mixed number problem solving

Fraction Word Problems - Mixed Numbers

Related Topics: Fraction Word Problems Worksheet More Fractions Worksheets Fraction Games

“Fraction Word Problems” Worksheets: Fraction Word Problems (Add, Subtract) 2-Step Fraction Word Problems (Add, Subtract)

1-Step Mixed Number Word Problems (Add, Subtract) 2-Step Mixed Number Word Problems (Add, Subtract)

Objective: I can solve one-step word problems involving addition and subtraction of mixed numbers.

Follow these steps to solve the mixed numbers word problems.

Step 1. Is it a problem in addition or subtraction?

Step 2. Do you need to find a common denominator?

Step 3. Can you simplify or reduce the answer?

Solve the following word problems. Mark ran 2 1 / 3 km and Shaun ran 3 1 / 5 km. Find the difference in the distance that they ran. Brandon and his son went fishing. Brandon caught 3 3 / 4 kg of fish while his son caught 2 1 / 5 kg of fish. What is the total weight of the fishes that they caught? For the school’s sports day, a group of students prepared 21 1 / 2 litres of lemonade. At the end of the day they had 2 5 / 8 litres left over. How many litres of lemonade were sold? Darren spent 2 1 / 2 hours on his homework on Monday. On Tuesday, he spent 1 3 / 5 hours on his homework. Find the total amount of time, in hours, that Darren spent doing his homework on Monday and Tuesday. Brian has a bamboo pole that was 6 ¾ m long. He cut off 1 1 / 4 m and another 2 1 / 3 m. What is the length of the remaining bamboo pole in m? Lydia bought 2 3 / 4 kg of vegetables, 1 1 / 4 kg of fish and 2 1 / 3 kg of mutton. What is the total mass, in kg, of the items that she bought? Kimberly has 3 1 / 2 bottles of milk in her refrigerator. She used 3 / 5 bottle in the morning and 1 1 / 4 bottle in the afternoon. How many bottles of milk does Kimberly have left over? A tank has 82 3 / 4 litres of water. 24 4 / 5 litres were used and the tank was filled with another 18 3 / 4 litres. What is the final volume of water in the tank?

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Mixed numbers

In previous lessons, it was said that a fraction consisting of a whole part and a fractional part is called a mixed number .

All fractions that have a whole part and a fraction part have one common name: mixed numbers .

Mixed numbers can be added, subtracted, multiplied, and divided, just like proper fractions . In this lesson we will look at each of these operations separately.

Adding whole number to a fraction

What conclusion can be drawn? If you need to add a number to a proper fraction, you can omit the plus sign and write the whole number and fraction together.

If you add half a pizza to two whole pizzas, you get two whole pizzas and half a pizza:

This is the first way. The second way is much easier. You can put an equal sign and write the whole part and the fractional part together. That is, omit the addition sign:

Apply the combinative law of addition . If we add two twos, we get 4:

Now let's roll up the resulting mixed number:

This is the final answer. The detailed solution of this example can be written as follows:

Adding mixed numbers

First, let's write down the mixed numbers in expanded form:

Apply the combinative law of addition . Group the whole and fractional parts separately:

Let's calculate the integers: 2 + 3 = 5. In the main expression, replace the expression in parentheses (2 + 3) with the resulting five:

Now let's calculate the fractional parts. This is the addition of fractions with different denominators. We already know how to add such fractions:

Now let's collapse the resulting mixed number:

Examples like this need to be solved quickly, without stopping for details. If we were in school, we would have to write down the solution to this example as follows:

If you see such a short solution in the future, don't be frightened. You already understand where it came from.

Let's write the mixed numbers in expanded form:

Let's group the integers and fractions separately:

Let's calculate the integers: 5 + 3 = 8. In the main expression, replace the expression in parentheses (5 + 3) with the resulting number 8

Now let's calculate the fractional parts:

Let's add the whole parts. We get 9

We wrap up the finished answer:

The complete solution of this example is as follows:

There is a universal rule for solving such examples. It looks like this:

To add up mixed numbers, you have to:

• reduce the fractional parts of these numbers to a common denominator;
• perform addition of integers and fractions separately.

