of 2/8 = 1/4.

(e) Here, three parts are shaded out of 4 equal parts (i.e., squares). Hence, this figure represents a fraction of 3/4.

(i) Here, six parts are shaded out of 18 equal parts (i.e., triangles). Hence, this figure represents a fraction of 6/18 = 1/3.

(ii) Here, four parts are shaded out of 8 equal parts (i.e., rectangles). Hence, this figure represents a fraction of 4/8 = 1/2.

(iii) Here, 12 parts are shaded out of total of 16 equal parts (i.e., squares). Hence, this figure represents a fraction of 12/16 = 3/4.

(iv) Here, eight parts are shaded out of 12 equal parts (i.e., rectangles). Hence, this figure represents a fraction of 8/12 = 2/3.

(v) Here, four parts are shaded out of 16 equal parts (i.e., triangles). Hence, this figure represents a fraction of 4/16 = 1/4.

Now, these figures above can be matched correctly as

(a)-(ii), (b)-(iv), (c)-(i), (d)-(v), (e)-(iii)

Question 26.

Fill in the blanks:

There is a large box of 36 small square boxes.

• 1/2 of it is _____.
• 2/3 of it is _____.
• If I make a bench of 20 small boxes, the fraction becomes _____.
• _____ boxes are required if the fraction is ⅚.
• ½ of 36 is equal to 18
• = 1/2 of 36 boxes

= 36/2 = 18 boxes.

2/3rd of 36 is equal to 24

• If a bench is made with 20 boxes out of 36 boxes, the fraction becomes 5/9.

So, if i make a bench of 20 small boxes, the fraction becomes 5/9

• __boxes are required for the fraction to be 5/6.

x = (36×5)÷6

So, 30 boxes are required for the fraction to be 5/6

Question 27. Solve:

(a) 1 / 18 + 1 / 18

(b) 8 / 15 + 3 / 15

(c) 7 / 7 – 5 / 7

(d) 1 / 22 + 21 / 22

(e) 12 / 15 – 7 / 15

(f) 5 / 8 + 3 / 8

(g) 1 – 2 / 3 (1 = 3 / 3)

(h) 1 / 4 + 0 / 4

(i) 3 – 12 / 5

= (1 + 1) / 18

= (8 + 3) / 15

= (7 – 5) / 7

= (1 + 21) / 22

(e) 12 /15 – 7 / 15

= (12 – 7) / 15

= (5 + 3) / 8

(g) 1 – 2 / 3

= 3 / 3 – 2 / 3

= (3 – 2) / 3

(h) 1 / 4 + 0

= 15 / 5 – 12/ 5

= (15 – 12) / 5

Question 28. Shubham had painted 2 / 3 of the wall space in his room. His sister Madhavi had helped and painted 1 / 3 of the wall space. How much did they paint together?

Wall space painted by Shubham in a room = 2 / 3

Wall space painted by Madhavi in a room = 1 / 3

Total space painted by both = (2 / 3 + 1 / 3)

= (2 + 1) / 3

∴ Shubham and Madhavi together painted one complete wall in a room.

Question 29. Nandini’s house is about 9 / 10 km from her school. She walked some distance towards her school and then took a bus for 1 / 2 km to reach the school. How far did she walk?

Distance of the school from house = 9 / 10 km

The distance she travelled by bus = 1 / 2 km.

Distance walked by Nandini = Total distance of the school – Distance she travelled by bus.

= 9 / 10 – 1 / 2

= [(9 × 1) – (1 × 5)] / 10

= (9 – 5) / 10

∴ The distance walked by Nandini is 2 / 5 km.

Question 30. Asha and Samuel had bookshelves of the same size, partly filled with books. Asha’s shelf is 5 / 6th full, and Samuel’s shelf is 2/ 5 th full. Whose bookshelf is more full? By what fraction?

Fraction of Asha’s bookshelf = 5 / 6

Fraction of Samuel’s bookshelf = 2 / 5

Convert these fractions into like fractions

5 / 6 = 5 / 6 × 5 / 5

= (5 × 5) / (6 × 5)

2 / 5 = 2 / 5 × 6 / 6

= (2 × 6) / (5 × 6)

25 / 30 > 12 / 30

5 / 6 > 2 / 5

∴ Asha’s bookshelf is little more full than Samuel’s bookshelf.

Difference = 5 / 6 – 2 / 5

= 25 / 30 – 12 / 30

Question 31. Jaidev takes around minutes to walk across the school ground. Rahul takes around 7 / 4 minutes to do the same. Who takes lesser time, and by what fraction?

Time is taken by Jaidev to walk across the school ground =

= 11 / 5 minutes

The time it took for Rahul to walk across the school ground = was 7 / 4 minutes.

11 / 5 = 11 / 5 × 4 / 4

= (11 × 4) / (5 × 4)

7 / 4 = 7 / 4 × 5 / 5

= (7 × 5) / (4 × 5)

Clearly, 44 / 20 > 35 / 20

11 / 5 > 7 / 4

∴ Rahul takes lesser time than Jaidev to walk across the school ground.

Difference = 11 / 5 – 7 / 4

= 44 / 20 – 35 / 20

Hence, Rahul walks across the school ground for 9 / 20 minutes.

Question 32. A small piece of wire 7 / 8 metre long broke into two pieces. One piece is 1 / 4 metre long. How long is the other piece?

Total length of the wire = 7 / 8 metre

Length of one piece of the wire = 1 / 4 metre

Length of another piece of the wire = Length of the original wire, and this one piece of wire

= 7 / 8 – 1 / 4

= [(7 × 1) – (1 × 2)] / 8

= (7 – 2) / 8

∴ Length of the other piece of the wire = 5 / 8 metre

Question 33. Sarita bought 2 / 5 metres of ribbon and Lalita 3 /4 metres of the ribbon. What is the total length of the ribbon that they bought?

Length of the ribbon bought by Sarita = 2 / 5 metre

Length of the ribbon bought by Lalita = 3 / 4 metre

Total length of the ribbon bought by two of them = 2 / 5 + 3 / 4

Taking LCM 20

= [(2 × 4) + (3 × 5)] / 20

= (8 + 15) / 20

= 23 / 20 metre

∴ The total length of the ribbon that was bought by both Sarita and Lalita is 23 / 20 metres.

Benefits of Solving Important Questions Class 6 Maths Chapter 7

One must practise scoring better marks in exams. The more one can practise, the better one can do in Maths. So, students must build the habit of solving questions from each chapter. It will help them clear their understanding of each concept and increase their confidence. Moreover, it will help them to score better in exams. There will be other benefits of solving the Important Questions Class 6 Maths Chapter 7. They are-

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Q.1 In the following figures, the figure that is representing the fraction 3/5 of the shaded region to the unshaded region is

(i) and (iii) both

In figure (i) 3-parts are shaded and 5-parts are unshaded. So, figure (i) is the correct figure.

Q.2 Which of the following fractions is written in the simplest form

Q.3 Which of the following fractions is the greatest

Q.4 Arrange the following in descending order.

i 4 6 , 5 8 , 7 12 , 5 16 ii 8 17 , 8 9 , 8 5 , 8 13

i 4 6 , 5 8 , 7 12 , 5 16 LCM of 6, 8, 12 and 16 2 6, 8, 12, 16 2 3, 4, 6, 8 2 3, 2, 3, 4 2 3, 1, 3, 2 3 3, 1, 3, 1 1, 1, 1, 1 LCM of 6, 8, 12 and 16 = 2 — 2 — 2 — 2 — 3 = 48 So , 4 6 , 7 12 , 5 8 , 5 16 = 4 — 8 6 — 8 , 7 — 4 12 — 4 , 5 — 6 8 — 6 , 5 — 3 16 — 3 = 32 48 , 28 48 , 30 48 , 15 48 Descending order is: 32 48 , 30 48 , 28 48 , 15 48 = 4 6 , 5 8 , 7 12 , 5 16

ii 8 17 , 8 9 , 8 5 , 8 13 Since , two fractions with same numerators are compared, the fraction with the greater denominator will be the er fraction. So, the ascending order of denominators is 5 < 9< 13< 17 Thus, descending order of fractions is 8 5 > 8 9 > 8 13 > 8 17

Q.5 Find the equivalent fraction of

with denominator 63.

5 9 = 5 — 7 9 — 7 = 35 63

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Cbse important questions for class 6 maths, chapter 1 - knowing our numbers.

Chapter 2 - Whole Numbers

Chapter 3 - playing with numbers, chapter 4 - basic geometrical ideas, chapter 5 - understanding elementary shapes, chapter 6 - integers, chapter 8 - decimals, chapter 9 - data handling, chapter 10 - mensuration, chapter 11 - algebra, chapter 12 - ratio and proportion, chapter 13 - symmetry, chapter 14 - practical geometry, faqs (frequently asked questions), 1. what is discussed in class 6 maths chapter 7.

Class 6 Maths Chapter 7 is about fractions. In simple words, a fraction is a part of the whole. The upper part of the fractions is called the numerator, and the lower part is called the denominator. There are three types of fractions depending on the numerator and denominator. If the numerator is smaller than the denominator, it is less than 1 or the whole. But if the former is larger than the latter, it is more than 1. You can follow the Important Questions Class 6 Maths Chapter 7 to solve different questions from the chapter. You’ll find the answers in the article too.

2. How can the Important Questions Class 6 Maths Chapter 7 help students?

Experts have collected the questions from different sources. They have taken help from the textbook exercise, important reference books, NCERT exemplar, CBSE sample papers and CBSE past years’ question papers. They have provided the answers which experienced professionals have further checked to ensure the best quality for students. Thus, the Important Questions Class 6 Maths Chapter 7 will help students practise more and clarify their doubts. Thus, it will help to increase their marks in exams. The question-answer series will save their time, boost their confidence and upgrade their exam preparations. You will find important questions for other chapters too.

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NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

Fractions Class 6 Extra Questions Maths Chapter 7

June 11, 2019 by Bhagya

Extra Questions for Class 6 Maths Chapter 7 Fractions

Fractions Class 6 Extra Questions Very Short Answer Type

Question 6. Write all the natural numbers from 1 to 15. What fraction of them are prime numbers? Solution: Natural numbers from 1 to 15 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15 Prime numbers from 1 to 15 are 2, 3, 5, 7, 11, 13, i.e., 6 prime numbers. ∴ Fraction of prime numbers = \(\frac { 6 }{ 15 }\)

Fractions Class 6 Extra Questions Short Answer Type

Question 12. Write any (a) three proper and three improper fractions with denominator 7. (b) two proper and two improper fractions with numerator 9. Solution: (a) Proper fractions with denominator 7 are: \(\frac { 2 }{ 7 }\) , \(\frac { 3 }{ 7 }\) and \(\frac { 5 }{ 7 }\) Improper fractions with denominator 7 are: \(\frac { 9 }{ 7 }\) , \(\frac { 11 }{ 7 }\) and \(\frac { 13 }{ 6 }\)

(b) Proper fractions with numerator 9 are: \(\frac { 9 }{ 11 }\) and \(\frac { 9 }{ 17 }\) Improper fractions with numerator 9 are: \(\frac { 9 }{ 2 }\) and \(\frac { 9 }{ 5 }\)

Fractions Class 6 Extra Questions Higher Order Thinking Skills (HOTS)

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Important Questions for CBSE Class 6 Maths Chapter 7 - Fractions

• Class 6 Important Question
• Chapter 7: Fractions

CBSE Class 6 Maths Important Questions Chapter 7 - Fractions - Free PDF Download

Class 6 maths chapter 7 important questions PDF consists of specially curated and previous year questions that help students get a rough idea of the types of questions that can be asked in their semester examinations. Important Questions For Class 6 Maths Chapter 7 help students in revising what they have studied in an orderly manner, making sure that they don’t miss any important topics.  The subject matter experts at Vedantu have made sure to cover all the important concepts and necessary points for Class 6 Maths chapter 7.

You can download important questions on fractions for class 6 from Vedantu, on your laptop, PC or phone and study at your convenience, whenever and wherever. It is portable.

Given below is a summarized version of fractions class 6 important questions. It is advised to brush up on all the topics before you start attempting important questions on fractions for class 6. Vedantu is a platform that provides free CBSE Solutions (NCERT) and other study materials for students. You can also register Online for NCERT Class 6 Science tuition on Vedantu.com to score more marks in CBSE board examination.

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Study Important Questions for Class 6 Maths Chapter 7 - Fraction

Very short answer questions                                                1 mark.

1. Write fraction representing the shaded portion

Ans: Given- A figure with some shaded squares in it.

We have to find fractions for the shaded portion.

Total number of squares $=12$

Number of shaded boxes $=6$

$\therefore $ the shaded portion $=\dfrac{6}{12}$

2. Shade in the given figure: $\dfrac{5}{9}$

Ans: Given: A figure having $9$ boxes.

We have to shade 5 boxes out of a total 9 boxes.

3. Write in fraction form of eight-ninths.

Ans: We are given eight-ninths

To find: the fraction form of eight-ninths

Eight - ninths means eight parts out of nine

So, the fraction will be $\dfrac{8}{9}$

4. Write down the fraction with numerator 3, denominator 9

Ans: Given, numerator =3

Denominator =9

We have to find the fraction.

We know that the numerator is the above part of a fraction and the denominator is the below part of the fraction.

$\therefore$ The fraction is $\dfrac{3}{9}$.

5. Fill up the blanks

$\mathbf{\dfrac{1}{12}\square 1}$

Ans: Given: $\dfrac{1}{12}\square 1$

We have to put a sign between the terms like $<,>,=$

Solve, $\dfrac{1}{12}$

We can see that the value is less than one.

$\therefore \dfrac{1}{12}<1$

$\mathbf{\dfrac{6512}{6512}\square 1}$

Ans: Given: $\dfrac{6512}{6512}\square 1$

Solve, $\dfrac{6512}{6512}$

$\dfrac{6512}{6512}=1$

6. Compare $\mathbf{\dfrac{4}{5}}$ and $\mathbf{\dfrac{3}{5}}$

Ans: Given: two terms $\dfrac{4}{5},\,\dfrac{3}{5}$

We have to compare the given terms.

We can see that the denominator of both the terms is the same. So we will compare the numerators only.

Here, 

 $\therefore \dfrac{4}{5}>\dfrac{3}{5}$

Short Answer Questions                                                           2 Marks

1. Find $\mathbf{\dfrac{3}{4}}$ of $\mathbf{12.}$

Ans: Given, two terms $\dfrac{3}{4},12$

We have to find $\dfrac{3}{4}$ of $12.$

We know that $x$ of $y$ means $x\times y$

$\therefore \dfrac{3}{4}$ of $12$\[\]

$ =\dfrac{3}{4}\times 12 $

2. What fraction of an hour is 35 minutes?

Ans: Given, a time

We have to find $35$ minutes will be what fraction of an hour.

We know that $1$ hour $=60$ minutes

$\therefore $ fraction will be $\dfrac{35}{60}.$

3. The figure given can be written in the fraction form as $\mathbf{\dfrac{2}{3}.}$ Say true or false.

Ans: Given: figure

We have to find if the figure shows fraction $\dfrac{2}{3}.$

As we can see that all parts of the figure are not similar. Therefore, it cannot be represented as a fraction. So, the statement is False.

4. Name the numerator and denominator in the $\mathbf{\dfrac{16}{20}}$

Ans: Given: $\dfrac{16}{20}$

To find: numerator and denominator

We know that the numerator is the above part of the fraction and the denominator is the below part.

$\therefore $ Numerator $=16$

Denominator $=20$

5. Convert $\mathbf{\dfrac{30}{8}}$ into a mixed fraction

Ans: Given: $\dfrac{30}{8}$

To find: mixed fraction of the given expression.

We got mixed fraction by dividing the fraction

We know if  $\dfrac{x}{y}=z$ then mixed fraction is $z\dfrac{x}{y}$

$\therefore $ $\dfrac{30}{8}$

$ =3\dfrac{6}{8} $

$ =3\dfrac{3}{4}$

6. Convert $\mathbf{6\dfrac{7}{9}}$ into improper fraction.

Ans: Given: $6\dfrac{7}{9}$

To find the improper form of the given expression

We know that \[z\dfrac{x}{y}=\dfrac{y\times z+x}{y}\]

So, $6\dfrac{7}{9}=9\times 6+7$ as numerator

Therefore, the improper fraction will be $\dfrac{61}{9}.$

7. Fill in the blanks $\mathbf{\dfrac{54}{63}=\dfrac{6}{\square }}$

Ans:  Given: $\dfrac{54}{63}=\dfrac{6}{\square }$

We need to fill the blank

On Left Hand Side, divide numerator and denominator y by $9$

Thus, $\dfrac{54}{63}\div \dfrac{9}{9}$

$=\dfrac{6}{7}$

Thus, the number which has to be filled at blank is $7.$

8. Simplify:

$\mathbf{\dfrac{3}{8}+\dfrac{4}{8}+\dfrac{2}{8}}$

Ans: Given: $\dfrac{3}{8}+\dfrac{4}{8}+\dfrac{2}{8}$

We have to simplify the fractions by adding them

As the denominator of each fraction is same then the $\text{L}\text{.C}\text{.M}$ will be $8.$

Now, simply add the numerator of each fraction, we get

$=\dfrac{3+4+2}{8}$ $=\dfrac{9}{8}.$

$\mathbf{\dfrac{8}{9}-\dfrac{6}{9}}$

Ans: We have to find the difference between the fractions.

We can see that the denominator of both fractions is same then the $\text{L}\text{.C}\text{.M}$will be $9.$

Now, simply subtract the numerators, we get

$ \dfrac{8-6}{9} $

$ =\dfrac{2}{9} $

Short Answer Questions                                                           3 Marks

1. Seema has 28 books. She gave $\mathbf{\dfrac{4}{10}}$ to Meera. How many books does Meena has? How much is left with Seema?

