subtracting decimals problem solving

Decimal Word Problems (Mixed Operations) Worksheet and Solutions

Decimal Word Problems Worksheets: 1-Step Word Problems, Add, Subtract 2-Step Word Problems, Add, Subtract Decimal Word Problems (Mixed Op) Decimal Word Problems (Mixed Op)

Objective: I can solve word problems involving addition, subtraction, multiplication and division of decimals.

Printable “Decimal Word Problems” Worksheets

Decimal Word Problems Worksheet #1 Decimal Word Problems Worksheet #2 Decimal Word Problems Worksheet #3 Decimal Word Problems Worksheet #4

Online “Decimal Word Problems” Worksheets

Solve the following word problems. Julia cut a string 8.46 m long into 6 equal pieces. What is the length of each piece of string? m The mass of a jar of sweets is 1.4 kg. What is the total mass of 7 such jars of sweets? kg The watermelon bought by Peter is 3 times as heavy as the papaya bought by Paul. If the watermelon bought by Peter has a mass of 4.2 kg, what is the mass of the papaya? kg There is 0.625 kg of powdered milk in each tin. If a carton contains 12 tins, find the total mass of powdered milk in the carton. kg Marcus bought 8.6 kg of sugar. He poured the sugar equally into 5 bottles. There was 0.35 kg of sugar left over. What was the mass of sugar in 1 bottle? kg

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Subtracting Decimals Word Problems Worksheets

• Pre-Algebra >
• Decimals >
• Subtraction >

Be streets ahead of your peers with our worksheets on subtracting decimals word problems, replete with realistic scenarios where decimal subtraction is center stage! Children are expected to read each problem and find the difference between the decimals. Chances are the budding mathematicians have already perfected the skill of subtracting decimals, so invite them to demonstrate their problem-solving skills in these printable tools and to impress by finding quick solutions to situations featuring weight, height, money, distance, and more. Our word problems on decimal subtraction are available in both customary and metric units. Begin your journey with our free worksheet.

We suggest these pdf worksheets for the 4th grade, 5th grade, and 6th grade students.

Related Printable Worksheets

▶ Subtracting Decimals with Tenths

▶ Subtracting Decimals with Hundredths

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Add and subtract with the algorithm

Adding and subtracting decimals

Here we will learn about adding and subtracting decimals, including calculations with two or more decimals, or with a mixture of decimals and whole numbers.

Students will first learn about adding and subtracting decimals as part of number and operations in base ten in 5th grade.

What is adding and subtracting decimals?

Adding and subtracting decimals involves the addition and subtraction of decimal numbers by understanding place value.

When adding or subtracting with decimals special care must be taken to ensure that the decimal points line up with each other. This means that each place value should also line up.

For example, let’s look at 12.5 + 6.23.

Decimal numbers are used in real life particularly when using measurements such as money, length, mass, and capacity. Therefore you may find the skill of adding and subtracting decimals useful when you are problem solving or answering word problems in a real-world context.

On this page, we will be focusing on using the standard algorithm to add or subtract decimals to the thousandths place. No calculations will involve negative numbers or recurring decimals. For information on calculating with negative numbers and different types of decimal numbers, you can follow these links.

See also: Adding and subtracting negative numbers

See also: Recurring decimals

Common Core State Standards

How does this relate to 5th grade math and 6th grade math?

• 5th grade – Numbers and Operations in Base Ten (5.NBT.7) Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used
• 6th grade – The Number System (6.NS.3) Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

How to add and subtract decimals

In order to add or subtract decimals:

• Make sure each number has a decimal point and write any \bf{0} placeholders that are required.

Stack the numbers, ensuring that the decimal points line up.

Use the standard algorithm for addition/subtraction, ensuring the decimal point is also written in the answer.

[FREE] Adding And Subtracting Decimals Worksheets (Grade 5 and 6)

Use this worksheet to check your grade 5 and 6 students’ understanding of adding and subtracting decimals . 15 questions with answers to identify areas of strength and support!

Adding and subtracting decimals examples

Example 1: adding two decimals using the standard algorithm with no regrouping.

Calculate 12.3 + 4.5.

Make sure each number has a decimal point and write any 0 placeholders that are required.

Each number has a decimal point and one decimal place, so no zero placeholders are required.

2 Stack the numbers, ensuring that the decimal points line up.

3 Use the standard algorithm for addition/subtraction, ensuring the decimal point is also written in the answer.

Adding the digits in each place value from right to left, we have

Note that the decimal point is placed in the same column in the solution.

So 12.3 + 4.5 = 16.8.

Example 2: adding a whole number and a decimal using the standard algorithm with no regrouping

Calculate 52 + 31.07.

The decimal number contains two decimal places, so we need to write 52 with a decimal point and two 0 placeholders. So, we write 52.00.

So 52 + 31.07 = 83.07.

Example 3: adding two decimals using the standard algorithm with regrouping

Calculate 6.7 + 9.31.

The first number contains one decimal place whereas the second number contains two decimal places, so we need to write a 0 placeholder on the first number. We will therefore write 6.70.

As 7 + 3 = 10, the 1 digit from the number 10 is placed above the ones place, not above the decimal point.