If adding fractions results in an improper fraction, isolate the whole part of the fraction and add it to the resulting whole.

The use of ready-made rules is acceptable if the essence of the topic is fully understood. A formulaic solution, looking at other similar examples, leads to errors that take extra time to find. Therefore, it is more reasonable to understand the topic first, and then use a ready-made rule.

Let's use a ready-made rule. Let's reduce the fractional parts to a common denominator, then add the whole and fractional parts separately:

Adding whole and mixed numbers

Let's try to represent this solution in the form of a picture. If you add three whole pizzas and a third of a pizza to two whole pizzas, you get five whole pizzas and a third of a pizza:

In this example, as in the previous one, you have to add up the whole parts:

Subtracting a fraction from a whole number

If there is one whole pizza and we subtract half a pizza from it, we have half a pizza:

If there are two whole pizzas and we subtract half from the bottom, that leaves one whole pizza and half:

Let's pretend that the number 3 is three pizzas:

Now imagine what three pizzas would look like if you cut off that third of them

Subtracting a mixed number from a whole number

If you subtract one whole pizza and one half pizza from five whole pizzas, you are left with three whole pizzas and one half pizza:

Examples on subtracting fractions from a number or subtracting mixed fractions from a number can again be done in the mind. This process is easy to imagine.

If you cover two-thirds of the pizza with your hand in the picture (it's shaded), you'll know right away.

Subtracting mixed numbers

If you subtract two whole pizzas and a third of a pizza from three whole pizzas, you are left with one whole pizza and one sixth of a pizza:

We'll come back to the subtraction of mixed numbers. There are many subtleties in subtracting fractions that a beginner is not yet prepared for. For example, it is possible that the minuend may be less than the subtrahend. This can lead us into the world of negative numbers, which we haven't yet studied.

In the meantime, we will study multiplication of mixed numbers. It is not as complicated as addition and subtraction.

Multiplying fractions by whole numbers

Any whole number can be multiplied by a fraction. All you have to do is multiply the number by the numerator of the fraction.

The answer is an improper fraction. Let's separate the whole part of the fraction:

If there are five whole pizzas and we take half of that number, we have two whole pizzas and half a pizza:

Also, you could have shortened the fraction. The result would have been the same. It would look like this:

If there are three whole pizzas and we take two thirds of that amount, we have two whole pizzas:

This example is solved in the same way as the previous ones. The whole and the numerator of the fraction must be multiplied:

Multiplying mixed numbers and fractions

To multiply a mixed number by a fraction, you must convert the mixed number to an improper fraction, then multiply the proper fractions.

Let's say there is one whole pizza and a half pizza:

Multiplying mixed numbers

Let's try to understand this example with the help of a picture. Let's say there is one whole pizza and one half of a pizza:

The multiplier 2 is clear: it means that one whole pizza and one half pizza must be taken twice. Let's take two whole pizzas and two halves:

Convert the mixed numbers into improper fractions and multiply those improper fractions. If the answer is an improper fraction, select the whole part of the fraction:

Dividing a whole number by a fraction

To divide a whole number by a fraction, multiply the whole by the inversed fraction.

Let's say there are three whole pizzas:

Indeed, if we divide each pizza in half, we have six halves:

Let's say there are two whole pizzas:

To answer this question, find the number of pizzas in the two pizzas shown in the following picture:

Two pizzas contain one whole pizza and one half pizza. This can be seen if the second pizza is cut in half:

Dividing a fraction by a whole number

To divide a fraction by a whole number, multiply the fraction by the inverse of the divisor. We did this kind of division in the last lesson . Let's go over it again.

Let there be half a pizza:

Let's divide it equally into two parts. Then each part will be one-fourth of a pizza:

Dividing a whole number by a mixed number

Dividing a mixed number by a whole number

To divide a mixed number by a whole number, you must convert the mixed number into an improper fraction, then multiply that fraction by the number inverse of the divisor.

Divide this amount of pizza equally into two parts. To do this, first divide a whole pizza into two parts:

Then divide equally into two parts and half:

Dividing mixed numbers

To divide mixed numbers, you need to convert them into improper fractions, then do the usual division of fractions. That is, multiply the first fraction by the inversed second fraction.