Ans: Given: Total books Seema has $=28$

Seema gave books to Meera $\dfrac{4}{10}$ of $28$

$\therefore $ Books with Meena $=\dfrac{4}{10}\times 28$

$=11$ Books

Now, books left with Seema $=28-11$

$=17$ Books

2. Represent $\mathbf{3\dfrac{2}{5}}$ on the number line.

Ans: Given: $3\dfrac{2}{5}$

We have to represent the fraction on the number line.

We can write the fraction as,

$3\dfrac{2}{5}=3+\dfrac{2}{5}$

Therefore, we represent it on the number line as 

(image will be uploaded soon)

3. Write a fraction equivalent to $\mathbf{\dfrac{4}{5}}$ with numerator 16.

Ans: Given: $\dfrac{4}{5}$

We have to find a fraction so that the numerator of fraction is $16.$

Multiply the numerator and denominator of the given fraction with $4$to get the required fraction.

$ \dfrac{4}{5}\times \dfrac{4}{4} $ 

$ =\dfrac{16}{20} $

4. Write a fraction equivalent to $\mathbf{\dfrac{42}{60}}$ with denominator 10.

Ans: Given: $\dfrac{42}{60}$

We have to find a fraction so that the denominator of fraction is $10.$

Divide the numerator and denominator of the given fraction with $6$ to get the required fraction.

$ \therefore \dfrac{42}{60}\div \dfrac{6}{6} $

$ =\dfrac{7}{10} $

5. Simplify $\mathbf{\dfrac{7}{10}}$ into the simplest form.

Ans: Given: $\dfrac{7}{10}$

We have to find the simplest form of the fraction.

The HCF of the terms \[7\text{ }\!\!\And\!\!\text{ }10\] is \[1.\]

Thus, the fraction $\dfrac{7}{10}$ is already in its simplest form.

6. Simplify \[\mathbf{2\dfrac{7}{9}+\dfrac{11}{15}+\dfrac{9}{24}-3\dfrac{1}{4}}\]

Ans: Given: \[2\dfrac{7}{9}+\dfrac{11}{15}+\dfrac{9}{24}-3\dfrac{1}{4}\]

We need to simplify the given expression. So we’ll find \[\text{LCM}\]and then simplify the expression.

\[\text{LCM}\]of numbers \[9,15,24,4=360\]

$ 2\dfrac{7}{9}+\dfrac{11}{15}+\dfrac{9}{24}-3\dfrac{1}{4} $ 

$ =\dfrac{25}{9}+\dfrac{11}{15}+\dfrac{9}{24}-\dfrac{13}{4} $

$ =\dfrac{1000+264+135-1170}{360} $

$ =\dfrac{1399-1170}{360} $

$ =\dfrac{229}{360} $

7. Subtract $\mathbf{3\dfrac{7}{8}-5\dfrac{1}{6}}$

Ans: Given: $3\dfrac{7}{8}-5\dfrac{1}{6}$

\[\text{LCM}\] of the numbers $6,8=24$

$ 3\dfrac{7}{8}-5\dfrac{1}{6} $

$ =\dfrac{31}{6}-\dfrac{31}{8}$ 

$ =\dfrac{31\times 4-31\times 3}{24} $

$ =\dfrac{124-93}{24} $

$ =\dfrac{31}{24} $

Long  Answer Questions                                                           4 Marks

1. Write four equivalent fraction for each of the following:

$\mathbf{\dfrac{3}{7}}$

 Ans: Given: $\dfrac{3}{7}$

To find: four equivalent fraction

Multiply and divide numerator and denominator with four different numbers

$ \dfrac{3}{7}\times \dfrac{2}{2}=\dfrac{6}{14} $

$ \dfrac{3}{7}\times \dfrac{3}{3}=\dfrac{9}{21} $

$ \dfrac{3}{7}\times \dfrac{4}{4}=\dfrac{12}{28} $

$ \dfrac{3}{7}\times \dfrac{5}{5}=\dfrac{15}{35} $

$\mathbf{\dfrac{300}{900}}$

Ans: To find four equivalent fraction

$ \dfrac{300}{900}\div \dfrac{2}{2}=\dfrac{150}{450}$ 

$ \dfrac{300}{900}\div \dfrac{3}{3}=\dfrac{100}{300} $

$ \dfrac{300}{900}\div \dfrac{5}{5}=\dfrac{60}{180} $

$ \dfrac{300}{900}\div \dfrac{10}{10}=\dfrac{30}{90} $ 

2. Show that $\mathbf{\dfrac{6}{7}}$ and $\mathbf{\dfrac{42}{49}}$ are equivalent fractions.

Ans: Given: Fractions, $\dfrac{6}{7}$, $\dfrac{42}{49}$

We need to show that both the fractions are equivalent.

Thus, $\dfrac{6}{7}=\dfrac{42}{49}$

Cross multiply, we get

$ 6\times 49=249........(1) $

$ 7\times 42=294........(2) $

$ \Rightarrow (1)=(2) $

Therefore, we can say that the given fractions are equivalent.

3. Reduce into simplest form: $\mathbf{\dfrac{225}{500}}$

Ans: Given: $\dfrac{225}{500}$

We need to find the simplest form of the given fraction.

Divide by \[5,\] we get

$\dfrac{225}{500}\div \dfrac{5}{5}=\dfrac{45}{100}$

Again, divide by \[5,\] we get

$\dfrac{45}{100}\div \dfrac{5}{5}=\dfrac{9}{20}$

We can see that the HCF of the terms of the fraction is $1$

$\therefore \dfrac{9}{20}$ is the simplest form of the given fraction.

4. Convert \[\mathbf{\dfrac{1}{4},\dfrac{5}{8},\dfrac{13}{24}}\] into like fractions.

Ans: Given: \[\dfrac{1}{4},\dfrac{5}{8},\dfrac{13}{24}\]

We need to convert the given fractions into like fractions.

The LCM of the denominators will be

\[\begin{align} & 4\left| \!{\underline {\, 4,8,24 \,}} \right.  \\ & 2\left| \!{\underline {\, 1,2,6 \,}} \right.  \\ & \left| \!{\underline {\, 1,1,3 \,}} \right.  \\ \end{align}\]

Therefore, LCM = $4\times 2\times 3$ 

$\quad\quad\quad\quad\quad\quad=24$ 

$=\dfrac{\left( 6\times 1 \right),\left( 5\times 3 \right),\left( 13 \right)}{24}$ 

$=\dfrac{6,15,13}{24}$

So, the required like fractions are $\dfrac{6}{24},\dfrac{15}{24},\dfrac{13}{24}$

5. Compare $\mathbf{\dfrac{8}{13}\text{and}\dfrac{8}{7}}$

Ans: Given: fractions $\dfrac{8}{13}\text{and}\dfrac{8}{7}$

We need to compare the fractions.

To compare the fractions the denominator of the fractions must be the same.

To convert into like terms, take LCM then we get

$ =13\times 7 $

$ \therefore \dfrac{8\times 7,8\times 13}{91} $

$ =\dfrac{56,104}{91} $

$ \therefore \dfrac{56}{91}<\dfrac{104}{91} $

6. Roshni bought a material of length $\mathbf{3\dfrac{2}{5}\text{m}}$ and one more piece of length $\mathbf{2\dfrac{7}{10}\text{m}\text{.}}$ How much material did she purchase in all?

Ans: Given: Length of first material bought by Roshni $=3\dfrac{2}{5}\text{m}$

Length of second material bought by Roshni $=2\dfrac{7}{10}\text{m}$

Total length of material purchased by Roshni will be

$ =3\dfrac{2}{5}+2\dfrac{7}{10} $

$ =3+\dfrac{2}{5}+2+\dfrac{7}{10} $

$ =5+\dfrac{2\times 2+7}{10} $

$ =5+\dfrac{4+7}{10} $

$ =5+\dfrac{11}{10} $

$ =\dfrac{61}{10} $

$ =6\dfrac{1}{10}\text{m} $

7. Ram bought $\mathbf{6\dfrac{1}{2}}$ litres of milk. Out of this $\mathbf{5\dfrac{1}{4}}$ litres was used. How much is the remaining milk?

Ans: Total milk bought by Ram $=6\dfrac{1}{2}\text{litres}$

Milk Used $=5\dfrac{1}{4}\text{litres}$

Remaining milk with Ram will be

$ =6\dfrac{1}{2}-5\dfrac{1}{4} $

$ =6+\dfrac{1}{2}-\left[ 5+\dfrac{1}{4} \right] $

$ =6-5+\left[ \dfrac{1}{2}-\dfrac{1}{4} \right] $

$ =1+\dfrac{1}{4} $

$ =1\dfrac{1}{4}\text{litres} $

Very Long  Answer Questions                                             6 Marks

1.  Classify each of the following into proper, improper and mixed fractions.

$\mathbf{\dfrac{1}{5}}$

 Ans: Proper fraction

$\mathbf{12}$

Ans: Improper fraction

$\mathbf{3\dfrac{1}{5}}$

Ans: Proper fraction

$\mathbf{\dfrac{15}{6}}$

$\mathbf{\dfrac{15}{20}}$

2. Compare $\mathbf{\dfrac{5}{8}}$ and $\mathbf{\dfrac{4}{9}}$

Ans: Given: $\dfrac{5}{8}$ and $\dfrac{4}{9}$

We need to compare the given fractions so we will convert both fractions into like fractions by taking LCM.

$ \text{LCM = 72} $

$ \text{=}\dfrac{5\times 9,4\times 8}{72} $

$ =\dfrac{45,32}{72} $

$ =\dfrac{5}{8}>\dfrac{4}{9} $

3. Arrange the following in ascending and descending order $\mathbf{\dfrac{2}{3},\dfrac{3}{4},\dfrac{7}{10},\dfrac{8}{15},\dfrac{5}{8}}$

Ans: Given: fractions $\dfrac{2}{3},\dfrac{3}{4},\dfrac{7}{10},\dfrac{8}{15},\dfrac{5}{8}$

We need to find the ascending and descending order of the fractions.

We will first convert the fractions in like terms and then find the order.

To convert into like terms. LCM will be

$\begin{align} & 4\left| \!{\underline {\, 3,4,10,15,8 \,}} \right.  \\ & 5\left| \!{\underline {\, 3,1,10,15,2 \,}} \right.  \\ & 3\left| \!{\underline {\, 3,1,2,3,2 \,}} \right.  \\ & 2\left| \!{\underline {\, 1,1,2,1,2 \,}} \right.  \\ & \left| \!{\underline {\, 1,1,1,1,1 \,}} \right.  \\ & \text{LCM = 4}\times \text{5}\times \text{3}\times \text{2} \\ & \text{=120} \\ \end{align}$

Then the fractions will be

$ \dfrac{2\times 20,3\times 30,7\times 12,8\times 8,5\times 15}{120} $

$ =\dfrac{80,90,84,64,75}{120}$

$=\dfrac{80}{120},\dfrac{90}{120},\dfrac{84}{120},\dfrac{64}{120},\dfrac{75}{120} $

Ascending order will be

$=\dfrac{64}{120},\dfrac{75}{120},\dfrac{80}{120},\dfrac{84}{120},\dfrac{90}{120} $

$ =\dfrac{8}{15},\dfrac{5}{8},\dfrac{2}{5},\dfrac{7}{10},\dfrac{3}{4} $

Descending order will be

$=\dfrac{90}{120},\dfrac{84}{120},\dfrac{80}{120},\dfrac{75}{120},\dfrac{64}{120} $

$ =\dfrac{3}{4},\dfrac{7}{10},\dfrac{2}{3},\dfrac{5}{8},\dfrac{8}{15} $

Definition of Fraction:

A fraction is a number that represents a part of a whole number. Fractions represent equal parts of a whole or a collection.

Representation of Fraction:

A fraction is represented by two parts separated by the “/” symbol. The number written above the line is called the numerator. It helps us to know how many equal parts of the whole or collection are taken. The number written below the line is known as the denominator. With the help of fraction, we can know the total number of equal parts which are there in a collection.

Types of Fractions

Proper fractions

Improper fractions

Mixed fractions

Like fractions

Unlike fractions

Equivalent fractions

Proper Fractions

The proper fractions are those fractions where the numerator is less than the denominator.

Example: 5/9 will be a proper fraction since “numerator < denominator”.

Improper Fractions

The improper fraction is a fraction where the numerator is greater than the denominator.

Example: 9/5 will be an improper fraction since “denominator < numerator”.

Mixed Fractions

The combination of the integer part and a proper fraction is called a mixed fraction also known as a mixed number.

Example: \[3\frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{7}{2}\]

Like Fractions

Like fractions are a fraction that has two or more fractions that have the same denominator. Example- Take ½ and 2/4, they are alike fractions since if we simplify it mathematically, we will get the same fraction.

Unlike Fractions

Unlike fractions are fractions that have different denominators.

Example: ½ and ⅓ are unlike fractions.

Equivalent Fractions

Two fractions are said to be equivalent to each other if after simplification either of two fractions is equal to the other one.

Example: ⅔ and 4/6 are equivalent fractions.

Since, 4/6 = (2 × 2)/(2 × 3) = ⅔

(Image will be uploaded soon)

There are some basic rules we should know before solving the problems based on fractions.

Before performing addition or subtraction on fractions, we must make sure that the denominators are equal. Hence, addition and subtraction of fractions are possible only when the denominator is common.

If we have multiplied two fractions, then the numerators are multiplied as well as the denominators are multiplied. Later, simplify the fraction.

When we divide a fraction from another fraction, we need to find the reciprocal of the other fraction and then multiply it to the first one to get the answer.

Addition of Fractions

The addition of fractions is easy when they have a common denominator, we need to just add the numerators here.

Example: ⅔ + 8/3 = (2 + 8)/3 = 10/3

If the denominators of the two fractions are different then we have to simplify them by finding the LCM of denominators and then making it common for both fractions.

Example: ⅔ + ¾

Here, the denominators are 3 and 4.

Hence, LCM of 3 and 4 is 12.

Therefore, we multiply  ⅔ by 4/4 and ¾ by 3/3, we get,

= 8/12 + 9/12

= (8 + 9)/12

Subtraction of Fractions

The rule for subtracting two or more fractions is the same as for addition. We should make denominators common to subtract two fractions.

Example: 9/2 – 7/2 = (9-7)/2 = 2/2 = 1

If the denominators of the two fractions are different, then we have to simplify them by finding the LCM of denominators after that making it common for both fractions.

For example ⅔ – ¾

8/12 – 9/12

= (8 – 9)/12

Multiplication of Fractions

As per rule 2, when two fractions are multiplied, then the top part (numerators) and the bottom part (denominators) are multiplied together.

Suppose a/b and c/d are two different fractions, then the multiplication of a/b and c/d will be:

(a/b) × (c/d) = (a × c)/(b × d) = (ac/bd)

Example: Multiply ⅔ and 3/7.

= (⅔) × (3/7) = (2 × 3)/(3 × 7) = 2/7

Division of Fractions

As per rule 3, if we have to divide any two fractions where we need to multiply the first fraction to the reciprocal of the second fraction.

Suppose, a/b and c/d are two different fractions, then the division a/b by c/d can be expressed as:

(a/b) ÷ (c/d) = (a/b) × (d/c) = (ad/bc)

Example: Divide ⅔ by 3/7.

(⅔) ÷ (3/7) = (⅔) × (7/3) = (2 × 7)/(3 × 3) = 14/9

What are the Benefits of Important Questions from Vedantu for Class 7 Math Chapter 7 - Fractions

Focus on key topics for efficient studying.

Prepares students for exams and reduces anxiety.

Reinforces understanding of fundamental concepts.

Teaches effective time management.

Enables self-assessment and progress tracking.

Strategic approach for higher scores.

Covers a wide range of topics for comprehensive understanding.

Supports exam preparation and boosts confidence.

Conclusion:

Fractions are a part of our day-to-day life. Fractions make the calculations easier. Also, fractions can be converted into decimals which are heavily used in our monetary system.

After going through the above-given summary, students are advised to attempt the questions provided in Class 6 maths chapter 7 important questions . Students can easily understand the concept behind the question and solve it easily.

Important Related Links for CBSE Class 6 Maths 

FAQs on Important Questions for CBSE Class 6 Maths Chapter 7 - Fractions

1. What is a fraction Class 6?

A fraction is a part of the whole. It is a numerical quantity which is not whole. Fractional numbers are used to represent a part of something. Some examples of fractions could be one-third, three-fourth etc.  A fraction is described in the form of p/q. The letter p expresses the numerator of the fraction whereas the letter q expresses the denominator of the fraction. In a fraction 3/8, 3 is the numerator and 8 is the denominator. It represents 3 portions of the 8.

2. What are types of fractions?

The chapter introduces you to the concept of fraction. The chapter explains five types of fractions, namely, proper fractions, improper fractions, mixed fractions, like fractions and unlike fractions. Proper fraction is when the denominator is greater than the numerator. Improper is when the denominator is less than a numerator. Mixed fractions are those which consist of a whole number and a fraction. Two fractions are called when they have the same denominators. Two fractions are unlike fractions if they have different denominators. 

3. Do whole numbers also have denominators?

Fractions are numbers expressed in the form of p/q. If a number can be expressed in the p/q form, it is called a fraction. Whole numbers are those numbers that can be drawn on a number line. It is possible to write whole numbers in the form of p/q. Numbers that are whole have the denominator 1. So, a number as 3 can also be written as 3/1, where 3 is the numerator and 1 is the denominator. Writing a whole number in the fraction form helps in our calculation immensely. 

4. What fraction of a day is 8 hours?

A day has 24 hours. So, 24 will be the denominator that represents the whole. When we want to find a fraction of 8 hours, 8 will be our nominator. So, our fraction will be 8/24. What we are trying to find will come in the place of numerator and what we already know will come in the place of denominator. 8 and 24 are both divisible by 8, so we can simplify the fraction by dividing both numerator and denominator by 8. 8/8 will give us 1, which will be our new numerator. 24/8 will give us 3, our new denominator. So, our new fraction will be the new numerator/new denominator. Our answer is ⅓. 8 hours is one-third of 24 hours. 