As 6 + 9 + 1 (which we carried over) = 16, we need to carry over the new 1 digit to the tens place and write this below the solution line.

So 6.7 + 9.31 = 16.01.

Example 4: subtracting two decimals using the standard algorithm with no regrouping

Calculate 26.87-14.2.

The two numbers in the question have a different number of decimal places and so we need to write a 0 placeholder on the second number. We will therefore write 14.20.

We subtract the digits in each place value going from right to left, ensuring the digit underneath is subtracted from the digit above.

So 26.87-14.2 = 12.67.

Example 5: subtracting a decimal from a whole number using the standard algorithm with regrouping

Calculate 16-9.4.

The first number is a whole number and the second number contains one decimal place, so we need to write a decimal point and a 0 placeholder on the first number. We will therefore write 16.0.

As the digit below is larger than the digit above in the tenths place, we first need to borrow “1” from the ones place (leaving us with “5” in this place value) for “10” in the tenths place (giving us “10” in this place value).

This means that we need to calculate 10-4, which is equal to 6.

As the digit below is larger than the digit above in the ones place, we need to regroup again. This time we borrow “1” from the tens place (leaving us with “0” in this place) for “10” in the ones place (giving us “15” in this place).

So 16-9.4 = 6.6.

Example 6: subtracting two decimals using the standard algorithm with regrouping

Calculate 2.04-0.952.

The first number has two decimal places and the second number has three decimal places and so we need to write a 0 placeholder on the first number. We will therefore write 2.040.

As the digit below is larger than the digit above in the thousandths place, we first need to borrow “1” from the hundredths place (leaving us with “3” in this place) for “10” in the thousandths place (giving us “10” in this place).

This means that we need to calculate 10-2, which is equal to 8.

As the digit below is larger than the digit above in the hundredths place, we need to use the process of regrouping again. However, we have an issue because the tenths place contains a 0. This means that we need to borrow twice.

First we borrow “1” from the ones place (leaving us with “1” in this place) for “10” in the tenths place (giving us “10” in this place).

Then we borrow “1” from the tenths place (leaving us with “9” in this place) for “10” in the hundredths place (giving us “13” in this place).

We can now calculate 13-5.

So 2.04-0.952 = 1.088.

Teaching tips for adding and subtracting decimals

• Review place values before beginning to add or subtract decimals, especially decimal place values. Not only will students need to line up the decimal point, but they also need to ensure that each place value is lined up, so their understanding of place values is vital.
• Students may struggle to line up the digits when stacking the numbers, so it may help to provide them with graph paper so they may write the numbers into boxes and keep them aligned. This will also help students see what place values are “missing” a number, and they can add in a zero placeholder into that box.
• Provide students with opportunities to solve real-world word problems involving adding or subtracting decimals, such as money or measurement. This will help them better understand the problems and what the numbers represent in a real-life context.

Easy mistakes to make

• Lining up decimal numbers in each place value incorrectly When using the standard algorithm for addition of decimals or subtraction of decimals, students can sometimes line up the numbers incorrectly. This is because younger students are sometimes told to line up the numbers from the right side, but this method only works for whole numbers. When stacking the decimal numbers, you must line up the decimal points. This will ensure that the digits are in the correct column according to their place value. Using zero placeholders can also help you to avoid making this mistake.

Related lessons on decimals

• Dividing decimals
• Multiplying decimals
• Multiplying and dividing decimals
• Adding decimals
• Decimal places
• Decimal number line
• Decimal place value
• Subtracting decimals
• Comparing decimals

Practice adding and subtracting decimals questions

1. Solve 58.1 + 0.46.

2. Solve 41.3 + 38.

3. Solve 10.62 + 7.73.

4. Solve 16.9-3.3.

5. Solve 27-1.24.

6. Solve 7.11-6.84.

Adding and subtracting decimals word problems

1. This table shows the 4 most recent world records for the men’s 100 meter race.

Usain Bolt holds the current world record for the men’s 100 meter race at 9.58 seconds.

How many seconds did he shave off the previous world record holder’s time?

9.74-9.58 = 0.16 seconds

2. Abi, Bobby and Cyrus each have some money.

They want to buy a ball from a local shop costing \$3.60 to play catch with.

They decide to put their money together in order to buy the ball.

Abi has \$2.30.

Bobby has \$1.25.

Cyrus has 9 cents.

If they buy the ball, how much change will they get?

Change is \$0.04 or 4 cents.

3. Ali is harvesting potatoes. He weighs and measures the length of a sample of 10 potatoes. Below is a table showing his results.

(a) Find the difference between the longest potato and the shortest potato in the sample.

(b) What is the total weight of the 3 longest potatoes?

(a) Longest – shortest = 6.1-2.98 = 3.12 \, cm

(b) Potatoes 1, 2, and 4\text{: } 36.1 + 60.8 + 27.7 = 124.6 \, g

Adding and subtracting decimals FAQs

The first step is to stack the numbers, lining up the numbers according to place value and lining up the decimal points.

To add or subtract decimals that do not have the same number of digits in the decimal places, you can use zeros as placeholders and then begin to solve.

In the answer, the decimal point should line up with the decimal points in the numbers you are adding or subtracting. It may be helpful to place the decimal point in the answer space first before beginning to solve.