Let's convert the mixed numbers into improper fractions. We obtain the following expression:

Let's finish this example to the end:

Let's say there are two whole and half pizzas:

Video lesson

• Actions with fractions
• Comparing Fractions

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Add & subtract mixed numbers

Mixed numbers word problems.

These grade 5 word problems involve adding and subtracting mixed numbers with both like and unlike denominators and sometimes more than two terms .  Some problems include superfluous data, forcing students to read and think about the questions, rather than simply recognizing a pattern to the solutions.

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Mixed number

• 1.1 Addition and Subtraction
• 1.2 Multiplication and Division

Operations with Mixed Numbers

Addition and subtraction.

When adding or subtracting mixed numbers, we generally add or subtract each part -- add/subtract fraction (sometimes with conversion to common denominator) and add/subtract whole numbers. Sometimes, we may need to regroup fractions or "borrow" from whole numbers -- much like regrouping or borrowing when adding multi-digit numbers.

Alternatively, we can convert to improper fractions and add/subtract like regular fractions.

Multiplication and Division

When multiplying or dividing mixed numbers, we can convert to improper fractions and proceed as usual.

• Mixed Numbers (Prealgebra)

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Solving Word Problems by Adding and Subtracting Fractions and Mixed Numbers

Learn how to solve fraction word problems with examples and interactive exercises.

Example 1: Rachel rode her bike for one-fifth of a mile on Monday and two-fifths of a mile on Tuesday. How many miles did she ride altogether?

Analysis: To solve this problem, we will add two fractions with like denominators.

Solution: 

Answer: Rachel rode her bike for three-fifths of a mile altogether.

Analysis: To solve this problem, we will subtract two fractions with unlike denominators.

Answer: Stefanie swam one-third of a lap farther in the morning.

Analysis: To solve this problem, we will add three fractions with unlike denominators. Note that the first is an improper fraction.

Answer: It took Nick three and one-fourth hours to complete his homework altogether.

Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having like denominators.

Answer: Diego and his friends ate six pizzas in all.

Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having like denominators.

Answer: The Cocozzelli family took one-half more days to drive home.

Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having unlike denominators.

Answer: The warehouse has 21 and one-half meters of tape in all.

Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having unlike denominators.

Answer: The electrician needs to cut 13 sixteenths cm of wire.

Analysis: To solve this problem, we will subtract a mixed number from a whole number.

Answer: The carpenter needs to cut four and seven-twelfths feet of wood.

Summary: In this lesson we learned how to solve word problems involving addition and subtraction of fractions and mixed numbers. We used the following skills to solve these problems: 

• Add fractions with like denominators.
• Subtract fractions with like denominators.
• Find the LCD.
• Add fractions with unlike denominators.
• Subtract fractions with unlike denominators.
• Add mixed numbers with like denominators.
• Subtract mixed numbers with like denominators.
• Add mixed numbers with unlike denominators.
• Subtract mixed numbers with unlike denominators.

Directions: Subtract the mixed numbers in each exercise below.  Be sure to simplify your result, if necessary.  Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

Note: To write the fraction three-fourths, enter 3/4 into the form. To write the mixed number four and two-thirds, enter 4, a space, and then 2/3 into the form.

Mixed Number Calculator

Enter the fractional expression below which you want to convert to a mixed number.

The mixed number calculator converts the given fractional expression to a mixed number.

Steps to convert fractional expression to a mixed number-

• Divide the numerator by the denominator.

• The quotient of the division becomes the whole part of the mixed number.

• The remainder of the division over the original denominator becomes the fractional part of the mixed number.

Click the blue arrow to submit. Choose "Convert to a Mixed Number" from the topic selector and click to see the result in our Basic Math Calculator!

Convert to a Mixed Number Convert to a Mixed Number

Popular Problems

Convert to a Mixed Number 7 4 Convert to a Mixed Number 5 3 Convert to a Mixed Number 8 3 Convert to a Mixed Number 1 7 6 Convert to a Mixed Number 2 3

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Mixed Number Calculator

Step-by-step calculator for mixed numbers.

• Solve for Variable
• Practice Mode
• Step-By-Step

Example (Click to view)

• Enter your mixed numbers in the boxes above, and press Calculate!
• To enter your mixed number, be sure to type a space in between the whole number and the fraction. For example: 1 1/3
• Or click the example.