5. What is the difference between proper and improper fractions?

A fraction consists of a numerator and a denominator. A number that occupies the place above the line is the numerator. The number that occupies the bottom is the denominator. A proper fraction is one in which the denominator is greater than the numerator. For example, 4/7 (7 is greater than 4), 3/11 (11 is greater than 3). However, if the numerator is greater than the denominator, then the fraction is called an improper fraction. For example, 8/7 and 13/6 where 8 and 13 are greater than 7 and 6 respectively.

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 Fractions         

We all have heard of this word in the field of mathematics as well as in our everyday lives. For example when we divide a chocolate in two pieces, it is a fraction. When we eat half of an apple it’s a fraction. In mathematics fraction plays a very important role and let’s find out how?

Understanding Fractions

A fraction consists of two parts:

• Numerator : The part which is written above the horizontal line is called as numerator.
• Denominator : The part which is written below the sleeping line horizontal line is called as denominator.

Thus a number is written above and a below the horizontal line and then the arrangement is called as fraction.

Types of Fractions

There are three types of fractions

• Proper Fraction : - Fraction whose numerator is less than the denominator is called a proper fraction.

Example 2 : 1/4, 5/8, 3/5, 4/7, etc.

• Improper Fraction : Fraction whose numerator is either equal or greater than the denominator.

Example 3 : 5/2, 7/4, 9/7, 13/11, 2/2, etc.

• Mixed Fraction : - A combination of a whole number and fraction together is called mixed fraction.

Example 4 : Convert the fraction 17/4 in mixed fraction.

Example 5 : Solve the above example.

Solution : To solve this we will follow 3 steps

• Multiply the whole no. with denominator. (2 x 3 = 6).
• Add the answer obtained in step 1 to the numerator

(6 +1 = 7).

• Place the result obtained in step 2 in the place of numerator and the denominator remains the same.

Hence the fraction becomes 7/3 which is an improper fraction.

There is another category of fractions called as

Equivalent Fractions : Those fractions which look different but on solving become same.

• To find an equivalent fraction of a given fraction, you may multiply both the numerator and the denominator of the given fraction by the same number.

• To find an equivalent fraction, we may divide both the numerator and the denominator by the same number.
• A fraction is said to be in the simplest (or lowest) form if its numerator and denominator have no common factor except 1 and HCF helps us to reduce a fraction to its lowest form .

Like and Unlike Fractions

Fractions with same denominators are called like fractions . For example 2/3, 4/3, 5/3 etc are all like fractions.

Fractions which don’t have same denominators are called as Unlike Fractions . For example, 2/5, 4/7, ½, etc. is unlike fractions

Comparing Fractions

Comparing means to find out some characteristics like which one is smaller and which is greater when two or more numbers are observed together which means compared together.

Here we are going to compare two fractions whose denominators are same that is they are like fractions.

Now observe the numerator, the fraction whose numerator is greater will be the greater fraction.

Example 7 : Compare who is greater 6/7 or 5/7.

Solution : Here both the fractions have the same denominator and hence on observing the numerators we get that 6 is greater than 5 there 6/7 is greater than 5/7.

When we have to compare two fractions which don’t have same denominators that is they are unlike fractions then we will compare them in the following manner:

• a) Check if the numerator is same or not, if yes then the fraction with the lower value of denominator will be greater.
• b) If the numerator is not same then try to make the either the numerator or denominator of both the fractions same then use the previous steps.

Computing operations on fractions

As we all know that addition, subtraction, multiplication and division are the computing operations.

Here we are going to study only the first two computation operations on fractions.

Addition and Subtraction of Fractions

Two fractions with the same denominator can be added or subtracted by using the two steps :

• Observe that the denominators of both the fractions are same.
• Add or subtract the numerators as asked in the questions.

Example 8 : Add and subtract 4/5 and 3/5.

Solution : As we can see the denominators of both the fractions is same and hence we can add and subtract them by using the numerators .

Therefore, 4/5 + 3/5 = 7/5 and 4/5 – 3/5 = 1/5.

• When the denominators are different then we will take the LCM of the denominators to make the denominators same and multiply the same factor with numerator and then add or subtract the numerators as asked in the question.

Practice Questions

Question 1 : Write the natural numbers from 102 to 113. What fraction of them are prime numbers?

Question 2 : Which one is smaller 1/13 or 13/13?

Question 3 : Solve the mixed fraction 5 ½.

Question 4 : State True or False:

• 5/9 = 10/18.
• 13 /11 is an improper fraction.
• 11/11 is a proper fraction.
• 15/17 is a proper fraction.

Question 6 : Compute the answers of the following:

• 4/3 + 5/2 = ?
• 17/12 – 15/6 = ?
• 5/2 + 1/4 = ?
• The part of a whole is fraction.
• Numerator and denominator are the parts of a fraction.
• Fractions can only contain integers
• If denominators are same then we can compare the fractions by comparing the numerators.
• If Numerator > or = Denominator then improper fraction.
• If Numerator
• A fraction is said to be in the simplest (or lowest) form if its numerator and the denominator have no common factor except 1 .

Quiz for Fractions

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Chapter 7 Class 6 Fractions

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NCERT Solutions of all exercise questions and examples have been solved for Chapter 7 Class 6 Fractions . Answers to all questions are provided in a step-by-step manner, with detailed explanation of each and every question.

In this chapter, we will learn

• What is a fraction
• and find fractions
• Then, we will draw a number line and represent fractions on the number line
• We learn what is Proper , Improper and Mixed Fractions
• How to find equivalent fractions
• And converting fractions to simplest form
• We learn what are like and unlike fractions
• And Compare like and unlike fractions
• Then, we learn how to add and subtract fractions (with same as well as different denominators)

Click on an exercise link below Serial Order Wise to study the chapter from the NCERT Way.

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• NCERT Solutions
• NCERT Class 6
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• Chapter 7: Fractions

NCERT Solutions For Class 6 Maths Chapter 7 Fractions

Subject experts at BYJU’S have prepared the NCERT Solutions For Class 6 Maths Chapter 7 Fractions as per the latest CBSE Syllabus for Class 6, so that students can practise well for the final exams. A fraction is a number representing part of a whole. The whole may be a single object or a group of objects where the parts have to be equal. Also, a fraction is said to be in the simplest (or lowest) form if its numerator and denominator have no common factor except 1. Learning and practising the NCERT Solutions is supposed to help the students in gaining the confidence to solve all the problems related to fractions they come across. The topics and sub-topics covered in Chapter 7 Fractions are as follows:

• 7.1 – Introduction
• 7.2 – A Fraction
• 7.3 – Fraction on the Number Line
• 7.4 – Proper Fractions
• 7.5 – Improper and Mixed Fractions
• 7.6 – Equivalent Fractions
• 7.7 – Simplest Form of a Fraction
• 7.8 – Like Fractions
• 7.9 – Comparing Fractions
• 7.10 – Addition and Subtraction of Fractions

Download Exclusively Curated Chapter Notes for Class 6 Maths Chapter 7 – Fractions

Download most important questions for class 6 maths chapter 7 – fractions.

• Chapter 1 Knowing our Numbers
• Chapter 2 Whole Numbers
• Chapter 3 Playing With Numbers
• Chapter 4 Basic Geometrical Ideas
• Chapter 5 Understanding Elementary Shapes
• Chapter 6 Integers
• Chapter 7 Fractions
• Chapter 8 Decimals
• Chapter 9 Data Handling
• Chapter 10 Mensuration
• Chapter 11 Algebra
• Chapter 12 Ratio And Proportion
• Chapter 13 Introduction To Symmetry
• Chapter 14 Practical Geometry
• Exercise 7.1 Chapter 7 Fractions
• Exercise 7.2 Chapter 7 Fractions
• Exercise 7.3 Chapter 7 Fractions
• Exercise 7.4 Chapter 7 Fractions
• Exercise 7.5 Chapter 7 Fractions
• Exercise 7.6 Chapter 7 Fractions

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

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Access NCERT Solutions for Class 6 Chapter 7: Fractions

Exercise 7.1 page no: 135

1. Write the fraction representing the shaded portion.

(i) Number of parts = 4

Shaded portion = 2

∴ Fraction = 2 / 4

(ii) Number of parts = 9

Shaded portion = 8

∴ Fraction = 8 / 9

(iii) Number of parts = 8

Shaded portion = 4

∴ Fraction = 4 / 8

(iv) Number of parts = 4

Shaded portion = 1

∴ Fraction = 1 / 4

(v) Number of parts = 7

Shaded portion = 3

∴ Fraction = 3 / 7

(vi) Number of parts = 12

∴ Fraction = 3 / 12

(vii) Number of parts = 10

Shaded portion = 10

∴ Fraction = 10 / 10

(viii) Number of parts = 9

∴ Fraction = 4 / 9

(ix) Number of parts = 8

(x) Number of parts = 2

∴ Fraction = 1 / 2

2. Colour the part according to the given fraction.

3. Identify the error, if any.

(i) The shaded portion is not half

Hence, this is not 1 / 2

(ii) Since the parts are not equal

∴ Shaded portion is not 1 / 4

(iii) Since the parts are not equal

∴ Shaded portion is not 3 / 4

4. What fraction of a day is 8 hours?

There are 24 hours in a day

We have 8 hours

Hence, required fraction is 8 / 24

5. What fraction of an hour is 40 minutes?

There are 60 minutes in 1 hour

∴ 1 hour = 60 minutes

Hence, required Fraction = 40 / 60

6. Arya, Abhimanyu, and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetable and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich.

(a) How can Arya divide his sandwiches so that each person has an equal share?

(b) What part of a sandwich will each boy receive?

(a) Arya has divided the sandwich into 3 equal parts. So each person will get one part.

(b) Each boy receive 1 / 3 part

∴ Required Fraction is 1 / 3

7. Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished?

Total number of dresses Kanchan has to dye = 30 dresses

Number of dresses she has finished = 20 dresses

∴ Required Fraction = 20 / 30 = 2 / 3

8. Write the natural numbers from 2 to 12. What fraction of them are prime numbers?

Natural numbers from 2 to 12 are

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Total number of natural numbers given= 11

Number of prime numbers = 5

∴ Required Fraction = 5 / 11

9. Write the natural numbers from 102 to 113. What fraction of them are prime numbers?

Natural numbers from 102 to 113 are

102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113

Total number of natural numbers given = 12

∴ Required Fraction = 4 / 12 = 1 / 3

10. What fraction of these circles have Xs in them?

Total number of circles in the figure = 8

Number of circles having Xs in them = 4

∴ Required Fraction = 4 / 8 = 1 / 2

11. Kristin received a CD player for her birthday. She bought 3 CDs and received 5 others as gifts. What fraction of her total CDs did she buy and what fraction did she receive as gifts?

Number of CDs Kristin bought from the market = 3

Number of CDs received as gifts = 5

Total number of CDs Kristin have = 3 + 5 = 8

∴ Fraction of CD she bought = 3 / 8

∴ Fraction of CDs received as gifts = 5 / 8

Exercise 7.2 page no: 141

1. Draw number lines and locate the points on them:

(a) 1 / 2, 1 / 4, 3 / 4, 4 / 4

(b) 1 / 8, 2 / 8, 3 / 8, 7 / 8

(c) 2 / 5, 3 / 5, 8 / 5, 4 / 5

Here divide the number line from 0 to 1 into four equal parts

C = 2 / 4 = 1 / 2

D = 3 / 4 and

E = 4 / 4 = 1

Divide the number line from 0 to 1 into eight equal parts

From the given number line, we have

2. Express the following as mixed fractions:

3. Express the following as improper fractions:

(a) (7 × 4 + 3) / 4 = 31 / 4

∴ The improper form is 31 / 4

(b) (5 × 7 + 6) / 7 = 41 / 7

∴ The improper form is 41 / 7

(c) (2 × 6 + 5) / 6 = 17 / 6

∴ The improper form is 17 / 6

(d) (10 × 5 + 3) / 5 = 53 / 5

∴ The improper form is 53 / 5

(e) (9 × 7 + 3) / 7 = 66 / 7

∴ The improper form is 66 / 7

(f) (8 × 9 + 4) / 9 = 76 / 9

∴ The improper form is 76 / 9

Exercise 7.3 page no: 146

1. Write the fractions. Are all these fractions equivalent?

(i) The shaded portion is 1 / 2

(ii) The shaded portion is 2 / 4 = (2 / 2) / (4 / 2) = 1 / 2

(iii) The shaded portion is 3 / 6 = (3 / 3) / (6 / 3) = 1 / 2

(iv) The shaded portion is 4 / 8 = (4 / 4) / (8 / 4) = 1 / 2

Hence, all fractions are equivalent.

(i) The shaded portion is 4 / 12 = (4 / 4) / (12 / 4) = 1 / 3

(ii)The shaded portion is 3 / 9 = (3 / 3) / (9 / 3) = 1 / 3

(iii) The shaded portion is 2 / 6 = (2 / 2) / (6 / 2) = 1 / 3

(iv) The shaded portion is 1 / 3

(v) The shaded portion is 6 / 15 = (6 / 3) / (15 / 3) = 2 / 5

All the fractions in their simplest form are not equal

Hence, they are not equivalent fractions.

2. Write the fractions and pair up the equivalent fractions from each row.

(b) 4 / 6 = (4 / 2) / (6 / 2)

(c) 3 / 9 = (3 / 3) / (9 / 3)

(d) 2 / 8 = (2 / 2) / (8 / 2)

(i) 6 / 18 = (6 / 6) / (18 / 6)

(ii) 4 / 8 = (4 / 4) / (8 / 4)

(iii) 12 / 16 = (12 / 4) / (16 / 4)

(iv) 8 / 12 = (8 / 4) / (12 / 4)

(v) 4 / 16 = (4 / 4) / (16 / 4)

The following are the equivalent fractions

(a) and (ii) = 1 / 2

(b) and (iv) = 2 / 3

(c) and (i) = 1 / 3

(d) and (v) = 1 / 4

(e) and (iii) = 3 / 4

3. Replace ☐ in each of the following by the correct number:

(a) 2 / 7 = 8 / ☐

(b) 5 / 8 = 10 / ☐

(c) 3 / 5 = ☐ / 20

(d) 45 / 60 = 15 / ☐

(e) 18 / 24 = ☐ / 4

2 / 7 = 8 / ☐

2 × ☐ = 7 × 8

☐ = (7 × 8) / 2

5 / 8 = 10 / ☐

☐ = (8 × 10) / 5

3 / 5 = ☐ / 20

☐ = (3 × 20) / 5

45 / 60 = 15 / ☐

☐ = (15 × 60) / 45

18 / 24 = ☐ / 4

☐ = (18 × 4) / 24

4. Find the equivalent fraction of 3 / 5 having

(a) denominator 20

(b) numerator 9

(c) denominator 30

(d) numerator 27

(a) We require denominator 20

Let M be the numerator of the fractions

∴ M / 20 = 3 / 5

5 × M = 20 × 3

M = (20 × 3) / 5

Therefore, the required fraction is 12 / 20

(b) We require numerator 9

Let N be the denominator of the fractions

∴ 9 / N = 3 / 5

3 × N = 9 × 5

N = (9 × 5) / 3

Therefore, the required fraction is 9 / 15

(c) We require denominator 30

Let D be the numerator of the fraction

∴ D / 30 = 3 / 5

5 × D = 3 × 30

D = (3 × 30) / 5

Therefore, the required fraction is 18 / 30

(d) We require numerator 27

Let N be the denominator of the fraction

∴ 27 / N = 3 / 5

3 × N = 5 × 27

N = (5 × 27) / 3

Therefore, the required fraction is 27 / 45

5. Find the equivalent fraction of 36 / 48 with

(a) numerator 9

(b) denominator 4

(a) Given numerator = 9

∴ 9 / D = 36 / 48

D × 36 = 9 × 48

D = (9 × 48) / 36

Hence, the equivalent fraction is 9 / 12

(b) Given, denominator = 4

∴ N / 4 = 36 / 48

N × 48 = 4 × 36

N = (4 × 36) / 48

Hence, the equivalent fraction is 3 / 4

6. Check whether the given fractions are equivalent:

(a) 5 / 9, 30 / 54

(b) 3 / 10, 12 / 50

(c) 7 / 13, 5 / 11

(a ) Given 5 / 9 and 30 / 54

We have 5× 54 = 270

9 × 30 = 270

5 × 54 = 9 × 30

Hence, 5 / 9 and 30 / 54 are equivalent fractions

(b) Given 3 / 10 and 12 / 50

We have 3 × 50 = 150

10 × 12 = 120

3 × 50 ≠ 10 × 12

Hence, 3 / 10 and 12 / 50 are not equivalent fractions

(c) Given 7 / 13 and 5 / 11

We have 7 × 11 = 77

5 × 13 = 65

7 × 11 ≠ 5 × 13

Hence, 7 / 13 and 5 / 11 are not equivalent fractions

7. Reduce the following fractions to simplest form:

(a) 48 / 60

(b) 150 / 60

(c) 84 / 98

(d) 12 / 52

(a) 48 / 60 = (12 × 4) / (12 × 5)

(b) 150 / 60 = (30 × 5) / (30 × 2)

(c) 84 / 98 = (14 × 6) / (14 × 7)

(d) 12 / 52 = (3 × 4) / (13 × 4)

(e) 7 / 28 = 7 / (7 × 4)

8. Ramesh had 20 pencils, Sheelu had 50 pencils and Jamaal had 80 pencils. After 4 months, Ramesh used up 10 pencils, Sheelu used up 25 pencils and Jamaal used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils.