The next lessons are

• Converting fractions, decimals, and percentages
• Algebraic expression
• Math equations

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Decimals Worksheets

Thanks for visiting the Decimals Worksheets page at Math-Drills.Com where we make a POINT of helping students learn. On this page, you will find Decimals worksheets on a variety of topics including comparing and sorting decimals, adding, subtracting, multiplying and dividing decimals, and converting decimals to other number formats. To start, you will find the general use printables to be helpful in teaching the concepts of decimals and place value. More information on them is included just under the sub-title.

Further down the page, rounding, comparing and ordering decimals worksheets allow students to gain more comfort with decimals before they move on to performing operations with decimals. There are many operations with decimals worksheets throughout the page. It would be a really good idea for students to have a strong knowledge of addition, subtraction, multiplication and division before attempting these questions.

Most Popular Decimals Worksheets this Week

Grids and Charts Useful for Learning Decimals

General use decimal printables are used in a variety of contexts and assist students in completing math questions related to decimals.

The thousandths grid is a useful tool in representing decimals. Each small rectangle represents a thousandth. Each square represents a hundredth. Each row or column represents a tenth. The entire grid represents one whole. The hundredths grid can be used to model percents or decimals. The decimal place value chart is a tool used with students who are first learning place value related to decimals or for those students who have difficulty with place value when working with decimals.

• Thousandths and Hundredths Grids Thousandths Grid Hundredths Grids ( 4 on a page) Hundredths Grids ( 9 on a page) Hundredths Grids ( 20 on a page)
• Decimal Place Value Charts Decimal Place Value Chart ( Ones to Hundredths ) Decimal Place Value Chart ( Ones to Thousandths ) Decimal Place Value Chart ( Hundreds to Hundredths ) Decimal Place Value Chart ( Thousands to Thousandths ) Decimal Place Value Chart ( Hundred Thousands to Thousandths ) Decimal Place Value Chart ( Hundred Millions to Millionths )

Decimals in Expanded Form

For students who have difficulty with expanded form, try familiarizing them with the decimal place value chart, and allow them to use it when converting standard form numbers to expanded form. There are actually five ways (two more than with integers) to write expanded form for decimals, and which one you use depends on your application or preference. Here is a quick summary of the various ways using the decimal number 1.23. 1. Expanded Form using decimals: 1 + 0.2 + 0.03 2. Expanded Form using fractions: 1 + 2 ⁄ 10 + 3 ⁄ 100 3. Expanded Factors Form using decimals: (1 × 1) + (2 × 0.1) + (3 × 0.01) 4. Expanded Factors Form using fractions: (1 × 1) + (2 × 1 ⁄ 10 ) + (3 × 1 ⁄ 100 ) 5. Expanded Exponential Form: (1 × 10 0 ) + (2 × 10 -1 ) + (3 × 10 -2 )

• Converting Decimals from Standard Form to Expanded Form Using Decimals Converting Decimals from Standard to Expanded Form Using Decimals ( 3 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 4 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 5 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 6 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 7 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 8 Decimal Places) Converting Decimals from Standard to Expanded Form Using Decimals ( 9 Decimal Places)
• Converting Decimals from Standard Form to Expanded Form Using Fractions Converting Decimals from Standard to Expanded Form Using Fractions ( 3 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 4 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 5 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 6 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 7 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 8 Decimal Places) Converting Decimals from Standard to Expanded Form Using Fractions ( 9 Decimal Places)
• Converting Decimals from Standard Form to Expanded Factors Form Using Decimals Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 3 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 4 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 5 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 6 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 7 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 8 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Decimals ( 9 Decimal Places)
• Converting Decimals from Standard Form to Expanded Factors Form Using Fractions Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 3 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 4 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 5 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 6 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 7 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 8 Decimal Places) Converting Decimals from Standard to Expanded Factors Form Using Fractions ( 9 Decimal Places)
• Converting Decimals from Standard Form to Expanded Exponential Form Converting Decimals from Standard to Expanded Exponential Form ( 3 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 4 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 5 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 6 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 7 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 8 Decimal Places) Converting Decimals from Standard to Expanded Exponential Form ( 9 Decimal Places)
• Retro Converting Decimals from Standard Form to Expanded Form Retro Standard to Expanded Form (3 digits before decimal; 2 after) Retro Standard to Expanded Form (4 digits before decimal; 3 after) Retro Standard to Expanded Form (6 digits before decimal; 4 after) Retro Standard to Expanded Form (12 digits before decimal; 3 after)
• Retro European Format Converting Decimals from Standard Form to Expanded Form Standard to Expanded Form (3 digits before decimal; 2 after) Standard to Expanded Form (4 digits before decimal; 3 after) Standard to Expanded Form (6 digits before decimal; 4 after)

Of course, being able to convert numbers already in expanded form to standard form is also important. All five versions of decimal expanded form are included in these worksheets.