Mixed Fractions

(Also called " Mixed Numbers ")

A Mixed Fraction is a whole number and a proper fraction combined. Such as 1 3 4

See how each example is made up of a whole number and a proper fraction together? That is why it is called a "mixed" fraction (or mixed number).

We can give names to every part of a mixed fraction:

Three Types of Fractions

There are three types of fraction:

Mixed Fractions or Improper Fractions

We can use either an improper fraction or a mixed fraction to show the same amount.

For example 1 3 4 = 7 4 , as shown here:

Converting Improper Fractions to Mixed Fractions

To convert an improper fraction to a mixed fraction, follow these steps:

• Divide the numerator by the denominator.
• Write down the whole number answer
• Then write down any remainder above the denominator.

Example: Convert 11 4 to a mixed fraction.

Write down the 2 and then write down the remainder (3) above the denominator (4).

That example can be written like this:

Example: Convert 10 3 to a mixed fraction.

Converting mixed fractions to improper fractions.

To convert a mixed fraction to an improper fraction, follow these steps:

• Multiply the whole number part by the fraction's denominator.
• Add that to the numerator
• Then write the result on top of the denominator.

Example: Convert 3 2 5 to an improper fraction.

Multiply the whole number part by the denominator:

Add that to the numerator:

Then write that result above the denominator:

We can do the numerator in one go:

Example: Convert 2 1 9 to an improper fraction.

Are improper fractions bad .

NO, they aren't bad!

For mathematics they are actually better than mixed fractions. Because mixed fractions can be confusing when we write them in a formula: should the two parts be added or multiplied?

But, for everyday use , people understand mixed fractions better.

Example: It is easier to say "I ate 2 1 4 sausages", than "I ate 9 4 sausages"

We Recommend:

• For Mathematics: Improper Fractions
• For Everyday Use: Mixed Fractions

4.6 Add and Subtract Mixed Numbers

Learning objectives.

• Model addition of mixed numbers with a common denominator
• Add mixed numbers with a common denominator
• Model subtraction of mixed numbers
• Subtract mixed numbers with a common denominator
• Add and subtract mixed numbers with different denominators

Be Prepared 4.6

Before you get started, take this readiness quiz.

• Draw figure to model 7 3 . 7 3 . If you missed this problem, review Example 4.6 .
• Change 11 4 11 4 to a mixed number. If you missed this problem, review Example 4.9 .
• Change 3 1 2 3 1 2 to an improper fraction. If you missed this problem, review Example 4.11 .

Model Addition of Mixed Numbers with a Common Denominator

So far, we’ve added and subtracted proper and improper fractions, but not mixed numbers. Let’s begin by thinking about addition of mixed numbers using money.

If Ron has 1 1 dollar and 1 1 quarter, he has 1 1 4 1 1 4 dollars.

If Don has 2 2 dollars and 1 1 quarter, he has 2 1 4 2 1 4 dollars.

What if Ron and Don put their money together? They would have 3 3 dollars and 2 2 quarters. They add the dollars and add the quarters. This makes 3 2 4 3 2 4 dollars. Because two quarters is half a dollar, they would have 3 3 and a half dollars, or 3 1 2 3 1 2 dollars.

When you added the dollars and then added the quarters, you were adding the whole numbers and then adding the fractions.

We can use fraction circles to model this same example:

Manipulative Mathematics

Example 4.81.

Model 2 1 3 + 1 2 3 2 1 3 + 1 2 3 and give the sum.

We will use fraction circles, whole circles for the whole numbers and 1 3 1 3 pieces for the fractions.

This is the same as 4 4 wholes. So, 2 1 3 + 1 2 3 = 4 . 2 1 3 + 1 2 3 = 4 .

Try It 4.161

Use a model to add the following. Draw a picture to illustrate your model.

1 2 5 + 3 3 5 1 2 5 + 3 3 5

Try It 4.162

2 1 6 + 2 5 6 2 1 6 + 2 5 6

Example 4.82

Model 1 3 5 + 2 3 5 1 3 5 + 2 3 5 and give the sum as a mixed number.