Total number of pencils Ramesh had = 20

Number of pencils used by Ramesh = 10

∴ Fraction = 10 / 20 = 1 / 2

Total number of pencils Sheelu had = 50

Number of pencils used by Sheelu = 25

∴ Fraction = 25 / 50 = 1 / 2

Total number of pencils Jamaal had = 80

Number of pencils used by Jamaal = 40

∴ Fraction = 40 / 80 = 1 / 2

Yes, each has used up an equal fraction of pencils i.e 1 / 2

9. Match the equivalent fractions and write two more for each.

(i) 250 / 400 (a) 2 / 3

(ii) 180 / 200 (b) 2 / 5

(iii) 660 / 990 (c) 1 / 2

(iv) 180 / 360 (d) 5 / 8

(v) 220 / 550 (e) 9 / 10

(i) 250 / 400

= (5 × 50) / (8 × 50)

25 / 40 and 30 / 48 are two more fractions

(ii) 180 / 200

= (9 × 20) / (10 × 20)

18 / 20 and 27 / 30 are two more fractions

(iii) 660 / 990

= (2 × 330) / (3 × 330)

20 / 30 and 200 / 300 are two more fractions

(iv) 180 / 360

= (1 × 180) / (2 × 180)

20 / 40 and 30 / 60 are two more fractions

(v) 220 / 550

= (2 × 110) / (5 × 110)

20 / 50 and 40 / 100 are two more fractions

∴ The equivalent fractions are

(i) 250 / 100 = (d) 5 / 8

(ii) 180 / 200 = (e) 9 / 10

(iii) 660 / 990 = (a) 2 / 3

(iv) 180 / 360 = (c) 1 / 2

(v) 220 / 550 = (b) 2 / 5

Exercise 7.4 page no: 152

1. Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign ‘’ between the fractions:

(c) Show 2 / 6, 4 / 6, 8 / 6 and 6 / 6 on the number line. Put appropriate signs between the fractions given.

5 / 6 ☐ 2 / 6, 3 / 6 ☐ 0, 1 / 6 ☐ 6 / 6, 8 / 6 ☐ 5 / 6

(a) First circle shows 3 shaded parts out of 8 equal parts. Hence, the fraction is 3 / 8

Second circle shows 6 shaded parts out of 8 equal parts. Hence, the fraction is 6 / 8

Third circle shows 4 shaded parts out of 8 equal parts. Hence, the fraction is 4 / 8

Fourth circle shows 1 shaded parts out of 8 equal parts. Hence, the fraction is 1 / 8

The arranged fractions are:

1 / 8 < 3 / 8 < 4 / 8 < 6 / 8

(b) First square shows 8 shaded parts out of 9 equal parts. Hence, the fraction is 8 / 9

Second square shows 4 shaded parts out of 9 equal parts. Hence, the fraction is 4 / 9

Third square shows 3 shaded parts out of 9 equal parts. Hence, the fraction is 3 / 9

Fourth square shows 6 shaded parts out of 9 equal parts. Hence, the fraction is 6 / 9

3 / 9 < 4 / 9 < 6 / 9 < 8 / 9

(c) Each unit length should be divided into 6 equal parts to represent the fractions 2 / 6, 4 / 6, 8 / 6 and

6 / 6 on number line. These fractions can be represented as follows:

5 / 6 > 2 / 6

3 / 6 > 0

1 / 6 < 6 / 6

8 / 6 > 5 / 6

2. Compare the fractions and put an appropriate sign.

(a) 3 / 6 ☐ 5 / 6

(b) 1 / 7 ☐ 1 / 4

(c) 4 / 5 ☐ 5 / 5

(d) 3 / 5 ☐ 3 / 7

(a) Here both fractions have same denominators. So, the fraction with greater numerator is the highest factor

∴ 3 / 6 < 5 / 6

(b) Multiply by 4

1 / 7 = (1 × 4) / (7 × 4)

Multiply by 7

1 / 4 = (1 × 7) / (4 × 7)

Here 4 < 7

∴ 1 / 7 < 1 / 4

(c) Here both fractions have same denominators. So, the fraction with greater numerator is the highest factor

∴ 4 / 5 < 5 / 5

(d) Here both numerators are same. So, the fraction having less denominator will be the highest factor

∴ 3 / 7 < 3 / 5

3. Make five more such pairs and put appropriate signs.

(a) 5 / 8 < 6 / 8

Here, the denominators are same. So, the fraction having greater numerator is the highest factor

(ii) 5 / 8 > 2 / 8

(iii) 6 / 13 > 6 / 18

Here, the numerators are same. So, the fraction having lesser denominator will be the highest factor

(iv) 5 / 25 > 3 / 25

(v) 9 / 50 < 9 / 45

4. Look at the figures and write ‘<’ or ‘>’, ‘=’ between the given pairs of fractions.

(a) 1 / 6 ☐ 1 / 3

(b) 3 / 4 ☐ 2 / 6

(c) 2 / 3 ☐ 2 / 4

(d) 6 / 6 ☐ 3 / 3

(e) 5 / 6 ☐ 5 / 5

(a) Here, the numerators are same. So, the fraction having lesser denominator is the greater

∴ 1 / 6 < 1 / 3

(b) 3 / 4 = (3 × 3) / (4 × 3)

2 / 6 = (2 × 2) / (6 × 2)

Between 4 / 12, 9 / 12

Both fractions have same denominators. So, the fraction having greater numerator will be the greater

∴ 9 / 12 > 4 / 12

3 / 4 > 2 / 6

(c) Here, the numerators are same. So, the fraction having lesser denominator is the greater

∴ 2 / 3 > 2 / 4

(d) We get 6 / 6 = 1 and 3 / 3 = 1

So, 6 / 6 = 3 / 3

(e) Here, the numerators are same. So, the fraction having lesser denominator is the greater

∴ 5 / 6 < 5 / 5

5. How quickly can you do this? Fill appropriate sign. ( ‘<’, ‘=’, ‘>’)

(a) 1 / 2 ☐ 1 / 5

(b) 2 / 4 ☐ 3 / 6

(c) 3 / 5 ☐ 2 / 3

(d) 3 / 4 ☐ 2 / 8

(e) 3 / 5 ☐ 6 / 5

(f) 7 / 9 ☐ 3 / 9

(g) 1 / 4 ☐ 2 / 8

(h) 6 / 10 ☐ 4 / 5

(i) 3 / 4 ☐ 7 / 8

(j) 6 / 10 ☐ 3 / 5

(k) 5 / 7 ☐ 15 / 21

(a) Here, the numerators are same. So, the fraction having lesser denominator is greater

∴ 1 / 2 > 1 / 5

(b) 2 / 4 = 1 / 2 and 3 / 6 = 1 / 2

∴ 2 / 4 = 3 / 6

(c) 3 / 5 = (3 × 3) / (5 × 3)

2 / 3 = (2 × 5) / 3 × 5)

Here, between 9 / 15 and 10 / 15 both have same denominators. Hence, the fraction having greater numerator will be the greater.

∴ 3 / 5 < 2 / 3

(d) Here, 2 / 8 = 1 / 4

As, 3 / 4 and 1 / 4 have same denominators. Hence, the fraction having greater numerator will be the greater

∴ 3 / 4 > 2 / 8

(e) Here, the denominators are same. So, the fraction having greater numerator will be the greater

∴ 3 / 5 < 6 / 5

(f) Here, the denominators are same. So, the fraction having greater numerator will be the greater

∴ 7 / 9 > 3 / 9

(g) We know 2 / 8 = 1 / 4

Hence, 1 / 4 = 2 / 8

(h) 6 / 10 = (3 × 2) / (5 × 2)

Between 3 / 5 and 4 / 5

Both have same denominators. So, the fraction having greater numerator will be greater

∴ 6 / 10 < 4 / 5

(i) 3 / 4 = (3 × 2) / (4 × 2)

Between 6 / 8 and 7 / 8

∴ 3 / 4 < 7 / 8

(j) 6 / 10 = (3 × 2) / (5 × 2)

∴ 6 / 10 = 3 / 5

(k) 5 / 7 = (5 × 3) / (7 × 3)

∴ 5 / 7 = 15 / 21

6. The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one to its simplest form.

(a) 2 / 12 (b) 3 / 15 (c) 8 / 50 (d) 16 / 100 (e) 10 / 60 (f) 15 / 75

(g) 12 / 60 (h) 16 / 96 (i) 12 / 75 (j) 12 / 72 (k) 3 / 18 (l) 4 / 25

(a) 2 / 12 = (1 × 2) / (6 × 2)

(b) 3 / 15 = (1 × 3) / (5 × 3)

(c) 8 / 50 = (4 × 2) / (25 × 2)

(d) 16 / 100 = (4 × 4) / (25 × 4)

(e) 10 / 60 = (1 × 10) / (6 × 10)

(f) 15 / 75 = (1 × 15) / (5 × 15)

(g) 12 / 60 = (1 × 12) / (5 × 12)

(h) 16 / 96

= (1 × 16) / (6 × 16)

(i) 12 / 75 = (4 × 3) / (25 × 3)

(j) 12 / 72 = (1 × 12) / 6 × 12)

(k) 3 / 18 = (1 × 3) / (6 × 3)

Totally there are 3 groups of equivalent fractions.

1 / 6 = (a), (e), (h), (j), (k)

1 / 5 = (b), (f), (g)

4 / 25 = (c), (d), (i), (l)

7. Find answers to the following. Write and indicate how you solved them.

(a) Is 5 / 9 equal to 4 / 5?

(b) Is 9 / 16 equal to 5 / 9?

(c) Is 4 /5 equal to 16 / 20?

(d) Is 1 / 15 equal to 4 / 30?

(a) 5 / 9, 4 / 5

Convert these fractions into like fractions

5 / 9 = (5 / 9) × (5 / 5)

4 / 5 = (4 / 5) × (9 / 9)

∴ 25 / 45 ≠ 36 / 45

Hence, 5 / 9 is not equal to 4 / 5

(b) 9 / 16, 5 / 9

Convert into like fractions

9 / 16 = (9 / 16) × (9 / 9)

5 / 9 = (5 / 9) × (16 / 16)

∴ 81 / 144 ≠ 80 / 144

Hence, 9 / 16 is not equal to 5 / 9

(c) 4 / 5, 16 / 20

16 / 20 = (4 × 4) / (5 × 4)

∴ 4 / 5 = 16 / 20

Hence, 4 / 5 is equal to 16 / 20

(d) 1 / 15, 4 / 30

4 / 30 = (2 × 2) / (15 × 2)

∴ 1 / 15 ≠ 4 / 30

Hence, 1 / 15 is not equal to 4 / 30

8. Ila read 25 pages of a book containing 100 pages. Lalita read 2 / 5 of the same book. Who read less?

Total number of pages a book has = 100 pages

Lalita read = 2 / 5 × 100 = 40 pages

Ila read = 25 pages

∴ Ila read less than Lalita.

9. Rafiq exercised for 3 / 6 of an hour, while Rohit exercised for 3 / 4 of an hour. Who exercised for a longer time?

Rafiq exercised = 3 / 6 of an hour

Rohit exercised = 3 / 4 of a hour

3 / 6, 3 / 4

Convert these into like fractions

3 / 6 = (3 × 2) / (6 × 2)

3 / 4 = (3 × 3) / (4 × 3)

Clearly, 9 / 12 > 6 / 12

∴ 3 / 4 > 3 / 6

Therefore Rohit exercised for a longer time than Rafiq.

10. In a class A of 25 students, 20 passed with 60% or more marks; in another class B of 30 students, 24 passed with 60% or more marks. In which class was a greater fraction of students getting with 60% or more marks?

Total number of students in Class A = 25

Students passed in first class in Class A = 20

Hence, fraction = 20 / 25

Total number of students in Class B = 30

Students passed in first class in Class B = 24

Hence, fraction = 24 / 30

∴ An equal fraction of students passed in first class in both the classes

Exercise 7.5 page no: 157

1. Write these fractions appropriately as additions or subtractions:

(a) Total number of parts each rectangle has = 5

No. of shaded parts in the first rectangle = 1 i.e 1 / 5

No. of shaded parts in the second rectangle = 2 i.e 2 / 5

No. of shaded parts in the third rectangle = 3 i.e 3 / 5

Clearly, the fraction represented by the third rectangle = Sum of the fractions represented by first and second rectangle

Hence, 1 / 5 + 2 / 5 = 3 / 5

(b) Total number of parts each circle has = 5

We may observe that the first, second and third circles represent 5, 3 and 2 shaded parts out of 5 equal parts respectively. Clearly, fraction represented by the third circle is the difference between the fractions represented by the first and second circles.

Hence, 5 / 5 – 3 / 5 = 2 / 5

(c) Here we may observe that first, second and third rectangles represents 2, 3 and 5 shaded parts out of 6 equal parts, respectively. Clearly, fraction represented by the third rectangle is the sum of fractions represented by the first and second rectangles.

Hence, 2 / 6 + 3 / 6 = 5 / 6

(a) 1 / 18 + 1 / 18

(b) 8 / 15 + 3 / 15

(c) 7 / 7 – 5 / 7

(d) 1 / 22 + 21 / 22

(e) 12 / 15 – 7 / 15

(f) 5 / 8 + 3 / 8

(g) 1 – 2 / 3 (1 = 3 / 3)

(h) 1 / 4 + 0 / 4

(i) 3 – 12 / 5

= (1 + 1) / 18

= (8 + 3) / 15

= (7 – 5) / 7

= (1 + 21) / 22

(e) 12 /15 – 7 / 15

= (12 – 7) / 15

= (5 + 3) / 8

(g) 1 – 2 / 3

= 3 / 3 – 2 / 3

= (3 – 2) / 3

(h) 1 / 4 + 0

= 15 / 5 – 12/ 5

= (15 – 12) / 5

3. Shubham painted 2 / 3 of the wall space in his room. His sister Madhavi helped and painted 1 / 3 of the wall space. How much did they paint together?

Wall space painted by Shubham in a room = 2 / 3

Wall space painted by Madhavi in a room = 1 / 3

Total space painted by both = (2 / 3 + 1 / 3)

= (2 + 1) / 3

∴ Shubham and Madhavi together painted 1 complete wall in a room.

4. Fill in the missing fractions.

(a) 7 / 10 – ▯ = 3 / 10

(b) ▯ – 3 / 21 = 5 / 21

(c) ▯ – 3 / 6 = 3 / 6

(d) ▯ + 5 / 27 = 12 / 27

(a) Given 7 / 10 – ▯ = 3 / 10

▯ = 7 / 10 – 3 / 10

▯ = (7 – 3) / 10

(b) Given ▯ – 3 / 21 = 5 / 21

▯ = 5 / 21 + 3 / 21

▯ = (5 + 3) / 21

(c) Given ▯ – 3 / 6 = 3 / 6

▯ = 3 / 6 + 3 / 6

▯ = (3 + 3) / 6

(d) Given ▯ + 5 / 27 = 12 / 27

▯ = 12 / 27 – 5 /27

▯ = (12 – 5) / 27

5. Javed was given 5 / 7 of a basket of oranges. What fraction of oranges was left in the basket?

Fraction of oranges given to Javed = 5 / 7

Fraction of oranges left in the basket = 1 – 5 / 7

= 7 / 7 – 5 / 7

Exercise 7.6 page no: 160

(a) 2 / 3 + 1 / 7

(b) 3 / 10 + 7 / 15

(c) 4 / 9 + 2 / 7

(d) 5 / 7 + 1 / 3

(e) 2 / 5 + 1 / 6

(f) 4 / 5 + 2 / 3

(g) 3 / 4 – 1 / 3

(h) 5 / 6 – 1 / 3

(i) 2 / 3 + 3 / 4 + 1 / 2

(j) 1/ 2 + 1 / 3 + 1 / 6

(m) 16 / 5 – 7 / 5

(n) 4 / 3 – 1 / 2

(a) 2 / 3 + 1/ 7

= (14 + 3) / 21

Taking LCM 30

= [(3 × 3) + (7 × 2)] / 30

= (9 + 14) / 30

(c) 4 / 9 + 2/ 7

Taking LCM 63

= [(4 × 7) + (2 × 9)] / 63

= (28 + 18) / 63

Taking LCM 21

= [(5 × 3) + (1 × 7)] / 21

= (15 + 7) / 21

= [(2 × 6) + (1 × 5)] / 30

= (12 + 5) / 30

Taking LCM 15

= [(4 × 3) + (2 × 5)] / 15

= (12 + 10) / 15

Taking LCM 12

= [(3 × 3) – (1 × 4)] / 12

= (9 – 4) / 12

Taking LCM 6

= [(5 × 1) – (1 × 2)] / 6

= (5 – 2) / 6

= [(2 × 4) + (3 × 3) + (1 × 6)] / 12

= (8 + 9 + 6) / 12

(j) 1 / 2 + 1 / 3 + 1 / 6

= [(1 × 3) + (1 × 2) + (1 × 1)] / 6

= (3 + 2 + 1) / 6

= [(3 × 1) + 1] / 3 + [(3 × 3) + 2] / 3

= (3 + 1) / 3 + (9 + 2) / 3

= 4/ 3 + 11 / 3

= (4 + 11) / 3

= [(3 × 4) + 2] / 3 + [(3 × 4) + 1] / 4

= 14 / 3 + 13 / 4

= [(14 × 4) + (13 × 3)] / 12

= (56 + 39) / 12

= (16 – 7) / 5

(n) 4 /3 – 1 / 2

= [(4 × 2) – (1 × 3)] / 6

= (8 – 3) /6

2. Sarita bought 2 / 5 metre of ribbon and Lalita 3 /4 metre of ribbon. What is the total length of the ribbon they bought?