• Converting Decimals to Standard Form from Expanded Form Using Decimals Converting Decimals from Expanded Form Using Decimals to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Form Using Decimals to Standard Form ( 9 Decimal Places)
• Converting Decimals to Standard Form from Expanded Form Using Fractions Converting Decimals from Expanded Form Using Fractions to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Form Using Fractions to Standard Form ( 9 Decimal Places)
• Converting Decimals to Standard Form from Expanded Factors Form Using Decimals Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Factors Form Using Decimals to Standard Form ( 9 Decimal Places)
• Converting Decimals to Standard Form from Expanded Factors Form Using Fractions Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Factors Form Using Fractions to Standard Form ( 9 Decimal Places)
• Converting Decimals to Standard Form from Expanded Exponential Form Converting Decimals from Expanded Exponential Form to Standard Form ( 3 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 4 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 5 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 6 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 7 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 8 Decimal Places) Converting Decimals from Expanded Exponential Form to Standard Form ( 9 Decimal Places)
• Retro Converting Decimals to Standard Form from Expanded Form Retro Expanded to Standard Form (3 digits before decimal; 2 after) Retro Expanded to Standard Form (4 digits before decimal; 3 after) Retro Expanded to Standard Form (6 digits before decimal; 4 after) Retro Expanded to Standard Form (12 digits before decimal; 3 after)
• Retro European Format Converting Decimals to Standard Form from Expanded Form Retro European Format Expanded to Standard Form (3 digits before decimal; 2 after) Retro European Format Expanded to Standard Form (4 digits before decimal; 3 after) Retro European Format Expanded to Standard Form (6 digits before decimal; 4 after)

Rounding Decimals Worksheets

Rounding decimals is similar to rounding whole numbers; you have to know your place value! When learning about rounding, it is also useful to learn about truncating since it may help students to round properly. A simple strategy for rounding involves truncating, using the digits after the truncation to determine whether the new terminating digit remains the same or gets incremented, then taking action by incrementing if necessary and throwing away the rest. Here is a simple example: Round 4.567 to the nearest tenth. First, truncate the number after the tenths place 4.5|67. Next, look at the truncated part (67). Is it more than half way to 99 (i.e. 50 or more)? It is, so the decision will be to increment. Lastly, increment the tenths value by 1 to get 4.6. Of course, the situation gets a little more complicated if the terminating digit is a 9. In that case, some regrouping might be necessary. For example: Round 6.959 to the nearest tenth. Truncate: 6.9|59. Decide to increment since 59 is more than half way to 99. Incrementing results in the necessity to regroup the tenths into an extra one whole, so the result is 7.0. Watch that students do not write 6.10. You will want to correct them right away in that case. One last note: if there are three truncated digits then the question becomes is the number more than half way to 999. Likewise, for one digit; is the number more than half way to 9. And so on...

We should also mention that in some scientific and mathematical "circles," rounding is slightly different "on a 5". For example, most people would round up on a 5 such as: 6.5 --> 7; 3.555 --> 3.56; 0.60500 --> 0.61; etc. A different way to round on a 5, however, is to round to the nearest even number, so 5.5 would be rounded up to 6, but 8.5 would be rounded down to 8. The main reason for this is not to skew the results of a large number of rounding events. If you always round up on a 5, on average, you will have slightly higher results than you should. Because most pre-college students round up on a 5, that is what we have done in the worksheets that follow.

• Rounding Decimals to Whole Numbers Round Tenths to a Whole Number Round Hundredths to a Whole Number Round Thousandths to a Whole Number Round Ten Thousandths to a Whole Number Round Various Decimals to a Whole Number
• Rounding Decimals to Tenths Round Hundredths to Tenths Round Thousandths to Tenths Round Ten Thousandths to Tenths Round Various Decimals to Tenths
• Rounding Decimals to Hundredths Round Thousandths to Hundredths Round Ten Thousandths to Hundredths Round Various Decimals to Hundredths
• Rounding Decimals to Thousandths Round Ten Thousandths to Thousandths
• Rounding Decimals to Various Decimal Places Round Hundredths to Various Decimal Places Round Thousandths to Various Decimal Places Round Ten Thousandths to Various Decimal Places Round Various Decimals to Various Decimal Places
• European Format Rounding Decimals to Whole Numbers European Format Round Tenths to a Whole Number European Format Round Hundredths to a Whole Number European Format Round Thousandths to a Whole Number European Format Round Ten Thousandths to Whole Number
• European Format Rounding Decimals to Tenths European Format Round Hundredths to Tenths European Format Round Thousandths to Tenths European Format Round Ten Thousandths to Tenths
• European Format Rounding Decimals to Hundredths European Format Round Thousandths to Hundredths European Format Round Ten Thousandths to Hundredths
• European Format Rounding Decimals to Thousandths European Format Round Ten Thousandths to Thousandths

Comparing and Ordering/Sorting Decimals Worksheets.

The comparing decimals worksheets have students compare pairs of numbers and the ordering decimals worksheets have students compare a list of numbers by sorting them.

Students who have mastered comparing whole numbers should find comparing decimals to be fairly easy. The easiest strategy is to compare the numbers before the decimal (the whole number part) first and only compare the decimal parts if the whole number parts are equal. These sorts of questions allow teachers/parents to get a good idea of whether students have grasped the concept of decimals or not. For example, if a student thinks that 4.93 is greater than 8.7, then they might need a little more instruction in place value. Close numbers means that some care was taken to make the numbers look similar. For example, they could be close in value, e.g. 3.3. and 3.4 or one of the digits might be changed as in 5.86 and 6.86.