We will use fraction circles, whole circles for the whole numbers and 1 5 1 5 pieces for the fractions.

Adding the whole circles and fifth pieces, we got a sum of 3 6 5 . 3 6 5 . We can see that 6 5 6 5 is equivalent to 1 1 5 , 1 1 5 , so we add that to the 3 3 to get 4 1 5 . 4 1 5 .

Try It 4.163

Model, and give the sum as a mixed number. Draw a picture to illustrate your model.

2 5 6 + 1 5 6 2 5 6 + 1 5 6

Try It 4.164

1 5 8 + 1 7 8 1 5 8 + 1 7 8

Add Mixed Numbers

Modeling with fraction circles helps illustrate the process for adding mixed numbers: We add the whole numbers and add the fractions, and then we simplify the result, if possible.

Add mixed numbers with a common denominator.

Step 1. Add the whole numbers.

Step 2. Add the fractions.

Step 3. Simplify, if possible.

Example 4.83

Add: 3 4 9 + 2 2 9 . 3 4 9 + 2 2 9 .

Try It 4.165

Find the sum: 4 4 7 + 1 2 7 . 4 4 7 + 1 2 7 .

Try It 4.166

Find the sum: 2 3 11 + 5 6 11 . 2 3 11 + 5 6 11 .

In Example 4.83 , the sum of the fractions was a proper fraction . Now we will work through an example where the sum is an improper fraction.

Example 4.84

Find the sum: 9 5 9 + 5 7 9 . 9 5 9 + 5 7 9 .

Try It 4.167

Find the sum: 8 7 8 + 7 5 8 . 8 7 8 + 7 5 8 .

Try It 4.168

Find the sum: 6 7 9 + 8 5 9 . 6 7 9 + 8 5 9 .

An alternate method for adding mixed numbers is to convert the mixed numbers to improper fractions and then add the improper fractions. This method is usually written horizontally.

Example 4.85

Add by converting the mixed numbers to improper fractions: 3 7 8 + 4 3 8 . 3 7 8 + 4 3 8 .

Since the problem was given in mixed number form, we will write the sum as a mixed number.

Try It 4.169

Find the sum by converting the mixed numbers to improper fractions:

5 5 9 + 3 7 9 . 5 5 9 + 3 7 9 .

Try It 4.170

3 7 10 + 2 9 10 . 3 7 10 + 2 9 10 .

Table 4.2 compares the two methods of addition, using the expression 3 2 5 + 6 4 5 3 2 5 + 6 4 5 as an example. Which way do you prefer?

Model Subtraction of Mixed Numbers

Let’s think of pizzas again to model subtraction of mixed numbers with a common denominator. Suppose you just baked a whole pizza and want to give your brother half of the pizza. What do you have to do to the pizza to give him half? You have to cut it into at least two pieces. Then you can give him half.

We will use fraction circles (pizzas!) to help us visualize the process.

Start with one whole.

Algebraically, you would write:

Example 4.86

Use a model to subtract: 1 − 1 3 . 1 − 1 3 .

Try It 4.171

Use a model to subtract: 1 − 1 4 . 1 − 1 4 .

Try It 4.172

Use a model to subtract: 1 − 1 5 . 1 − 1 5 .

What if we start with more than one whole? Let’s find out.

Example 4.87

Use a model to subtract: 2 − 3 4 . 2 − 3 4 .

Try It 4.173

Use a model to subtract: 2 − 1 5 . 2 − 1 5 .

Try It 4.174

Use a model to subtract: 2 − 1 3 . 2 − 1 3 .

In the next example, we’ll subtract more than one whole.

Example 4.88

Use a model to subtract: 2 − 1 2 5 . 2 − 1 2 5 .

Try It 4.175

Use a model to subtract: 2 − 1 1 3 . 2 − 1 1 3 .

Try It 4.176

Use a model to subtract: 2 − 1 1 4 . 2 − 1 1 4 .

What if you start with a mixed number and need to subtract a fraction? Think about this situation: You need to put three quarters in a parking meter, but you have only a $1 $1 bill and one quarter. What could you do? You could change the dollar bill into 4 4 quarters. The value of 4 4 quarters is the same as one dollar bill, but the 4 4 quarters are more useful for the parking meter. Now, instead of having a $1 $1 bill and one quarter, you have 5 5 quarters and can put 3 3 quarters in the meter.