Ribbon length bought by Sarita = 2 / 5 metre

Ribbon length bought by Lalita = 3 / 4 metre

Total length of the ribbon bought by both of them = 2 / 5 + 3 / 4

Taking LCM 20

= [(2 × 4) + (3 × 5)] / 20

= (8 + 15) / 20

= 23 / 20 metre

∴ Total length of the ribbon bought by both Sarita and Lalita is 23 / 20 metre

Total amount of cake given to both of them = 3 / 2 + 4 / 3

= [(3 × 3) + (4 × 2)] / 6

= (9 + 8) / 6

4. Fill in the boxes:

(a) ▯ – 5 / 8 = 1 / 4

(b) ▯ – 1 / 5 = 1 / 2

(c) 1 / 2 – ▯ = 1 / 6

▯ = 1 / 4 + 5 / 8

▯ = [(1 × 2 + 5)] / 8

▯ = 1 / 2 + 1 / 5

▯ = [(1 × 5) + (1 × 2)] / 10

▯ = (5 + 2) / 10

▯ = 1 / 2 – 1 / 6

▯ = [(1 × 3) – (1 × 1)] / 6

▯ = (3 – 1) / 6

5. Complete the addition and subtraction box.

(a) 2 / 3 + 4 / 3

= (2 + 4) / 3

1 / 3 + 2 / 3

= (1 + 2) / 3

2 / 3 – 1 / 3

= (2 – 1) / 3

4 / 3 – 2 / 3

= (4 – 2) / 3

Hence, the complete given box is

(b) 1 / 2 + 1 / 3

= [(1 × 3) + (1 × 2)] / 6

= (3 + 2) / 6

1 / 3 + 1 / 4

= [(1 × 4) + (1 × 3)] / 12

= (4 + 3) / 12

1 / 2 – 1 / 3

= [(1 × 3) – (1 × 2)] / 6

= (3 – 2) / 6

1 / 3 – 1 / 4

= [(1 × 4) – (1 ×3)] / 12

= (4 – 3) / 12

1 / 6 + 1 / 12

= [(1 × 2) + 1] / 12

= (2 + 1) / 12

6. A piece of wire 7 / 8 metre long broke into two pieces. One piece was 1 / 4 metre long. How long is the other piece?

Total length of wire = 7 / 8 metre

Length of one piece of wire = 1 / 4 metre

Length of other piece of wire = Length of the original wire and this one piece of wire

= 7 / 8 – 1 / 4

= [(7 × 1) – (1 × 2)] / 8

= (7 – 2) / 8

∴ Length of the other piece of wire = 5 / 8 metre

7. Nandini’s house is 9 / 10 km from her school. She walked some distance and then took a bus for 1 / 2 km to reach the school. How far did she walk?

Distance of the school from house = 9 / 10 km

Distance she travelled by bus = 1 / 2 km

Distance walked by Nandini = Total distance of the school – Distance she travelled by bus

= 9 / 10 – 1 / 2

= [(9 × 1) – (1 × 5)] / 10

= (9 – 5) / 10

∴ Distance walked by Nandini is 2 / 5 km

8. Asha and Samuel have bookshelves of the same size partly filled with books. Asha’s shelf is 5 / 6 th full and Samuel’s shelf is 2/ 5 th full. Whose bookshelf is more full? By what fraction?

Fraction of Asha’s bookshelf = 5 / 6

Fraction of Samuel’s bookshelf = 2 / 5

5 / 6 = 5 / 6 × 5 / 5

= (5 × 5) / (6 × 5)

2 / 5 = 2 / 5 × 6 / 6

= (2 × 6) / (5 × 6)

25 / 30 > 12 / 30

5 / 6 > 2 / 5

∴ Asha’s bookshelf is more full than Samuel’s bookshelf

Difference = 5 / 6 – 2 / 5

= 25 / 30 – 12 / 30

Time taken by Rahul to walk across the school ground = 7 / 4 minutes

11 / 5 = 11 / 5 × 4 / 4

= (11 × 4) / (5 × 4)

7 / 4 = 7 / 4 × 5 / 5

= (7 × 5) / (4 × 5)

Clearly, 44 / 20 > 35 / 20

11 / 5 > 7 / 4

∴ Rahul takes less time than Jaidev to walk across the school ground

Difference = 11 / 5 – 7 / 4

= 44 / 20 – 35 / 20

Hence, Rahul walks across the school ground by 9 / 20 minutes

Frequently Asked Questions on NCERT Solutions for Class 6 Maths Chapter 7

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6th Class Mathematics Fractions Question Bank

Done arithmetic total questions - 114.

question_answer 1) 16.37 and 18.97 are

A) like decimal fractions done clear

B) unlike decimal fractions done clear

C) equivalent decimal fractions done clear

D) none of these done clear

question_answer 2) If 2805 \[\div \] 2.55 = 1100, then 280.5 \[\div \] 25.5 =

A) 1.1                   done clear

B)          1.01 done clear

C) 0.11                done clear

D)          11 done clear

question_answer 3) The smallest possible decimal fraction up to three decimal places is

A) 0.101                done clear

B)          0.111 done clear

C) 0.001               done clear

D)          0.011 done clear

question_answer 4) What fraction will come in place of * ? \[\frac{1}{4},\,\frac{3}{16},\,\frac{5}{36},\,\frac{7}{64},\,*,\,\frac{11}{144}\].

A)  \[\frac{8}{18}\]                      done clear

B)           \[\frac{9}{100}\] done clear

C)  \[\frac{10}{81}\]                    done clear

D)           \[\frac{9}{121}\] done clear

question_answer 5) For representing \[7\frac{1}{3}\] on the number line, in how many equal parts the unit distance between 7 and 8 should be divided?

A) 7                      done clear

B)          8 done clear

C) 3                      done clear

D)          1 done clear

question_answer 6) Solve \[\left[ \frac{3}{8} \right]\,\div \,\left[ -\frac{24}{27} \right]\]

A)  \[\frac{1}{3}\]                        done clear

B)          1.33 done clear

C)  \[\frac{1}{9}\]                        done clear

D)          None of these done clear

question_answer 7) Which of the following fractions will be in middle if the given fractions are arranged in the descending order of their values? \[\frac{9}{17},\,\frac{13}{26},\,\frac{7}{15},\,\frac{5}{8},\,\frac{3}{7}\]

A)  \[\frac{7}{15}\]                      done clear

B)           \[\frac{9}{17}\] done clear

C)  \[\frac{13}{26}\]                    done clear

D)           \[\frac{5}{8}\] done clear

question_answer 8) A monkey climbs up a wall 1.8 km high. He suddenly slips down and falls by 900m where he finds support. How high is he from the ground?

A) 27km               done clear

B)          270m done clear

C) 0.9km              done clear

D)          18m done clear

question_answer 9) If \[\frac{3}{5}\] of the property costs Rs 15,000 what is the cost of \[\frac{1}{2}\] of it?

A) Rs. 7500          done clear

B)          Rs. 12500 done clear

C) Rs. 25000         done clear

D)          Rs. 10000 done clear

question_answer 10) Insert the correct number in the box: \[\frac{28}{35}=\frac{\square }{30}\]

A) 24  done clear

B)          23 done clear

C) 20                    done clear

D)          7 done clear

question_answer 11) If the denominator of a fraction is 1 more than thrice its numerator and if the numerator is increased by one and denominator is reduced by two then its value is 0.5. Find the fraction.  

A)  \[\frac{1}{2}\]                        done clear

B)           \[\frac{4}{13}\] done clear

C)  \[\frac{3}{10}\]                      done clear

D)           \[\frac{2}{7}\] done clear

question_answer 12) The cost of 1 litre milk is Rs. 7.50 then the cost of 30.5 litre milk is

A) Rs. 225.75        done clear

B)          Rs. 223.75 done clear

C) Rs. 228.75        done clear

D)          Rs. 243.60 done clear

question_answer 13) The fractional form of 0.4999 is

A)  \[\frac{4999}{100}\]  done clear

B)           \[\frac{4999}{10000}\] done clear

C)  \[\frac{4999}{1000}\]            done clear

D)           \[\frac{4999}{100000}\] done clear

question_answer 14) The expanded form of 31.005 is

A)  \[3\times 10+1\times 1+\frac{5}{100}\] done clear

B)  \[3\times 10+1\times 1+\frac{5}{1000}\] done clear

C)  \[3\times 100+1\times 10+\frac{5}{1000}\] done clear

D)  \[3+1\times 100+\frac{5}{1000}\] done clear

question_answer 15) The descending order of the following decimals 3.35, 2.59, 28.1, 6.0, 6.7, 3.51s

A) 28.1, 2.59, 6.7, 6.0, 3.5, 3.35 done clear

B) 3.35, 28.1, 6.7, 6.0, 3.5, 2.59 done clear

C) 28.1, 6.7, 6.0, 3.5, 3.35, 2.59 done clear

D) 28.1, 6.0, 6.7, 3.35, 3.5, 2.59 done clear

question_answer 16) Ravi bought some medicines for Rs 495.75 and gave the chemist a 1000- rupee note. What amount did the chemist return ?

A) Rs. 500.75        done clear

B)          Rs. 504.50 done clear

C) Rs. 500.25        done clear

D)          Rs. 504.25 done clear

question_answer 17) The middle terms of proportion are

A) antecedents    done clear

B)         means done clear

C) extremes        done clear

D)          consequents done clear

question_answer 18) ________ is a fraction in which numerator is greater than or equal to the denominator.

A) Proper fractions           done clear

B) Unlike fractions done clear

C) Improper fraction         done clear

D) Mixed fraction. done clear

question_answer 19) The equivalent fraction of \[\frac{2}{3}\] having the denomiator 18 is

A)  \[\frac{2}{18}\]                      done clear

B)           \[\frac{18}{3}\] done clear

C)  \[\frac{12}{18}\]                    done clear

D)           \[\frac{18}{27}\] done clear

question_answer 20) The decimal form of \[\frac{15}{1000}\] is

A) 15.00               done clear

B)          1.50 done clear

C) 0.15                  done clear

D)          0.015 done clear

question_answer 21) The sum of two numbers is 31.021. The other number will be _____, if one of them is 11.56.

A) 19.461             done clear

B)          17.461 done clear

C) 18.641             done clear

D)          19.561 done clear

question_answer 22) ____ is the simplest form of the ratio 144 : 28

A) 28 : 4               done clear

B)          36 : 7 done clear

C) 7: 36                done clear

D)          1 : 2 done clear

question_answer 23) The cost of one saree is _____, if cost of 12 sarees is Rs 3600.

A) Rs. 300           done clear

B)                      Rs. 350 done clear

C) Rs. 250            done clear

D)          Rs. 200 done clear

question_answer 24) Ratio symbol is ____ and is read as____

A) : :,equal to     done clear

B)          :,equal to done clear

C) :, is to               done clear

D)          : :, is to done clear

question_answer 25) Decimal representation of \[\frac{1629}{1000}\] is

A) 16.29               done clear

B)          1.629 done clear

C) 0.1629             done clear

D)          162.9 done clear

question_answer 26) The sum of 47.027 and 109.01 is

A) 156.037           done clear

B)          154.031 done clear

C) 156.038        done clear

D)          154.038 done clear

question_answer 27) The mixed form of the fraction \[\frac{77}{4}\] is

A)  \[18\frac{1}{4}\]        done clear

B)           \[12\frac{3}{4}\] done clear

C)  \[19\frac{1}{4}\]                    done clear

D)           \[17\frac{5}{4}\] done clear

question_answer 28) Complete the passage given below by choosing the correct option. To find equivalent fraction of a number written in the fraction form, (i)______ or (ii) ______ the (iii) ______ and (iv) ________ by the (v) _______ number.

A) divide (ii) numerator (iii) multiply (iv) same (v) denominator done clear

B) multiply (ii) divide (iii) numerator (iv) denominator(v) same done clear

C) same (ii) divide (iii) denominator (iv) multiply (v) numerator done clear

D) numerator (ii) denominator (iii) divide (iv) multiply (v) same done clear

A) A ? r; B ? p; C ? q; D ? s done clear

B) A ? r; B ? s; C ? p; D ? q done clear

C) A ? p; B ? r; C ? s; D ? q done clear

D) A ? s; B ? q; C ? r; D ? p done clear

A) A - r; B - q; C - s; D ? p done clear

C) A - p; B - r; C - s; D ? q done clear

A) A ? p; B ? s; C ? q; D ? r done clear

B) A ? s; B ? q; C ? p; D ? r done clear

C) A ? r; B ? p; C ? s; D ? q done clear

D) A ? q; B ? r; C ? p; D ? s done clear

A) A ? p; B ? r; C ? q; D ? s done clear

B) q; B ? p; C ? r; D ? s done clear

C) A ? r; B ? q; C ? s; D ? p done clear

D) A ? s; B ? r; C ? p; D ? q done clear

A) A ? p; B ? q; C ? r; D ? s done clear

B) A ? r; B ? p; C ? s; D ? q done clear

C) A ? s; B ? r; C ? q; D ? p         done clear

D) A ? q; B ? s; C ? r; D ? p done clear

question_answer 34) DIRECTIONS: Passage ? 1: Read the passage(s) given below and answer the questions that follow. My elder sister divided a watermelon into 18 parts. I ate 7 out of them. My friend ate 4. How much did we eat between us?

A)  \[\frac{7}{18}\]                      done clear

B)           \[\frac{12}{18}\] done clear

C)  \[\frac{11}{18}\]                    done clear

D)           \[\frac{9}{18}\] done clear

question_answer 35) DIRECTIONS: Passage ? 1: Read the passage(s) given below and answer the questions that follow. My elder sister divided a watermelon into 18 parts. I ate 7 out of them. My friend ate 4. How much more of watermelon did I eat as compared to my friend?

A)  \[\frac{3}{18}\]                      done clear

B)           \[\frac{5}{18}\] done clear

C) \[\frac{4}{18}\]                       done clear

D)           \[\frac{7}{18}\] done clear

question_answer 36) DIRECTIONS: Passage ? 1: Read the passage(s) given below and answer the questions that follow. My elder sister divided a watermelon into 18 parts. I ate 7 out of them. My friend ate 4. What amount of watermelon remained?

A)  \[\frac{5}{18}\]                      done clear

B)           \[\frac{4}{18}\] done clear

C)  \[\frac{7}{18}\]                      done clear

D)           \[\frac{3}{18}\] done clear

question_answer 37) DIRECTIONS: Passage ? 2: Read the passage(s) given below and answer the questions that follow. \[\frac{2}{3}\] of the pens Mrs. Sonia bought were blue and the rest were red. She gave away \[\frac{3}{4}\] of the blue pens and \[\frac{1}{4}\] of the red pens and had 90 pens left. Write the fraction which represents red pens.

A)  \[\frac{4}{3}\]                        done clear

B)           \[\frac{1}{3}\] done clear

C)  \[\frac{2}{3}\]                        done clear

question_answer 38) DIRECTIONS: Passage ? 2: Read the passage(s) given below and answer the questions that follow. \[\frac{2}{3}\] of the pens Mrs. Sonia bought were blue and the rest were red. She gave away \[\frac{3}{4}\] of the blue pens and \[\frac{1}{4}\] of the red pens and had 90 pens left. How many pens Mrs. Sonia bought?

A) 216                  done clear

B)          196 done clear

C) 150                  done clear

D)          250 done clear

question_answer 39) DIRECTIONS: Passage ? 2: Read the passage(s) given below and answer the questions that follow. \[\frac{2}{3}\] of the pens Mrs. Sonia bought were blue and the rest were red. She gave away \[\frac{3}{4}\] of the blue pens and \[\frac{1}{4}\] of the red pens and had 90 pens left. How many red pens did she give away?

A) 16                    done clear

B)          12 done clear

C) 18                    done clear

D)          24 done clear

question_answer 40) DIRECTIONS: Passage ? 3: Read the passage(s) given below and answer the questions that follow. Jay selected two decimals numbers 35.41 and 4.05. The sum of these decimal is

A) 38.46               done clear

B)          49.06 done clear

C) 39.46               done clear

D)          39.47 done clear

question_answer 41) DIRECTIONS: Passage ? 3: Read the passage(s) given below and answer the questions that follow. Jay selected two decimals numbers 35.41 and 4.05. When Jay subtract these decimals, he will get

A) 314.6               done clear

B)          31.36 done clear

C) 31.45               done clear

D)          31.64 done clear

question_answer 42) DIRECTIONS: Passage ? 3: Read the passage(s) given below and answer the questions that follow. Jay selected two decimals numbers 35.41 and 4.05. The product of 35.41 and 4.05 is

A) 141.4105       done clear

B)          143.5045 done clear

C) 143.4705       done clear

D)          143.4105 done clear

question_answer 43) DIRECTIONS: Passage ? 4: Read the passage(s) given below and answer the questions that follow. A rectangular field having length 17.8 m and breadth 12.7m. The perimeter of the rectangular field is

A) 60.0m              done clear

B)          61.0m done clear

C) 64.0m              done clear

D)          65.0m done clear

question_answer 44) DIRECTIONS: Passage ? 4: Read the passage(s) given below and answer the questions that follow. A rectangular field having length 17.8 m and breadth 12.7m. The difference of length and breadth of rectangular field is

A) 5.1m                done clear

B)          4.1m done clear

C) 4.5 m               done clear

D)          5.5 m done clear

question_answer 45) DIRECTIONS: Passage ? 4: Read the passage(s) given below and answer the questions that follow. A rectangular field having length 17.8 m and breadth 12.7m. The area of the rectangular field is

A) 225.06\[{{m}^{2}}\]      done clear

B)          226.06\[{{m}^{2}}\] done clear

C) 226.66\[{{m}^{2}}\]       done clear

D)          224.6\[{{m}^{2}}\] done clear

question_answer 46) DIRECTIONS: Passage ? 5: Read the passage(s) given below and answer the questions that follow. Prateek runs an ice cream parlour. He earns Rs 3500 per month. He is able to save Rs 1400 but spends the rest. Find the ratio of Prateek's income to his expenditure

A) 5 : 2                 done clear

B)          5 : 3 done clear

C) 3 : 5                 done clear

D)          2 : 5 done clear

question_answer 47) DIRECTIONS: Passage ? 5: Read the passage(s) given below and answer the questions that follow. Prateek runs an ice cream parlour. He earns Rs 3500 per month. He is able to save Rs 1400 but spends the rest. Find the ratio of Prateek's income to his saving.