• Comparing Decimals up to Tenths Comparing Decimals up to Tenths ( Both Numbers Random ) Comparing Decimals up to Tenths ( One Digit Differs ) Comparing Decimals up to Tenths ( Both Numbers Close in Value ) Comparing Decimals up to Tenths ( Various Tricks )
• Comparing Decimals up to Hundredths Comparing Decimals up to Hundredths ( Both Numbers Random ) Comparing Decimals up to Hundredths ( One Digit Differs ) Comparing Decimals up to Hundredths ( Two Digits Swapped ) Comparing Decimals up to Hundredths ( Both Numbers Close in Value ) Comparing Decimals up to Hundredths ( One Number has an Extra Digit ) Comparing Decimals up to Hundredths ( Various Tricks )
• Comparing Decimals up to Thousandths Comparing Decimals up to Thousandths Comparing Decimals up to Thousandths ( One Digit Differs ) Comparing Decimals up to Thousandths ( Two Digits Swapped ) Comparing Decimals up to Thousandths ( Both Numbers Close in Value ) Comparing Decimals up to Thousandths ( One Number has an Extra Digit ) Comparing Decimals up to Thousandths ( Various Tricks )
• Comparing Decimals up to Ten Thousandths Comparing Decimals up to Ten Thousandths Comparing Decimals up to Ten Thousandths ( One Digit Differs ) Comparing Decimals up to Ten Thousandths ( Two Digits Swapped ) Comparing Decimals up to Ten Thousandths ( Both Numbers Close in Value ) Comparing Decimals up to Ten Thousandths ( One Number has an Extra Digit ) Comparing Decimals up to Ten Thousandths ( Various Tricks )
• Comparing Decimals up to Hundred Thousandths Comparing Decimals up to Hundred Thousandths Comparing Decimals up to Hundred Thousandths ( One Digit Differs ) Comparing Decimals up to Hundred Thousandths ( Two Digits Swapped ) Comparing Decimals up to Hundred Thousandths ( Both Numbers Close in Value ) Comparing Decimals up to Hundred Thousandths ( One Number has an Extra Digit ) Comparing Decimals up to Hundred Thousandths ( Various Tricks )
• European Format Comparing Decimals European Format Comparing Decimals up to Tenths European Format Comparing Decimals up to Tenths (tight) European Format Comparing Decimals up to Hundredths European Format Comparing Decimals up to Hundredths (tight) European Format Comparing Decimals up to Thousandths European Format Comparing Decimals up to Thousandths (tight)

Ordering decimals is very much like comparing decimals except there are more than two numbers. Generally, students determine the least (or greatest) decimal to start, cross it off the list then repeat the process to find the next lowest/greatest until they get to the last number. Checking the list at the end is always a good idea.

• Ordering/Sorting Decimals Ordering/Sorting Decimal Hundredths Ordering/Sorting Decimal Thousandths
• European Format Ordering/Sorting Decimals European Format Ordering/Sorting Decimal Tenths (8 per set) European Format Ordering/Sorting Decimal Hundredths (8 per set) European Format Ordering/Sorting Decimal Thousandths (8 per set) European Format Ordering/Sorting Decimal Ten Thousandths (8 per set) European Format Ordering/Sorting Decimals with Various Decimal Places(8 per set)

Converting Decimals to Fractions and Other Number Formats

There are many good reasons for converting decimals to other number formats. Dealing with a fraction in arithmetic is often easier than the equivalent decimal. Consider 0.333... which is equivalent to 1/3. Multiplying 300 by 0.333... is difficult, but multiplying 300 by 1/3 is super easy! Students should be familiar with some of the more common fraction/decimal conversions, so they can switch back and forth as needed.

• Converting Between Decimals and Fractions Converting Fractions to Terminating Decimals Converting Fractions to Terminating and Repeating Decimals Converting Terminating Decimals to Fractions Converting Terminating and Repeating Decimals to Fractions Converting Fractions to Hundredths
• Converting Between Decimals, Fraction, Percents and Ratios Converting Fractions to Decimals, Percents and Part-to-Part Ratios Converting Fractions to Decimals, Percents and Part-to-Whole Ratios Converting Decimals to Fractions, Percents and Part-to-Part Ratios Converting Decimals to Fractions, Percents and Part-to-Whole Ratios Converting Percents to Fractions, Decimals and Part-to-Part Ratios Converting Percents to Fractions, Decimals and Part-to-Whole Ratios Converting Part-to-Part Ratios to Fractions, Decimals and Percents Converting Part-to-Whole Ratios to Fractions, Decimals and Percents Converting Various Fractions, Decimals, Percents and Part-to-Part Ratios Converting Various Fractions, Decimals, Percents and Part-to-Whole Ratios Converting Various Fractions, Decimals, Percents and Part-to-Part Ratios with 7ths and 11ths Converting Various Fractions, Decimals, Percents and Part-to-Whole Ratios with 7ths and 11ths