This models what happens when we subtract a fraction from a mixed number. We subtracted three quarters from one dollar and one quarter.

We can also model this using fraction circles, much like we did for addition of mixed numbers.

Example 4.89

Use a model to subtract: 1 1 4 − 3 4 1 1 4 − 3 4

Try It 4.177

Use a model to subtract. Draw a picture to illustrate your model.

1 1 3 − 2 3 1 1 3 − 2 3

Try It 4.178

1 1 5 − 4 5 1 1 5 − 4 5

Subtract Mixed Numbers with a Common Denominator

Now we will subtract mixed numbers without using a model. But it may help to picture the model in your mind as you read the steps.

• Step 1. Rewrite the problem in vertical form.
• If the top fraction is larger than the bottom fraction, go to Step 3.
• If not, in the top mixed number, take one whole and add it to the fraction part, making a mixed number with an improper fraction.
• Step 3. Subtract the fractions.
• Step 4. Subtract the whole numbers.
• Step 5. Simplify, if possible.

Example 4.90

Find the difference: 5 3 5 − 2 4 5 . 5 3 5 − 2 4 5 .

Since the problem was given with mixed numbers, we leave the result as mixed numbers.

Try It 4.179

Find the difference: 6 4 9 − 3 7 9 . 6 4 9 − 3 7 9 .

Try It 4.180

Find the difference: 4 4 7 − 2 6 7 . 4 4 7 − 2 6 7 .

Just as we did with addition, we could subtract mixed numbers by converting them first to improper fractions. We should write the answer in the form it was given, so if we are given mixed numbers to subtract we will write the answer as a mixed number .

Subtract mixed numbers with common denominators as improper fractions.

Step 1. Rewrite the mixed numbers as improper fractions.

Step 2. Subtract the numerators.

Step 3. Write the answer as a mixed number, simplifying the fraction part, if possible.

Example 4.91

Find the difference by converting to improper fractions:

9 6 11 − 7 10 11 . 9 6 11 − 7 10 11 .

Try It 4.181

Find the difference by converting the mixed numbers to improper fractions:

6 4 9 − 3 7 9 . 6 4 9 − 3 7 9 .

Try It 4.182

4 4 7 − 2 6 7 . 4 4 7 − 2 6 7 .

Add and Subtract Mixed Numbers with Different Denominators

To add or subtract mixed numbers with different denominators, we first convert the fractions to equivalent fractions with the LCD. Then we can follow all the steps we used above for adding or subtracting fractions with like denominators.

Example 4.92

Add: 2 1 2 + 5 2 3 . 2 1 2 + 5 2 3 .

Since the denominators are different, we rewrite the fractions as equivalent fractions with the LCD, 6 . 6 . Then we will add and simplify.

We write the answer as a mixed number because we were given mixed numbers in the problem.

Try It 4.183

Add: 1 5 6 + 4 3 4 . 1 5 6 + 4 3 4 .

Try It 4.184

Add: 3 4 5 + 8 1 2 . 3 4 5 + 8 1 2 .

Example 4.93

Subtract: 4 3 4 − 2 7 8 . 4 3 4 − 2 7 8 .

Since the denominators of the fractions are different, we will rewrite them as equivalent fractions with the LCD 8 . 8 . Once in that form, we will subtract. But we will need to borrow 1 1 first.

We were given mixed numbers, so we leave the answer as a mixed number.

Try It 4.185

Find the difference: 8 1 2 − 3 4 5 . 8 1 2 − 3 4 5 .

Try It 4.186

Find the difference: 4 3 4 − 1 5 6 . 4 3 4 − 1 5 6 .

Example 4.94

Subtract: 3 5 11 − 4 3 4 . 3 5 11 − 4 3 4 .

We can see the answer will be negative since we are subtracting 4 4 from 3 . 3 . Generally, when we know the answer will be negative it is easier to subtract with improper fractions rather than mixed numbers.

Try It 4.187

Subtract: 1 3 4 − 6 7 8 . 1 3 4 − 6 7 8 .