B)          2 : 5 done clear

C) 5 : 4                 done clear

D)          4 : 5 done clear

question_answer 48) DIRECTIONS: Passage ? 5: Read the passage(s) given below and answer the questions that follow. Prateek runs an ice cream parlour. He earns Rs 3500 per month. He is able to save Rs 1400 but spends the rest. Find the ratio of Prateek's expenditure to his saving.

A) 2 : 3                 done clear

D)          3 : 2 done clear

question_answer 49) DIRECTIONS: Passage ? 6: Read the passage(s) given below and answer the questions that follow. Anuj makes a figure and divides it into 7 equal parts. He colours each of the parts with different colours. Red, Orange, Yellow, Green, Blue, Violet, Black Fractional form of the yellow part of the figure is

A)  \[\frac{2}{7}\]                        done clear

B)           \[\frac{3}{7}\] done clear

C)  \[\frac{1}{7}\] done clear

D)           \[\frac{5}{7}\] done clear

question_answer 50) DIRECTIONS: Passage ? 6: Read the passage(s) given below and answer the questions that follow. Anuj makes a figure and divides it into 7 equal parts. He colours each of the parts with different colours. Red, Orange, Yellow, Green, Blue, Violet, Black Fractional form of the sum of Red and Black part of the figure is

B)           \[\frac{8}{7}\] done clear

C)  \[\frac{1}{7}\]                        done clear

question_answer 51) DIRECTIONS: Passage ? 6: Read the passage(s) given below and answer the questions that follow. Anuj makes a figure and divides it into 7 equal parts. He colours each of the parts with different colours. Red, Orange, Yellow, Green, Blue, Violet, Black Fractional form of the subtraction of Green and violet part of the figure is

B)          0 done clear

D)           \[\frac{7}{7}\] done clear

question_answer 52) DIRECTIONS: Passage ? 7: Read the passage(s) given below and answer the questions that follow. Hitakshi is in class - VI. Hitakshi had 24 pencils. She gave 8 pencils to her sister Meenakshi and 6 pencils to her brother Lakshya. She gave remaining to her mother. What fraction of pencils did she give to Meenakshi?

A)  \[\frac{8}{12}\]                      done clear

B)           \[\frac{4}{3}\] done clear

C)  \[\frac{3}{2}\]                        done clear

D)           \[\frac{1}{3}\] done clear

question_answer 53) DIRECTIONS: Passage ? 7: Read the passage(s) given below and answer the questions that follow. Hitakshi is in class - VI. Hitakshi had 24 pencils. She gave 8 pencils to her sister Meenakshi and 6 pencils to her brother Lakshya. She gave remaining to her mother. What fraction of pencils did she give to Laksya?

A)  \[\frac{1}{4}\]                        done clear

B)  \[\frac{1}{3}\] done clear

C)  \[\frac{3}{4}\]                        done clear

D)           \[\frac{2}{3}\] done clear

question_answer 54) DIRECTIONS: Passage ? 7: Read the passage(s) given below and answer the questions that follow. Hitakshi is in class - VI. Hitakshi had 24 pencils. She gave 8 pencils to her sister Meenakshi and 6 pencils to her brother Lakshya. She gave remaining to her mother. What fraction of pencils did she give to her mother?

A)  \[\frac{12}{5}\]                      done clear

B)           \[\frac{5}{12}\] done clear

C)  \[\frac{7}{12}\]                      done clear

D)           \[\frac{12}{7}\] done clear

question_answer 55) DIRECTIONS: Each of these questions contains an Assertion followed by Reason. Read them carefully and answer the question on the basis of following options. You have to select the one that best describes the two statements. Assertion: If X and Y represent whole part and decimal part for the decimals respectively, then extreme right digit of Y comes in the thousandths column in y comes in the thousandths column in the place value chart.  Reason (R): Decimal places of a decimal is determined by the number of digits present in the decimal part.                         

A) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion. done clear

B) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion. done clear

C) If Assertion is correct but Reason is incorrect. done clear

D) If Assertion is incorrect but Reason is correct. done clear

question_answer 56) DIRECTIONS: Each of these questions contains an Assertion followed by Reason. Read them carefully and answer the question on the basis of following options. You have to select the one that best describes the two statements. Assertion: Proper fractions are related with the decimals which have 0 as integral part. Reason (R): All like decimals have same denominator when they are converted into fraction.                                     

question_answer 57) DIRECTIONS: Each of these questions contains an Assertion followed by Reason. Read them carefully and answer the question on the basis of following options. You have to select the one that best describes the two statements. Let \[\frac{p}{q}\] and \[\frac{r}{s}\] are two fractions. Assertion: If (q) is 5th multiple of s, then  \[\frac{p}{q}\] and \[\frac{r}{s}\] are unlike fractions. Reason (R): If (q) is \[{{(x+2)}^{th}}\] multiple of x and 's' is (x + 2)^ multiple of x then \[\frac{p}{q}\] and \[\frac{r}{s}\] are unlike fractions.

question_answer 58) Read the following statements carefully and choose the correct option. (i) Ratios 2:4 and 12:24 are equivalent ratios. (ii) A team won 6 games out of 10. The ratio of the games won to the games lost is 3 : 2.

A) Only (i) is true. done clear

B) Only (ii) is true. done clear

C) Both (i) and (ii) are true. done clear

D) Neither (i) nor (ii) is true. done clear

question_answer 59) Read the following statements carefully and choose the correct option. (i) Saurabh had Rs 50. He bought chocolates for Rs 45.25. Then the amount of money left with Saurabh is Rs 4.75. (ii) The weight of 3 bags of rice is 3kg 200g, 5 kg 675g and 6 kg 115g. The total weight of rice is 14 kg 890g.

B) Only (ii) is true done clear

C) Neither (i), nor (it) is true. done clear

D) Both (i) and (ii) are true. done clear

question_answer 60) Read the following statement carefully and choose the correct option. (i) The sum of decimals 0.552, 23.45 and 8.236 is 32.228 (ii) The sum of decimals 6.023, 12.5 and 0.54 is 19.083.

C) Neither (i) nor (ii) is true. done clear

question_answer 61) Read the following statements carefully and choose the correct option. (i) Proper fractions are related with the decimals which have 0 as integral part. (ii) All like decimals have same denominator when they are converted into fraction.

A) is correct only. done clear

B) (ii) is correct only. done clear

C) Both (i) and (ii) are correct. done clear

D) Neither (i) nor (ii) is correct. done clear

question_answer 62) Consider the following two statements, (i) A proper fraction has smaller numerator than denominator. (ii) An improper fraction has greater numerator than denominator. Which one of the following is correct?

A) is false and (ii) is true. done clear

B) true and (ii) is false. done clear

C) Both are true. done clear

D) Both are false. done clear

A)  \[\frac{5}{16}\]                      done clear

B)           \[\frac{11}{16}\] done clear

C)  \[\frac{1}{4}\]                        done clear

D)           \[\frac{2.5}{16}\] done clear

A)  \[\frac{3}{8}\]                        done clear

B)           \[\frac{5}{8}\] done clear

C)  \[\frac{6}{8}\]                        done clear

D)           \[\frac{7}{16}\] done clear

A)  \[\frac{3}{12}\]                      done clear

B)           \[\frac{1}{4}\] done clear

C)  \[\frac{1}{3}\]                        done clear

D)           \[\frac{3}{8}\] done clear

A) Aditya              done clear

B)          Yuvraj done clear

C) Sanya              done clear

question_answer 67) Which of the following figures represent equivalent fractions?

question_answer 68) If \[63.3605\,=6A=\frac{3}{13}\,+3C+\frac{3}{D}\,+5E,\] then the value of 4A + 7B + 6C + D + 3E is

A) 47.6003                       done clear

B) 4.7603 done clear

C) 147.6003        done clear

D) 47.603 done clear

question_answer 69) Consider the following quotients: 368.39 divided by 17. 170.50 divided by 62. 875.65 divided by 83. Their correct sequence in decreasing order is

A) I, III, II              done clear

B)          III, I, II done clear

C) II, I, III              done clear

D)          II, III, I done clear

question_answer 70) Page contains 60 lines. A chapter contains 125 pages. A book contains 5 chapters. 20 such books form a bound. If there are 30 lakh lines in x bounds, then the value of x is

A) 4                      done clear

B)          2 done clear

C) 5                      done clear

D)          6 done clear

question_answer 71) The product of two numbers is 936. If their ratio is 13 : 18 then the smallest number is

A) 39                    done clear

B)          36 done clear

C) 54                    done clear

D)          26 done clear

question_answer 72) Age of a man is four times the age of a boy, the ratio of their ages will be

A) 2 : 5                 done clear

B)          4 : 3 done clear

C) 1 :4                  done clear

D)          2 : 3 done clear

question_answer 73) Find the value of m if 4, m and 6 are in continued proportion.

A)  \[2\sqrt{3}\]                done clear

B)  \[2\sqrt{6}\] done clear

C) 16                    done clear

D)          32 done clear

question_answer 74) Riya spent Rs. 34.60 on purchasing a basket. How much money is left if she had Rs 100?

A) Rs. 65.40         done clear

B)          Rs. 10.50 done clear

C) Rs. 65.10         done clear

D)          Rs. 50.75 done clear

question_answer 75) On the number line, the decimal number 3.7 is exactly between which one of the following numbers?

A) 1 and 2            done clear

B)          3 and 4 done clear

C) 4 and 5            done clear

D)          0 and 1 done clear

question_answer 76) Numerator of a fraction is 6 less than the denominator. If the sum of numerator and denominator is 16, then the fraction is

A)  \[\frac{5}{11}\]                      done clear

B)           \[\frac{6}{35}\] done clear

C)  \[\frac{8}{105}\]                    done clear

D)           \[\frac{5}{42}\] done clear

question_answer 77) The cost of a wood piece is Rs 100. What would be the cost of each piece of wood cutting it into 7 equal parts?

A) Rs. 14.22          done clear

B)          Rs. 13.28 done clear

C) Rs. 12.25           done clear

D)          Rs. 14.28 done clear

question_answer 78) Container has \[16\frac{1}{2}\] litres of milk. How many times a glass has to be filled with milk from the tub to empty it, if one glass contains 1.5 litres of milk?

A) 15                    done clear

B)          10 done clear

C) 12                    done clear

question_answer 79) A brick is broken down into two pieces in such a way that each is 0.937 m long. What would be the total length of the brick?

A) 2.784m            done clear

B)          1.349m done clear

C) 1.874m            done clear

D)          1.972m done clear

question_answer 80) 12 slices of apple pie divided in the ratio 1 : 1 means Abhishek will get __(i)___ slices and Armaan will get  ___(ii)___ slices.

A) (i)-6; (ii) ? 6 done clear

B) (i)-10; (ii) ? 350 done clear

C) (i)-6; (ii)-6 done clear

D) (i)-150; (ii)-350 done clear

question_answer 81) 500 ml of orange juice shared in the ratio 3 : 7 means Suhana will get ____(i)____ ml juice. and Aashima will get (ii) ml juice.

A) (i)-350; (ii)- 150 done clear

B) (i)-100; (ii)-350 done clear

C) (i)-150; (ii) -350 done clear

D) ? 6; (ii) ? 6 done clear

question_answer 82) The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is:

A) 20                    done clear

B)          30 done clear

C) 38                    done clear

D)          48 done clear

question_answer 83) Two numbers are such as that square of one is 224 less than 8 times the square of the other. If the numbers are in the ratio of 3 : 4, they are:

A) 12, 16              done clear

B)          6, 8 done clear

C) 9, 12                done clear

question_answer 84) If A : B = 2 : 3, B : C = 4: 5 and C : D = 6 : 7, then A : D = _____.

A) 2 : 7                 done clear

B)          16 : 35       done clear

C) 4 : 13               done clear

D)          7 : 8        done clear

question_answer 85) The salaries of A and B are in the ratio 8 : 3. The salaries of B and C are in the ratio 5:12. Salaries of A, B and C in the form of a ratio is

A) 8 : 15 : 12      done clear

B)          8 : 40 : 36 done clear

C) 16 : 15 : 36     done clear

D)          40 : 15 : 36 done clear

question_answer 86) Three numbers A, B and C are in the ratio 12 : 15 : 25. If the sum of these numbers is 312, then the ratio between the difference of A and B and the difference of C and B is ________

A) 3 : 10               done clear

B)          7 : 3 done clear

C) 3 : 7                 done clear

D)          10 : 3 done clear

A)  \[A-(iv);\,B-(iii);\,C-(ii);\,D-(i)\] done clear

B)  \[A-\,(iii);\,B-(iv);\,C-(ii);\,D-(i)\] done clear

C)  \[A-\,(iv);\,B-(iii);\,C-(i);\,D-(ii)\]  done clear

D)  \[A-\,(iii);\,B-(iv);\,C-(i);\,D-(ii)\] done clear

B)  \[A-(iii);\,B-(iv);\,C-(ii);\,D-(i)\] done clear

C)  \[A-(iii);\,B-(iv);\,C-(i);\,D-(ii)\] done clear

D)  \[A-(iv);\,B-(iii);\,C-(i);\,D-(ii)\] done clear

A)  \[A-(i);\,B-(ii);\,C-(iv);\,D-(iii)\] done clear

B)  \[A-(ii);\,B-(i);\,C-(iii);\,D-(iv)\] done clear

C)  \[A-(i);\,B-(ii);\,C-(iii);\,D-(iv)\] done clear

D)  \[A-(ii);\,B-(i);\,C-(iv);\,D-(iii)\] done clear

question_answer 90) DIRECTIONS: Passage-1 Read the passage(s) given below and answer the questions that follow. Tina wanted to paint her room. She mixed two colours to get her favourite colour. She mixed 2 parts of red paint with 3 parts of white paint. If 20 cans of paint were the numbers of cans of each colour she used?

A) Red cans = 8              white cans =12     done clear

B) Red cans = 12 white cans = 8 done clear

C) Red cans = 10 white cans =10      done clear

D)          Red cans = 2 white cans = 3 done clear

question_answer 91) DIRECTIONS: Passage-1 Read the passage(s) given below and answer the questions that follow. Tina wanted to paint her room. She mixed two colours to get her favourite colour. She mixed 2 parts of red paint with 3 parts of white paint. If 10 cans of paint were used altogether then how many cans of red colour she used?

A) 2 cans              done clear

B)          3 cans done clear

C) 4 cans              done clear

D)          8 cans done clear

question_answer 92) DIRECTIONS: Passage-1 Read the passage(s) given below and answer the questions that follow. Tina wanted to paint her room. She mixed two colours to get her favourite colour. She mixed 2 parts of red paint with 3 parts of white paint. If she used \[\frac{2}{3}\] part of red paint and \[\frac{1}{3}\] part of white paint then what is the ratio of red paint to the white paint she used?

A) 2 : 3                 done clear

B)          1 : 3 done clear

C) 2 : 6                 done clear

D)          2 : 1 done clear

question_answer 93) DIRECTIONS: Passage-2 Read the passage(s) given below and answer the questions that follow. \[\frac{1}{9}\]of the shirts sold at Mr. Sharma's shop are striped. \[\frac{5}{8}\] of the remain are printed. Rest of the shirts are plain coloured shirts. 81 plain coloured shirts are in the Mr. Sharma's shop. Which of the following diagram shows the above information correctly?

question_answer 94) DIRECTIONS: Passage-2 Read the passage(s) given below and answer the questions that follow. \[\frac{1}{9}\]of the shirts sold at Mr. Sharma's shop are striped. \[\frac{5}{8}\] of the remain are printed. Rest of the shirts are plain coloured shirts. 81 plain coloured shirts are in the Mr. Sharma's shop. How many more printed shirts than plain shirts does the shop have?

A) 54                    done clear

B)          45 done clear

C) 27                    done clear

D)          72 done clear

question_answer 95) DIRECTIONS: Passage-3 Read the passage(s) given below and answer the questions that follow. "The ratio of the price of a pencil to the price of an eraser is 5 : 1" Which of the following object is more expensive?

A) Eraser  done clear

B)          Pencil done clear

C) Both                 done clear

question_answer 96) DIRECTIONS: Passage-3 Read the passage(s) given below and answer the questions that follow. "The ratio of the price of a pencil to the price of an eraser is 5 : 1" If the price of the pencil is Rs 10, can the price of the eraser be Rs 20?

A) No                   done clear

B)          yes done clear

C) can't say          done clear

D)          Data is insufficient done clear

question_answer 97) DIRECTIONS: Passage-3 Read the passage(s) given below and answer the questions that follow. "The ratio of the price of a pencil to the price of an eraser is 5 : 1" If the price of the eraser is Rs. 1, then what will be the price of the pencil?