Adding and Subtracting Decimals

Try the following mental addition strategy for decimals. Begin by ignoring the decimals in the addition question. Add the numbers as if they were whole numbers. For example, 3.25 + 4.98 could be viewed as 325 + 498 = 823. Use an estimate to decide where to place the decimal. In the example, 3.25 + 4.98 is approximately 3 + 5 = 8, so the decimal in the sum must go between the 8 and the 2 (i.e. 8.23)

• Adding Tenths Adding Decimal Tenths with 0 Before the Decimal (range 0.1 to 0.9) Adding Decimal Tenths with 1 Digit Before the Decimal (range 1.1 to 9.9) Adding Decimal Tenths with 2 Digits Before the Decimal (range 10.1 to 99.9)
• Adding Hundredths Adding Decimal Hundredths with 0 Before the Decimal (range 0.01 to 0.99) Adding Decimal Hundredths with 1 Digit Before the Decimal (range 1.01 to 9.99) Adding Decimal Hundredths with 2 Digits Before the Decimal (range 10.01 to 99.99)
• Adding Thousandths Adding Decimal Thousandths with 0 Before the Decimal (range 0.001 to 0.999) Adding Decimal Thousandths with 1 Digit Before the Decimal (range 1.001 to 9.999) Adding Decimal Thousandths with 2 Digits Before the Decimal (range 10.001 to 99.999)
• Adding Ten Thousandths Adding Decimal Ten Thousandths with 0 Before the Decimal (range 0.0001 to 0.9999) Adding Decimal Ten Thousandths with 1 Digit Before the Decimal (range 1.0001 to 9.9999) Adding Decimal Ten Thousandths with 2 Digits Before the Decimal (range 10.0001 to 99.9999)
• Adding Various Decimal Places Adding Various Decimal Places with 0 Before the Decimal Adding Various Decimal Places with 1 Digit Before the Decimal Adding Various Decimal Places with 2 Digits Before the Decimal Adding Various Decimal Places with Various Numbers of Digits Before the Decimal
• European Format Adding Decimals European Format Adding decimal tenths with 0 before the decimal (range 0,1 to 0,9) European Format Adding decimal tenths with 1 digit before the decimal (range 1,1 to 9,9) European Format Adding decimal hundredths with 0 before the decimal (range 0,01 to 0,99) European Format Adding decimal hundredths with 1 digit before the decimal (range 1,01 to 9,99) European Format Adding decimal thousandths with 0 before the decimal (range 0,001 to 0,999) European Format Adding decimal thousandths with 1 digit before the decimal (range 1,001 to 9,999) European Format Adding decimal ten thousandths with 0 before the decimal (range 0,0001 to 0,9999) European Format Adding decimal ten thousandths with 1 digit before the decimal (range 1,0001 to 9,9999) European Format Adding mixed decimals with Various Decimal Places European Format Adding mixed decimals with Various Decimal Places (1 to 9 before decimal)

Base ten blocks can be used for decimal subtraction. Just redefine the blocks, so the big block is a one, the flat is a tenth, the rod is a hundredth and the little cube is a thousandth. Model and subtract decimals using base ten blocks, so students can "see" how decimals really work.

• Subtracting Tenths Subtracting Decimal Tenths with No Integer Part Subtracting Decimal Tenths with an Integer Part in the Minuend Subtracting Decimal Tenths with an Integer Part in the Minuend and Subtrahend
• Subtracting Hundredths Subtracting Decimal Hundredths with No Integer Part Subtracting Decimal Hundredths with an Integer Part in the Minuend and Subtrahend Subtracting Decimal Hundredths with a Larger Integer Part in the Minuend
• Subtracting Thousandths Subtracting Decimal Thousandths with No Integer Part Subtracting Decimal Thousandths with an Integer Part in the Minuend and Subtrahend
• Subtracting Ten Thousandths Subtracting Decimal Ten Thousandths with No Integer Part Subtracting Decimal Ten Thousandths with an Integer Part in the Minuend and Subtrahend
• Subtracting Various Decimal Places Subtracting Various Decimals to Hundredths Subtracting Various Decimals to Thousandths Subtracting Various Decimals to Ten Thousandths
• European Format Subtracting Decimals European Format Decimal subtraction (range 0,1 to 0,9) European Format Decimal subtraction (range 1,1 to 9,9) European Format Decimal subtraction (range 0,01 to 0,99) European Format Decimal subtraction (range 1,01 to 9,99) European Format Decimal subtraction (range 0,001 to 0,999) European Format Decimal subtraction (range 1,001 to 9,999) European Format Decimal subtraction (range 0,0001 to 0,9999) European Format Decimal subtraction (range 1,0001 to 9,9999) European Format Decimal subtraction with Various Decimal Places European Format Decimal subtraction with Various Decimal Places (1 to 9 before decimal)

Adding and subtracting decimals is fairly straightforward when all the decimals are lined up. With the questions arranged horizontally, students are challenged to understand place value as it relates to decimals. A wonderful strategy for placing the decimal is to use estimation. For example if the question is 49.2 + 20.1, the answer without the decimal is 693. Estimate by rounding 49.2 to 50 and 20.1 to 20. 50 + 20 = 70. The decimal in 693 must be placed between the 9 and the 3 as in 69.3 to make the number close to the estimate of 70.