Try It 4.188

Subtract: 10 3 7 − 22 4 9 . 10 3 7 − 22 4 9 .

ACCESS ADDITIONAL ONLINE RESOURCES

• Adding Mixed Numbers
• Subtracting Mixed Numbers

Section 4.6 Exercises

Practice makes perfect.

Model Addition of Mixed Numbers

In the following exercises, use a model to find the sum. Draw a picture to illustrate your model.

1 1 5 + 3 1 5 1 1 5 + 3 1 5

2 1 3 + 1 1 3 2 1 3 + 1 1 3

1 3 8 + 1 7 8 1 3 8 + 1 7 8

1 5 6 + 1 5 6 1 5 6 + 1 5 6

Add Mixed Numbers with a Common Denominator

In the following exercises, add.

5 1 3 + 6 1 3 5 1 3 + 6 1 3

2 4 9 + 5 1 9 2 4 9 + 5 1 9

4 5 8 + 9 3 8 4 5 8 + 9 3 8

7 9 10 + 3 1 10 7 9 10 + 3 1 10

3 4 5 + 6 4 5 3 4 5 + 6 4 5

9 2 3 + 1 2 3 9 2 3 + 1 2 3

6 9 10 + 8 3 10 6 9 10 + 8 3 10

8 4 9 + 2 8 9 8 4 9 + 2 8 9

In the following exercises, use a model to find the difference. Draw a picture to illustrate your model.

1 1 6 − 5 6 1 1 6 − 5 6

1 1 8 − 5 8 1 1 8 − 5 8

In the following exercises, find the difference.

2 7 8 − 1 3 8 2 7 8 − 1 3 8

2 7 12 − 1 5 12 2 7 12 − 1 5 12

8 17 20 − 4 9 20 8 17 20 − 4 9 20

19 13 15 − 13 7 15 19 13 15 − 13 7 15

8 3 7 − 4 4 7 8 3 7 − 4 4 7

5 2 9 − 3 4 9 5 2 9 − 3 4 9

2 5 8 − 1 7 8 2 5 8 − 1 7 8

2 5 12 − 1 7 12 2 5 12 − 1 7 12

In the following exercises, write the sum or difference as a mixed number in simplified form.

3 1 4 + 6 1 3 3 1 4 + 6 1 3

2 1 6 + 5 3 4 2 1 6 + 5 3 4

1 5 8 + 4 1 2 1 5 8 + 4 1 2

7 2 3 + 8 1 2 7 2 3 + 8 1 2

9 7 10 − 2 1 3 9 7 10 − 2 1 3

6 4 5 − 1 1 4 6 4 5 − 1 1 4

2 2 3 − 3 1 2 2 2 3 − 3 1 2

2 7 8 − 4 1 3 2 7 8 − 4 1 3

Mixed Practice

In the following exercises, perform the indicated operation and write the result as a mixed number in simplified form.

2 5 8 · 1 3 4 2 5 8 · 1 3 4

1 2 3 · 4 1 6 1 2 3 · 4 1 6

2 7 + 4 7 2 7 + 4 7

2 9 + 5 9 2 9 + 5 9

1 5 12 ÷ 1 12 1 5 12 ÷ 1 12

2 3 10 ÷ 1 10 2 3 10 ÷ 1 10

13 5 12 − 9 7 12 13 5 12 − 9 7 12

15 5 8 − 6 7 8 15 5 8 − 6 7 8

5 9 − 4 9 5 9 − 4 9

11 15 − 7 15 11 15 − 7 15

4 − 3 4 4 − 3 4

6 − 2 5 6 − 2 5

9 20 ÷ 3 4 9 20 ÷ 3 4

7 24 ÷ 14 3 7 24 ÷ 14 3

9 6 11 + 7 10 11 9 6 11 + 7 10 11

8 5 13 + 4 9 13 8 5 13 + 4 9 13

3 2 5 + 5 3 4 3 2 5 + 5 3 4

2 5 6 + 4 1 5 2 5 6 + 4 1 5

8 15 · 10 19 8 15 · 10 19

5 12 · 8 9 5 12 · 8 9

6 7 8 − 2 1 3 6 7 8 − 2 1 3

6 5 9 − 4 2 5 6 5 9 − 4 2 5

5 2 9 − 4 4 5 5 2 9 − 4 4 5

4 3 8 − 3 2 3 4 3 8 − 3 2 3

Everyday Math

Sewing Renata is sewing matching shirts for her husband and son. According to the patterns she will use, she needs 2 3 8 2 3 8 yards of fabric for her husband’s shirt and 1 1 8 1 1 8 yards of fabric for her son’s shirt. How much fabric does she need to make both shirts?