A) Rs. 6                done clear

B)          Rs. 4 done clear

C) Rs. 5                done clear

D) Rs. 10 done clear

A)  \[\frac{1}{5}\]            done clear

B)                       \[\frac{3}{5}\] done clear

C)  \[\frac{7}{5}\]                        done clear

D)           \[\frac{5}{2}\]  done clear

D) None of these done clear

A)  \[\frac{5}{4}\]                        done clear

B)           \[\frac{4}{5}\] done clear

C)  \[\frac{6}{5}\]                        done clear

D)           \[\frac{5}{6}\] done clear

question_answer 101) Assertion/Reason Based MCQ Direction: The questions in this segment consists of two statements, one labelled as "Assertion? and the other labelled as" Reason (R)". You are to examine these two statements carefully and decide the assertion A and reason R are individually true and if so, whether the reason is a correct explanation of the assertion. Select your answers to these interns using codes given below. Assertion: If the numerator and denominator of a proper fraction are increased by the same quantity, then the resulting fraction is always greater than the original fraction. Reason (R): Fractions obtained on multiplying or dividing both numerator and denominator of given fraction by the same non- zero number are called Improper fraction.

question_answer 102) Direction: The questions in this segment consists of two statements, one labelled as "Assertion? and the other labelled as" Reason (R)". You are to examine these two statements carefully and decide the assertion A and reason R are individually true and if so, whether the reason is a correct explanation of the assertion. Select your answers to these interns using codes given below. Assertion: An equality of two ratios is called a proportion. Reason (R): Four quantities a, b, c, d are said to be in proportion if a : b = c : d

question_answer 103) Direction: The questions in this segment consists of two statements, one labelled as "Assertion? and the other labelled as" Reason (R)". You are to examine these two statements carefully and decide the assertion A and reason R are individually true and if so, whether the reason is a correct explanation of the assertion. Select your answers to these interns using codes given below. Assertion: The price of 349 coconuts is 2094. The price of 26 dozens of coconuts is 1872. Reason (R): The method of finding the value of the required number of a quantity by first finding the value of the unit quantity is known as unitary method.

question_answer 104) Direction: The questions in this segment consists of two statements, one labelled as "Assertion? and the other labelled as" Reason (R)". You are to examine these two statements carefully and decide the assertion A and reason R are individually true and if so, whether the reason is a correct explanation of the assertion. Select your answers to these interns using codes given below. Assertion: If \[\frac{1}{5}:\frac{1}{x}::\,\frac{1}{x}\,:\frac{1}{1.25}\] then the value of x is 2.5. Reason (R): Three quantities a, b, c are said to be in continued proportion if \[a:b=6:c\,\,\text{ie},\,{{b}^{2}}=ac\]

question_answer 105) Direction: The questions in this segment consists of two statements, one labelled as "Assertion? and the other labelled as" Reason (R)". You are to examine these two statements carefully and decide the assertion A and reason R are individually true and if so, whether the reason is a correct explanation of the assertion. Select your answers to these interns using codes given below. Assertion: The Sum is divided among four persons in the ratio 3:4:5:8. If the second largest share is Rs 2500 then the total sum is 10, 000. Reason: If we have to divide a given number A in the ratio a : b : c, then. First part \[=\frac{a}{a+b+c}\times A\] Second part \[=\frac{b}{a+b+c}\times A\] Third part \[=\frac{c}{a+b+c}A\].

question_answer 106) Direction: The questions in this segment consists of two statements, one labelled as "Assertion? and the other labelled as" Reason (R)". You are to examine these two statements carefully and decide the assertion A and reason R are individually true and if so, whether the reason is a correct explanation of the assertion. Select your answers to these interns using codes given below. Assertion: Lakshya multiplies two unit fraction and finds that the resultant fraction is also a unit fraction. Reason (R): when a fraction is multiplied or divided by 1, the fraction remains same.

question_answer 107) Direction: The questions in this segment consists of two statements, one labelled as "Assertion? and the other labelled as" Reason (R)". You are to examine these two statements carefully and decide the assertion A and reason R are individually true and if so, whether the reason is a correct explanation of the assertion. Select your answers to these interns using codes given below. Assertion: If \[\frac{1}{P}>\frac{1}{Q}\] then \[\frac{1}{P\times Q}\] and \[\frac{1}{Q\times P}\] are like fractions. Reason (R): If \[\frac{1}{P}>\frac{1}{Q}\] then \[\frac{1}{P}\] and \[\frac{1}{Q}\] are equivalent fractions if 2p = Q.

question_answer 108) Direction: The questions in this segment consists of two statements, one labelled as "Assertion? and the other labelled as" Reason (R)". You are to examine these two statements carefully and decide the assertion A and reason R are individually true and if so, whether the reason is a correct explanation of the assertion. Select your answers to these interns using codes given below. Assertion: \[\frac{p}{q}\] and \[\frac{r}{s}\] are two fractions. If HCF of q and s is q and HCF of p and r is p then \[\frac{p}{q}\] and \[\frac{r}{s}\] are equivalent fractions. Reason (R): if p and q are multiples of r and s respectively, then \[\frac{p}{q}\] and \[\frac{r}{s}\] are equivalent fractions.

question_answer 109) Read the following statements carefully and choose the correct option. Value of \[\left( 1-\frac{1}{2} \right)\,\left( 1-\frac{1}{3} \right)\,\left( 1-\frac{1}{4} \right).....\left( 1-\frac{1}{x} \right)\] is equal to \[\frac{1}{x}\]. (ii) If \[2=x+\frac{1}{1+\frac{1}{3+\frac{1}{4}}}\] then value of x is \[\frac{21}{17}\] (iii) Value of \[999\frac{1}{7}+999\frac{2}{7}\,+999\frac{3}{7}+999\frac{4}{7}\]\[+999\frac{5}{7}\,+999\frac{6}{7}\] is 5999.

A) and (ii) are true while (iii) is false. done clear

B) and (iii) are true while (ii) is false. done clear

C) (ii) and (iii) are true while (i) is false. done clear

D) Neither (i) and (ii) nor (iii) is true. done clear

question_answer 110) Read the following statements carefully and choose the correct option. Value of \[\frac{0.216+0.064}{0.36+0.16-0.24}\] is 1. If \[4.175\,=\frac{1}{0.2395}\] then the value of \[\frac{1}{0.0004175}\] is equal to 2935. (iii) Value of [0.9 -{2.3 - 3.2 - (7.1 - 5. 4 -3.5)}] is 0.

D) All the given (i), (ii) and (iii) are true. done clear

A)  \[\frac{5}{12}\]                      done clear

B)           \[\frac{5}{24}\] done clear

D)           \[\frac{11}{24}\] done clear

A) 4g                    done clear

B)          40 g done clear

C) 160                  done clear

D)          100 g done clear

A) 60 eggs            done clear

B)          2 eggs done clear

C) 6 eggs              done clear

D)          3 eggs done clear

A) 6g                                done clear

B) 200 g done clear

C) 2g                    done clear

D)          10 g done clear

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Question - Arithmetic

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Hint: Represent a number as a part of the whole in order to determine the fraction.

(a) \frac{3}{5} (b) \frac{5}{3} (c) \frac{3}{8} (d) \frac{5}{8}

Question.2. In which of the following models, the fraction represented by shaded portion is the same as the fraction represented by unshaded portion?

Hint: Determine part and whole in order to label numerator and denominator of a fraction.

Question.3. Ajay wants to represents a fraction \frac{3}{5} in a rectangular model. What is the minimum number of equal parts he needs to divide the rectangular model into?

(a) 2 (b) 3 (c) 5 (d) 8

Question.4. Ajay divided a square into b equal parts and shaded a parts. Which of these represents the numerator of the fraction that represents the unshaded portion?

(a) a (b) a-b (c) b-a (d) a+b

Ans.3. (c) 5 Ans.4. (c) b-a

Hint: Draw equal parts between the whole numbers in order to represent fractions on a number line.

(a) \frac{3}{7} (b) \frac{3}{8} (c) \frac{4}{8} (d) \frac{4}{9}

Question.6. Akriti followed the given steps to represent a fraction on a number line. Step 1: Using tick marks, she divided the number line between 0 and 1 into 5 equal parts. Step 2: She plotted a point at the 4th tick mark to the right of 0. What fraction does the point show?

(a) \frac{1}{5} (b) \frac{3}{5} (c) \frac{4}{5} (d) \frac{4}{9}

Ans.5. (b) \frac{3}{8} Ans.6. (c) \frac{4}{5}

Hint: Write proper fractions in order to deduce that they are always less than 1 or numerator is less than denominator.

Question.7. If \frac{m}{4} is a proper fraction, which option shows the possible values of m ?

(a) 1, 2 and 3 (b) 1, 2, 3 and 4 (c) 5, 6 and 7 (d) 4, 5, 6 and 7

Question.8. Which of these will always be a proper fraction for any natural number m>1 ?

(a) \frac{m}{m+1} (b) \frac{m+1}{m} (c) \frac{m}{m} (d) \frac{m}{m-1}

Ans.7. (a) 1, 2 and 3 Ans.8. (a) \frac{m}{m+1}

Hint: Write fractions where numerator is greater than denominator in order to determine improper fractions.

Question.9. For what value of s and t , \frac{s}{t} will be an improper fraction?

(a) s=3 , t=3 (b) s=3 , t=5 (c) s=0 , t=5 (d) s=5 , t=3

Question.10. If the fraction \frac{6}{y} is an improper fraction, which of these could be the value of y ?

(a) 4 (b) 6 (c) 9 (d) 12

Ans.9. (d) s=5 , t=3 Ans.10. (a) 4

Hint: Write the improper fraction in the form of mixed fraction in order to represent it as a combination of whole and a part.

Question.11. If the fraction \frac{119}{19} is represented in the form of j\frac{k}{19} , what is the value of j and k ?

(a) j=10 , k=0 (b) j=5 , k=6 (c) j=6 , k=5 (d) j=6 , k=6

Question.12. If 4\frac{k}{13} can also be written as \frac{59}{13} , what is the value of k ?

(a) 4 (b) 5 (c) 6 (d) 7

Ans.11. (c) j=6 , k=5 Ans.12. (d) 7

Hint: Multiply/Divide the numerator and denominator with the same number in order to find equivalent fractions.

Question.13. If \frac{3}{t} and \frac{51}{119} are equivalent fractions, what is the value of t ?

(a) 3 (b) 7 (c) 8 (d) 17

Question.14. A teacher creates an assignment consisting of 19 questions. Of these 19 questions, 7 were easy. The teacher now needs to create another assignment and wants the fraction of easy questions in this assignment to be the same as in the previous one. If the new assignment will have a total of 76 questions, how many easy questions will be there in the assignment?

(a) 7 (b) 11 (c) 19 (d) 28

Ans.13. (b) 7 Ans.14. (d) 28

Hint: Perform cross multiplication among two fractions in order to verify their equivalence.

Question.15. Which of the following must be true for fractions \frac{x}{6} and \frac{12}{y} to be equivalent?

(a) The sum of x and y is equal to 18. (b) The sum of x and y is equal to 72. (c) The product of x and y is equal to 18. (d) The product of x and y is equal to 72.

Question.16. Consider the fractions \frac{a}{b} , \frac{c}{d} and \frac{p}{q} and the following relationships. Relation 1: a\times d=a\times q=c\times q =12 Relation 2: b\times c=b\times p=d\times p =12 Which of the given relations verify that the fractions are equivalent?

(a) Both relations together are sufficient, but neither relation is sufficient alone (b) Relation 2 is sufficient alone, but not Relation 1 (c) Relation 1 is sufficient alone, but not Relation 2 (d) Relations 1 and 2 together are not sufficient

Ans.15. (d) The product of x and y is equal to 72. Ans.16. (a) Both relations together are sufficient, but neither relation is sufficient alone

Hint: Reduce the fraction in order to determine its simplest form.

Question.17. Which of these shows the way to express \frac{16}{24} in its simplest form?

(a) Divide 16 and 24 by their HCF (b) Divide 16 and 24 by their LCM (c) Multiply 16 and 24 by their LCM (d) Multiply 16 and 24 by their HCF

Question.18. The HCF of numbers a and b is 5. If the simplest form of fraction \frac{a}{b} is \frac{8}{19} , what could be the fraction?

(a) \frac{3}{14} (b) \frac{8}{19} (c) \frac{13}{24} (d) \frac{40}{95}

Ans.17. (a) Divide 16 and 24 by their HCF Ans.18. (d) \frac{40}{95}

Hint: Check the denominators of the fractions in order distinguish between like and unlike fractions.

Question.19. Amrita writes a fraction which is the simplest form of \frac{5}{15} . If the fraction she writes and \frac{2}{b} are like fractions, which of these can be the value of b ?

(a) 1 (b) 2 (c) 3 (d) 5

Question.20. If the fractions \frac{3}{5} and \frac{m}{n} are unlike fractions ( n ≠ 0 ), which of these shows the possible values of m and n ?

(a) m=3 ; n=5 (b) m can take any value except 3; n=5 (c) m=3 , n can take any value except 5 (d) m can take any value, n can take any value except 5

Ans.19. (c) 3 Ans.20. (d) m can take any value, n can take any value except 5

Hint: Inspect the numerators of the like fractions in order to determine larger and smaller fraction(s).

Question.21. If the fraction \frac{m}{9} is greater than \frac{6}{9} , which of these shows the value of m ?

(a) 0 < m < 3 (b) 0 < m < 6 (c) 3 < m < 9 (d) 6 < m < 9

Question.22. If the fraction \frac{9}{m} is less than \frac{k}{m} , which of these can be the value of k ?

(a) 1 (b) 4 (c) 9 (d) 15

Ans.21. (d) 6 < m < 9 Ans.22. (d) 15

Hint: Determine the LCM of the unlike fractions in order to compare them.

Question.23. Which option correctly arranges the fractions \frac{2}{5} , \frac{2}{6} and \frac{7}{15} in increasing order?

(a) \frac{2}{5} < \frac{2}{6} < \frac{7}{15} (b) \frac{2}{6} < \frac{2}{5} < \frac{7}{15} (c) \frac{7}{15} < \frac{2}{5} < \frac{2}{6} (d) \frac{7}{15} < \frac{2}{6} < \frac{2}{5}

Question.24. Which of the following is true about the fractions M and N shown below? M = 2\frac{5}{8} N = 2\frac{4}{5}

(a) M<N , because \frac{5}{8} < \frac{4}{5} (b) M=N , because their whole parts are equal (c) M>N , because \frac{5}{8} > \frac{4}{5} (d) M and N can’t be compared because they are mixed numbers

Ans.23. (b) \frac{2}{6} < \frac{2}{5} < \frac{7}{15} Ans.24. (a) M<N , because \frac{5}{8} < \frac{4}{5}

Hint: Solve (addition/subtraction) the numerator and retain the denominator of the like fractions in order to perform addition and subtraction on the given fraction.

Question.25. If the difference of like fractions \frac{7}{m} and \frac{3}{n} is \frac{4}{11} , which of the following is true about m and n ?

(a) m-n=11 (b) m+n=11 (c) m=n=4 (d) m=n=11

Question.26. Which of these shows the sum of like fractions \frac{3}{7} and \frac{p}{q} ?

(a) \frac{3p}{7} (b) \frac{3+p}{7} (c) \frac{3}{7+q} (d) \frac{3+p}{7+q}

Ans.25. (d) m=n=11 Ans.26. (b) \frac{3+p}{7}

Hint: Convert the given fractions into its equivalent fractions in order to perform addition and subtraction on them.

Question.27. The total distance between Ajay’s home and his office is 3\frac{1}{6} km. He covered first \frac{1}{2} km walking and then took a bus. He again walks for \frac{2}{3} km to reach his office. What is the distance that Ajay covered by bus?

(a) 1\frac{2}{3} km (b) 2 km (c) 2\frac{1}{2} km (d) 4 km

Question.28. The steps followed by a student to subtract 1\frac{7}{8} from 3\frac{3}{4} are shown below: Step 1: 3\frac{3}{4} – 1\frac{7}{8} Step 2: (3-1)+\left(\frac{3}{4}-\frac{7}{8}\right) Step 3: 2+\left(\frac{6}{8}-\frac{7}{8}\right) Step 4: 2+\left(\frac{7-6}{8}\right) Step 5: 2\frac{1}{8} In which step did the student make her first error? What is the correct step?

(a) Step 2; \left(\frac{15}{4}-\frac{15}{8}\right) (b) Step 2; (3-1)+\left(\frac{3}{4}+\frac{7}{8}\right) (c) Step 3; 2+\left(\frac{7}{8}-\frac{6}{8}\right) (d) Step 3; 2+\left(\frac{3}{8}-\frac{6}{8}\right)

Ans.27. (b) 2 km Ans.28. (a) Step 2; \left(\frac{15}{4}-\frac{15}{8}\right)

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• CBSE Class 6 Maths...

CBSE Class 6 Maths Fractions Chapter 7 Extra Questions

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CBSE Class 6 Maths Fractions Chapter 7 Extra Questions. myCBSEguide has just released Chapter Wise Question Answers for class 6 Maths. There chapter wise Practice Questions with complete solutions are available for download in  myCBSEguide   website and mobile app. These Extra Questions with solution are prepared by our team of expert teachers who are teaching grade in CBSE schools for years. There are around 4-5 set of solved Mathematics Extra questions from each and every chapter. The students will not miss any concept in these Chapter wise question that are specially designed to tackle Exam. We have taken care of every single concept given in  CBSE Class 6 Mathematics   syllabus  and questions are framed as per the latest marking scheme and blue print issued by CBSE for Class 6.

CBSE Class 6 Maths Extra Questions

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Important Questions for Class 6 Chapter 7 Maths

Ch-7 Fractions

• Which of the following is a smaller fraction? (a)  {tex}\frac{4}{5}{/tex}  (b)  {tex}\frac{5}{3}{/tex}  (c)  {tex}\frac{5}{6}{/tex}  (d)  {tex}\frac{5}{2}{/tex}
• {tex}2\frac{7}{9}{/tex}
• {tex}1\frac{5}{9}{/tex}
• {tex}1\frac{7}{9}{/tex}
• {tex}2\frac{5}{9}{/tex}
• None of these
• {tex}\frac{3}{4}{/tex}
• {tex}\frac{1}{4}{/tex}
• {tex}\frac{1}{2}{/tex}
• {tex}\frac{{17}}{{101}}\_\_\_\_\frac{{12}}{{101}}{/tex} (a)  None of these (b)   > (c)   = (d)   <
• {tex}\frac{4}{{16}}{/tex}
• {tex}\frac{9}{{16}}{/tex}
• {tex}\frac{5}{{16}}{/tex}
• {tex}\frac{{10}}{{16}}{/tex}

Match the following:

Fill in the blanks: There is a large box of 36 small square boxes.