The above strategy will go a long way in students understanding operations with decimals, but it is also important that they have a strong foundation in place value and a proficiency with efficient strategies to be completely successful with these questions. As with any math skill, it is not wise to present this to students until they have the necessary prerequisite skills and knowledge.

• Horizontally Arranged Adding Decimals Adding Decimals to Tenths Horizontally Adding Decimals to Hundredths Horizontally Adding Decimals to Thousandths Horizontally Adding Decimals to Ten Thousandths Horizontally Adding Decimals Horizontally With Up to Two Places Before and After the Decimal Adding Decimals Horizontally With Up to Three Places Before and After the Decimal Adding Decimals Horizontally With Up to Four Places Before and After the Decimal
• Horizontally Arranged Subtracting Decimals Subtracting Decimals to Tenths Horizontally Subtracting Decimals to Hundredths Horizontally Subtracting Decimals to Thousandths Horizontally Subtracting Decimals to Ten Thousandths Horizontally Subtracting Decimals Horizontally With Up to Two Places Before and After the Decimal Subtracting Decimals Horizontally With Up to Three Places Before and After the Decimal Subtracting Decimals Horizontally With Up to Four Places Before and After the Decimal
• Horizontally Arranged Mixed Adding and Subtracting Decimals Adding and Subtracting Decimals to Tenths Horizontally Adding and Subtracting Decimals to Hundredths Horizontally Adding and Subtracting Decimals to Thousandths Horizontally Adding and Subtracting Decimals to Ten Thousandths Horizontally Adding and Subtracting Decimals Horizontally With Up to Two Places Before and After the Decimal Adding and Subtracting Decimals Horizontally With Up to Three Places Before and After the Decimal Adding and Subtracting Decimals Horizontally With Up to Four Places Before and After the Decimal

Multiplying and Dividing Decimals

Multiplying decimals by whole numbers is very much like multiplying whole numbers except there is a decimal to deal with. Although students might initially have trouble with it, through the power of rounding and estimating, they can generally get it quite quickly. Many teachers will tell students to ignore the decimal and multiply the numbers just like they would whole numbers. This is a good strategy to use. Figuring out where the decimal goes at the end can be accomplished by counting how many decimal places were in the original question and giving the answer that many decimal places. To better understand this method, students can round the two factors and multiply in their head to get an estimate then place the decimal based on their estimate. For example, multiplying 9.84 × 91, students could first round the numbers to 10 and 91 (keep 91 since multiplying by 10 is easy) then get an estimate of 910. Actually multiplying (ignoring the decimal) gets you 89544. To get that number close to 910, the decimal needs to go between the 5 and the 4, thus 895.44. Note that there are two decimal places in the factors and two decimal places in the answer, but estimating made it more understandable rather than just a method.

• Multiplying Decimals by 1-Digit Whole Numbers Multiply 2-digit tenths by 1-digit whole numbers Multiply 2-digit hundredths by 1-digit whole numbers Multiply 2-digit thousandths by 1-digit whole numbers Multiply 3-digit tenths by 1-digit whole numbers Multiply 3-digit hundredths by 1-digit whole numbers Multiply 3-digit thousandths by 1-digit whole numbers Multiply various decimals by 1-digit whole numbers
• Multiplying Decimals by 2-Digit Whole Numbers Multiplying 2-digit tenths by 2-digit whole numbers Multiplying 2-digit hundredths by 2-digit whole numbers Multiplying 3-digit tenths by 2-digit whole numbers Multiplying 3-digit hundredths by 2-digit whole numbers Multiplying 3-digit thousandths by 2-digit whole numbers Multiplying various decimals by 2-digit whole numbers
• Multiplying Decimals by Tenths Multiplying 2-digit whole by 2-digit tenths Multiplying 2-digit tenths by 2-digit tenths Multiplying 2-digit hundredths by 2-digit tenths Multiplying 3-digit whole by 2-digit tenths Multiplying 3-digit tenths by 2-digit tenths Multiplying 3-digit hundredths by 2-digit tenths Multiplying 3-digit thousandths by 2-digit tenths Multiplying various decimals by 2-digit tenths
• Multiplying Decimals by Hundredths Multiplying 2-digit whole by 2-digit hundredths Multiplying 2-digit tenths by 2-digit hundredths Multiplying 2-digit hundredths by 2-digit hundredths Multiplying 3-digit whole by 2-digit hundredths Multiplying 3-digit tenths by 2-digit hundredths Multiplying 3-digit hundredths by 2-digit hundredths Multiplying 3-digit thousandths by 2-digit hundredths Multiplying various decimals by 2-digit hundredths
• Multiplying Decimals by Various Decimal Places Multiplying 2-digit by 2-digit numbers with various decimal places Multiplying 3-digit by 2-digit numbers with various decimal places
• Decimal Long Multiplication in Various Ranges Decimal Multiplication (range 0.1 to 0.9) Decimal Multiplication (range 1.1 to 9.9) Decimal Multiplication (range 10.1 to 99.9) Decimal Multiplication (range 0.01 to 0.99) Decimal Multiplication (range 1.01 to 9.99) Decimal Multiplication (range 10.01 to 99.99) Random # Digits Random # Places
• European Format Multiplying Decimals by 2-Digit Whole Numbers European Format 2-digit whole × 2-digit hundredths European Format 2-digit tenths × 2-digit whole European Format 2-digit hundredths × 2-digit whole European Format 3-digit tenths × 2-digit whole European Format 3-digit hundredths × 2-digit whole European Format 3-digit thousandths × 2-digit whole
• European Format Multiplying Decimals by 2-Digit Tenths European Format 2-digit whole × 2-digit tenths European Format 2-digit tenths × 2-digit tenths European Format 2-digit hundredths × 2-digit tenths European Format 3-digit whole × 2-digit tenths European Format 3-digit tenths × 2-digit tenths European Format 3-digit hundredths × 2-digit tenths European Format 3-digit thousandths × 2-digit tenths
• European Format Multiplying Decimals by 2-Digit Hundredths European Format 2-digit tenths × 2-digit hundredths European Format 2-digit hundredths × 2-digit hundredths European Format 3-digit whole × 2-digit hundredths European Format 3-digit tenths × 2-digit hundredths European Format 3-digit hundredths × 2-digit hundredths European Format 3-digit thousandths × 2-digit hundredths
• European Format Multiplying Decimals by Various Decimal Places European Format 2-digit × 2-digit with various decimal places European Format 3-digit × 2-digit with various decimal places
• Dividing Decimals by Whole Numbers Divide Tenths by a Whole Number Divide Hundredths by a Whole Number Divide Thousandths by a Whole Number Divide Ten Thousandths by a Whole Number Divide Various Decimals by a Whole Number