Sewing Pauline has 3 1 4 3 1 4 yards of fabric to make a jacket. The jacket uses 2 2 3 2 2 3 yards. How much fabric will she have left after making the jacket?

Printing Nishant is printing invitations on his computer. The paper is 8 1 2 8 1 2 inches wide, and he sets the print area to have a 1 1 2 1 1 2 -inch border on each side. How wide is the print area on the sheet of paper?

Framing a picture Tessa bought a picture frame for her son’s graduation picture. The picture is 8 8 inches wide. The picture frame is 2 5 8 2 5 8 inches wide on each side. How wide will the framed picture be?

Writing Exercises

Draw a diagram and use it to explain how to add 1 5 8 + 2 7 8 . 1 5 8 + 2 7 8 .

Edgar will have to pay $3.75 $3.75 in tolls to drive to the city.

ⓐ Explain how he can make change from a $10 $10 bill before he leaves so that he has the exact amount he needs.

ⓑ How is Edgar’s situation similar to how you subtract 10 − 3 3 4 ? 10 − 3 3 4 ?

Add 4 5 12 + 3 7 8 4 5 12 + 3 7 8 twice, first by leaving them as mixed numbers and then by rewriting as improper fractions. Which method do you prefer, and why?

Subtract 3 7 8 − 4 5 12 3 7 8 − 4 5 12 twice, first by leaving them as mixed numbers and then by rewriting as improper fractions. Which method do you prefer, and why?

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ After reviewing this checklist, what will you do to become confident for all objectives?

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Access for free at https://openstax.org/books/prealgebra/pages/1-introduction

• Authors: Lynn Marecek, MaryAnne Anthony-Smith
• Publisher/website: OpenStax
• Book title: Prealgebra
• Publication date: Sep 25, 2015
• Location: Houston, Texas
• Book URL: https://openstax.org/books/prealgebra/pages/1-introduction
• Section URL: https://openstax.org/books/prealgebra/pages/4-6-add-and-subtract-mixed-numbers

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• Inspiration

Mixed Number – Definition, Example, Facts

What are mixed numbers, parts of a mixed number, properties of mixed numbers , adding mixed numbers .

• Real Life Examples

A mixed number is a whole number , and a proper fraction represented together.  It generally represents a number between any two whole numbers. 

Look at the given image, it represents a fraction that is greater than 1 but less than 2. It is thus, a mixed number. 

Some other examples of mixed numbers are

Recommended Games

A mixed number is formed by combining three parts: a whole number , a numerator , and a denominator . The numerator and denominator are part of the proper fraction that makes the mixed number.

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• It is partly a whole number.  
• It is partly a fraction.

Converting improper fractions to mixed fractions.

Step 1 : Divide the numerator by the denominator.

Step 2 : Write down the quotient as the whole number.

Step 3 : Write down the remainder as the numerator and the divisor as the denominator.

For example, we follow the given steps to convert 7/3 into a mixed number form .

Step 1 : Divide 7 by 3

Step 2 : Write quotient, divisor and remainder in form as in step 2 and step 3 above.

One can add mixed numbers by rearranging the whole numbers, adding them separately and adding the leftover fractions individually and in the end combing them all.  

1  1 ⁄ 2  + 3  3 ⁄ 4  

Adding the whole numbers separately and the fractions separately. 

For whole numbers:

For fractions:  Find the LCM and then add

In the end, adding both the parts together. 

4+1  1 ⁄ 4  =5  1 ⁄ 4  

Real Life Examples of Mixed Numbers

We can check our understanding of mixed fractions by expressing the parts of a whole as mixed fractions while serving a pizza or a pie at home. Leftover pizzas, half-filled glasses of milk form examples of mixed fractions.

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