• {tex}\frac{1}{2}{/tex} of it is _____.
• {tex}\frac{2}{3}{/tex} of it is _____.
• If I make a bench of 20 small boxes, the fraction becomes _____.
• _____ boxes are required if fraction is {tex}\frac{5}{6}{/tex} .

State True or False:

• In {tex}\frac{3}{7}{/tex} , 3 is the part of whole.
• On a number line, {tex}\frac{2}{7}{/tex} is to the right of zero.
• {tex}\frac{2}{5}{/tex} is smaller than {tex}\frac{1}{5}{/tex} .
• {tex}\frac{{28}}{{45}}{/tex} and {tex}\frac{3}{5}{/tex} represent equivalent fractions.
• Solve : {tex}\frac{16}5-\;\frac75{/tex}
• Colour the part according to {tex}\frac{3}{4}{/tex} .
• Find the equivalent fraction {tex}\frac35{/tex} having numerator 27.

Rewrite the fractions in the simplest form

• {tex}\frac{8}{6}{/tex}
• {tex}\frac{{44}}{{72}}{/tex}
• Express the following as mixed fracton : {tex}\frac{19}6{/tex}
• Show {tex}\frac{10}{10}{/tex} on the number line.

Find the missing entries in the tables:

• {tex}\frac{4}{5}{/tex} Explanation: 4/5, 5/6 , 5/3 , 5/2 lcm of denominator(5,6,3,2)=30 {tex}{4 \over 5},{5 \over 6},{5 \over 3},{5 \over 2} = {{24,25,50,75} \over {30}}{/tex} smaller fraction = {tex}24 \over 30{/tex} i.e {tex}4 \over 5{/tex}
• {tex}1\frac{7}{9}{/tex} Explanation: {tex}16 \div 9{/tex} quotient is 1 which is a whole number and remainder is 7 which is a numerator of a proper fraction and denominator of proper fraction is 9 so mixed fraction = {tex}1\frac{7}{9}{/tex}
• {tex}\frac{3}{4}{/tex} Explanation: 1 hour = 60 minutes {tex}{{45} \over {60}} = {{45 \div 15} \over {60 \div 15}} = {3 \over 4}{/tex}
• > Explanation: denominator is 101 so {tex}{{17} \over {101}} > {{12} \over {101}}{/tex}
• {tex}\frac{{10}}{{16}}{/tex} Explanation: Total part = 16, shaded part = 10 Fraction = {tex}\frac{{10}}{{16}}{/tex}
• {tex} \to {/tex} (iv) 4 parts are shaded out of 5 parts. Therefore, the shaded portion = {tex}\frac{4}{5}{/tex}
• {tex} \to {/tex} (i) 5 parts are shaded out of 9 parts. Therefore, the shaded portion = {tex}\frac{5}{9}{/tex}
• {tex} \to {/tex} (ii) 3 parts are shaded out of 6 parts. Therefore, the shaded portion = {tex}\frac{3}{6}=\frac{3\div3}{6\div3}=\frac{1}{2}{/tex}
• {tex} \to {/tex} (iii) 1 part is shaded out of 3 parts. Therefore, the shaded portion = {tex}\frac{1}{3}{/tex}
• 18 {tex}\frac{1}{2}{/tex} of 36 boxes = {tex}\frac{1}{2}\times{/tex} 36 = {tex}\frac{36}{2}{/tex} = 18 boxes.
• 24 {tex}\frac{2}{3}{/tex} of 36 boxes = {tex}\frac{2}{3}\times{/tex} 36 = {tex}\frac{2\times36}{3}{/tex} = 2 x 12 = 24 boxes.
• {tex}\frac{5}{9}{/tex} If a bench is made with 20 boxes out of 36 boxes, the fraction = {tex}\frac{20}{36}= \frac{20\div4}{36\div4}= \frac{5}{9}{/tex}
• 30 Let {tex}x{/tex} boxes out of 36 boxes makes fraction {tex}\frac{5}{6}{/tex} i.e., {tex}\frac{x}{36}= \frac{5}{6}{/tex} {tex}x = \frac{5}{6}\times36= \frac{5\times36}{6}{/tex} = 5 x 6 = 30. Therefore, 30 boxes makes the fraction {tex}\frac{5}{6}{/tex}
• True In the fraction, {tex}\frac{3}{7}{/tex} , numerator is 3 and denominator is 7, which means that a unit has been divided into 7 equal parts out of which 3 parts have been taken into account.
• True All positive fractions are greater than zero and lies to the right of zero.
• False When denominators are same in two fractions, the fraction with the greater numerator is greater than the other fraction. Here, in the frations {tex}\frac{2}{5} and \frac{1}{5}{/tex} , denominators are same and in the numerators 2 and 1, 2 is greater than 1. So, {tex}\frac{2}{5} > \frac{1}{5}{/tex}
• False In the fractions, {tex}\frac{28}{45}{/tex} and {tex}\frac{3}{5}{/tex} comparing their cross products, {tex}28 \times 5 = 140{/tex} and {tex}45 \times 3 = 135{/tex} , we observe that they are not equal. Hence, {tex}\frac{28}{45}{/tex} and {tex}\frac{3}{5}{/tex} are not equivalent fractions.
• {tex}\frac{16}5-\;\frac75=\;\frac{16-7}5=\;\frac95=\;1\frac45\;{/tex}
• {tex}\frac35=\frac{3\times9}{5\;\times\;9}=\frac{27}{45}{/tex}
• {tex}\frac{8}{6} ={/tex} {tex}\frac{{8 \div 2}}{{6 \div 2}} = \frac{4}{3}{/tex}
• {tex}\frac{44}{72} = {/tex} {tex}\frac{{44 \div 2}}{{72 \div 2}} = \frac{{22 \div 2}}{{36 \div 2}} = \frac{{11}}{{18}}{/tex}

Chapter Wise Extra Questions for Class 6 Mathematics

• Knowing our Numbers
• Whole Numbers
• Playing with Numbers
• Basic Geometrical Ideas
• Understanding Elementary Shapes
• Data handling
• Mensuration
• Ratio and Proportion
• Practical Geometry

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NCERT Solutions for Class 6 Maths Chapter 7 Fractions

NCERT Solutions for Class 6 Maths Chapter 7 Fractions are provided below. Our solutions covered each questions of the chapter and explains every concept with a clarified explanation. It helps the students to understand slowly and to get practice well to become perfect and again a good score in their examination.

These materials are prepared based on Class 6 NCERT syllabus, taking the types of questions asked in the NCERT textbook into consideration. Further, all the CBSE Class 6 Solutions Maths Chapter 7 Fractions are in accordance with the latest CBSE guidelines and marking schemes

Class 6 Maths Chapter 7 Exercise 7.1 Solutions

Class 6 Maths Chapter 7 Exercise 7.2 Solutions

Class 6 Maths Chapter 7 Exercise 7.3 Solutions

Class 6 Maths Chapter 7 Exercise 7.4 Solutions

Class 6 Maths Chapter 7 Exercise 7.5 Solutions

Class 6 Maths Chapter 7 Exercise 7.6 Solutions

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MCQ Questions for Class 6 Maths Chapter 7 Fractions with Answers

We have compiled the NCERT MCQ Questions for Class 6 Maths Chapter 7 Fractions with Answers Pdf free download covering the entire syllabus. Practice MCQ Questions for Class 6 Maths with Answers on a daily basis and score well in exams. Refer to the Fractions Class 6 MCQs Questions with Answers here along with a detailed explanation.

Fractions Class 6 MCQs Questions with Answers

Choose the correct option.

Question 1. If the numerator and denominator of a fraction are equal, then the fraction: (a) is equal to 1 (b) is less than 1 (c) is equal to 0 (d) is greater than 1

Answer: (a) is equal to 1

Question 2. A fraction whose denominator is greater than its numerator is called a: (a) proper fraction (b) unit fraction (c) improper fraction (d) none of the above

Answer: (a) proper fraction

Question 3. A fraction with numerator 1 is called a (a) mixed number (b) proper fraction (c) unit fraction (d) like fraction

Answer: (c) unit fraction

Question 4. The denominator of the fraction \(\frac {4}{11}\) is (a) 4 (b) 11 (c) 4 + 11 (d) 11 – 4

Answer: (b) 11

Question 5. If \(\frac {3}{4}\) is equivalent to \(\frac {x}{24}\), then the of x is: (a) 4 (b) 6 (c) 12 (d) 18

Answer: (d) 18

Question 6. 1\(\frac {3}{5}\) is: (a) \(\frac {3}{10}\) (b) \(\frac {8}{5}\) (c) \(\frac {5}{13}\) (d) \(\frac {10}{3}\)

Answer: (b) \(\frac {8}{5}\)

Question 7. The largest of the fractions \(\frac {4}{5}\), \(\frac {4}{7}\), \(\frac {4}{9}\), \(\frac {4}{11}\) is: (a) \(\frac {4}{5}\) (b) \(\frac {4}{7}\) (c) \(\frac {4}{9}\) (d) \(\frac {4}{11}\)

Answer: (a) \(\frac {4}{5}\)

Question 8. The smallest of the fractions \(\frac {3}{4}\), \(\frac {2}{4}\), \(\frac {5}{4}\) and \(\frac {7}{4}\) is: (a) \(\frac {3}{4}\) (b) \(\frac {2}{4}\) (c) \(\frac {5}{7}\) (d) \(\frac {7}{4}\)

Answer: (b) \(\frac {2}{4}\)

Question 9. 4\(\frac {3}{4}\) is (a) \(\frac {19}{4}\) (b) \(\frac {17}{4}\) (c) \(\frac {23}{4}\) (d) \(\frac {17}{5}\)

Answer: (a) \(\frac {19}{4}\)

Question 10. The numerator of the fraction \(\frac {6}{7}\) is (a) 6 (b) 7 (c) 6 + 7 (d) 7 – 6

Answer: (a) 6

Question 11. \(\frac {5}{6}\) is a: (a) proper fraction (b) improper fraction (c) mixed fraction (d) none of these

Question 12. Which ofthefollowing is an improper fraction? (a) \(\frac {3}{4}\) (b) \(\frac {4}{3}\) (c) \(\frac {4}{7}\) (d) \(\frac {5}{16}\)

Answer: (b) \(\frac {4}{3}\)

Fill in the blanks

Question 1. A fraction is a part of a ………………….

Answer: Whole

Question 2. The denominator of proper fraction is always …………………. than numerator.

Answer: Greater

Question 3. Fractions with different denominators are called …………………. fractions.

Answer: Unlike

Question 4. …………………. fraction have a combination of a whole number and a proper fraction.

Answer: Mixed

Question 5. The fractions obtained by multiplying or dividing a fraction by the same non-zero number are called …………………. fractions.

Answer: Equivalent

Question 6. A ……………… is a number representing a part of whole.

Answer: Fraction

Question 7. In a ……………… fraction, the numerator is smaller than the denominator.

Answer: Proper

Question 8. Fractions with the ……………… denominators are called like fractions.

Answer: Same

Question 9. Fractions with ……………… denominators are called unlike fractions.

Answer: Different

Question 10. A combination of whole number and a proper fraction is called a ……………… number.

Answer: mixed

Question 11. A fraction is said to be in its ……………… if the HCF of its numerator and denominator is I.

Answer: Lowest Terms

Question 12. \(\frac {12}{17}\) is a ……………… Fraction

Answer: proper

Question 13. 2\(\frac {3}{5}\) is a ……………… fraction.

Write True or False

Question 1. \(\frac {10}{15}\) is an equivalent fraction of \(\frac {2}{3}\)

Answer: True

Question 2. To add two unlike fractions, we add their numerators, leaving the denominator unchanged.

Answer: False

Question 3. A fraction whose denominator is greater than or equal to its numerator is called an improper fraction.

Question 4. The simplest form of equivalent fraction is always equal to each other.

Question 5. For the subtraction of unlike fractions, we first convert them into like fractions and then subtract.

Match the Following

Hope the information shed above regarding NCERT MCQ Questions for Class 6 Maths Chapter 7 Fractions with Answers Pdf free download has been useful to an extent. If you have any other queries of CBSE Class 6 Maths Fractions MCQs Multiple Choice Questions with Answers, feel free to reach us so that we can revert back to us at the earliest possible.

Fraction Extra Questions Solution for Class 6

Fraction class 6 mathematics extra question and answers for cbse / ncert board students.

Fraction Extra Questions and Answers for Class 6 Level Students of CBSE / NCERT Board Published in this Page. Here we provided 01 Marks that’s mean MCQ Type Questions and their Solution And Long Answer Type Questions & Solution. Class VI Students can follow this Page.

Long Answer Type Extra Questions:

What fraction of bal is red ?

What fraction of ball is black ?

MCQ Type Extra Questions:

(a) Mixed fraction

Short Answer Type Extra Questions:

Solution MCQ & Short Answer Type:

Very Short Answer Type Extra Questions:

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• Symmetry Class 7 Case Study Questions Maths Chapter 12

Last Updated on September 8, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 7 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 7 maths. In this article, you will find case study questions for CBSE Class 7 Maths Chapter 12 Symmetry. It is a part of Case Study Questions for CBSE Class 7 Maths Series.

Table of Contents

Case Study Questions on Symmetry

The picture shows a girl and her reflection in a mirror.

Difficulty Level: Medium

Q. 1. Can you draw a line of symmetry on this picture? Mention Yes or No. Justify your choice.

Ans. No, there is no fixed line which divides the figure into two identical parts.

Q. 2. The girl has her right hand raised. Why does it look like her left hand in the mirror image?

Ans. The girl has her right hand raised. It looks like her left hand in the mirror image because in mirror reflection, left-right orientation changes.

Q. 3. Points P, Q, R and S are marked on the girl and their mirror reflections P’, Q’, R’ and S’ are marked on the image. Which point and its image in the mirror have the greatest distance between them? (a) P and Q (b) Q and Q’ (c) R and R’ (d) P’ and S’

Ans. Option (c) is correct. Explanation: It is so because the distance of point R is maximum from the mirror.

Q. 4. Which type of symmetry does the picture show? (a) Line symmetry (b) Point symmetry (c) Rotation symmetry (d) Reflection symmetry

Ans. Option (d) is correct. Explanation: Reflection symmetry

Q. 5. In the above picture, XYZW is a mirror. Why does it produce a symmetric image? Give your explanation using the points shown in the image.

Ans. It produces a symmetric image because (1) The distance between a point on the object and a point on its image is the same from the mirror surface. (2) mirrors produce point symmetry across its plane.

• Visualizing Solid Shapes Class 7 Case Study Questions Maths Chapter 13
• Exponents and Powers Class 7 Case Study Questions Maths Chapter 11
• Algebraic Expressions Class 7 Case Study Questions Maths Chapter 10
• Perimeter and Area Class 7 Case Study Questions Maths Chapter 9
• Rational Numbers Class 7 Case Study Questions Maths Chapter 8
• Comparing Quantities Class 7 Case Study Questions Maths Chapter 7
• Triangle and its Properties Class 7 Case Study Questions Maths Chapter 6
• Lines and Angles Class 7 Case Study Questions Maths Chapter 5
• Simple Equations Class 7 Case Study Questions Maths Chapter 4
• Data Handling Class 7 Case Study Questions Maths Chapter 3

Fractions and Decimals Class 7 Case Study Questions Maths Chapter 2

Integers class 7 case study questions maths chapter 1, topics from which case study questions may be asked.

• Lines of symmetry for regular
• Rotational symmetry
• Line symmetry

A figure is symmetrical about the line which divides the figure into two identical parts. The line which divides the figure into two identical parts is called the line of symmetry or mirror line.

Regular polygons have as many lines of symmetry as they have sides.

Case study questions from the above given topic may be asked.

Exponents are also called Powers or Indices . The exponent says how many times to use the number in a multiplication .

Download Customised White Label Study Materials in MS Word Format

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Frequently Asked Questions (FAQs) on Symmetry Case Study

Q1: what is symmetry.

A1: Symmetry refers to a balanced and proportionate similarity between two halves of an object. An object is said to be symmetric if it can be divided into two or more identical parts that are mirror images of each other.

Q2: What are the different types of symmetry?

A2: There are three main types of symmetry: Line symmetry : When an object can be divided into two identical halves by a line. Rotational symmetry : When an object looks the same after a certain amount of rotation. Point symmetry : When every part of an object has a matching part at an equal distance from a central point.

Q3: What is line symmetry?

A3: Line symmetry occurs when an object can be divided into two identical halves by a straight line. The line is called the line of symmetry or axis of symmetry. For example, a square has four lines of symmetry.

Q4: How many lines of symmetry does a circle have?

A4: A circle has an infinite number of lines of symmetry because it can be divided into identical halves by any line passing through its center.

Q5: What is rotational symmetry?

A5: Rotational symmetry occurs when an object looks the same after being rotated by a certain angle around a central point. For example, a regular pentagon has rotational symmetry because it looks the same after a rotation of 72 0 .

Q6: What is the angle of rotation?

A6: The angle of rotation is the smallest angle by which an object can be rotated to look exactly the same as its original position. For example, the angle of rotation of an equilateral triangle is 12 0 .

Q7: Can an object have both line and rotational symmetry?

A7: Yes, an object can have both line and rotational symmetry. For example, a square has four lines of symmetry and also has rotational symmetry of order 4.

Q10: Are there any online resources or tools available for practicing Symmetry case study questions?

A10: We provide case study questions for CBSE Class 7 Maths on our  website . Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.

Q11: How do you find the line of symmetry of a shape?

A11: To find the line of symmetry of a shape, try dividing the shape into two identical halves. If the halves are mirror images of each other, the line along which the division is made is the line of symmetry.

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