In case you aren't familiar with dividing with a decimal divisor, the general method for completing questions is by getting rid of the decimal in the divisor. This is done by multiplying the divisor and the dividend by the same amount, usually a power of ten such as 10, 100 or 1000. For example, if the division question is 5.32/5.6, you would multiply the divisor and dividend by 10 to get the equivalent division problem, 53.2/56. Completing this division will result in the exact same quotient as the original (try it on your calculator if you don't believe us). The main reason for completing decimal division in this way is to get the decimal in the correct location when using the U.S. long division algorithm.

A much simpler strategy, in our opinion, is to initially ignore the decimals all together and use estimation to place the decimal in the quotient. In the same example as above, you would complete 532/56 = 95. If you "flexibly" round the original, you will get about 5/5 which is about 1, so the decimal in 95 must be placed to make 95 close to 1. In this case, you would place it just before the 9 to get 0.95. Combining this strategy with the one above can also help a great deal with more difficult questions. For example, 4.584184 ÷ 0.461 can first be converted the to equivalent: 4584.184 ÷ 461 (you can estimate the quotient to be around 10). Complete the division question without decimals: 4584184 ÷ 461 = 9944 then place the decimal, so that 9944 is about 10. This results in 9.944.

Dividing decimal numbers doesn't have to be too difficult, especially with the worksheets below where the decimals work out nicely. To make these worksheets, we randomly generated a divisor and a quotient first, then multiplied them together to get the dividend. Of course, you will see the quotients only on the answer page, but generating questions in this way makes every decimal division problem work out nicely.

• Decimal Long Division with Quotients That Work Out Nicely Dividing Decimals by Various Decimals with Various Sizes of Quotients Dividing Decimals by 1-Digit Tenths (e.g. 0.72 ÷ 0.8 = 0.9) Dividing Decimals by 1-Digit Tenths with Larger Quotients (e.g. 3.2 ÷ 0.5 = 6.4) Dividing Decimals by 2-Digit Tenths (e.g. 10.75 ÷ 2.5 = 4.3) Dividing Decimals by 2-Digit Tenths with Larger Quotients (e.g. 387.75 ÷ 4.7 = 82.5) Dividing Decimals by 3-Digit Tenths (e.g. 1349.46 ÷ 23.8 = 56.7) Dividing Decimals by 2-Digit Hundredths (e.g. 0.4368 ÷ 0.56 = 0.78) Dividing Decimals by 2-Digit Hundredths with Larger Quotients (e.g. 1.7277 ÷ 0.39 = 4.43) Dividing Decimals by 3-Digit Hundredths (e.g. 31.4863 ÷ 4.61 = 6.83) Dividing Decimals by 4-Digit Hundredths (e.g. 7628.1285 ÷ 99.91 = 76.35) Dividing Decimals by 3-Digit Thousandths (e.g. 0.076504 ÷ 0.292 = 0.262) Dividing Decimals by 3-Digit Thousandths with Larger Quotients (e.g. 2.875669 ÷ 0.551 = 5.219)

These worksheets would probably be used for estimating and calculator work.

• Horizontally Arranged Decimal Division Random # Digits Random # Places
• European Format Dividing Decimals with Quotients That Work Out Nicely European Format Divide Tenths by a Whole Number European Format Divide Hundredths by a Whole Number European Format Divide Thousandths by a Whole Number European Format Divide Ten Thousandths by a Whole Number European Format Divide Various Decimals by a Whole Number

In the next set of questions, the quotient does not always work out well and may have repeating decimals. The answer key shows a rounded quotient in these cases.

• European Format Dividing Decimals by Whole Numbers European Format Divide Tenths by a Whole Number European Format Divide Hundredths by a Whole Number European Format Divide Thousandths by a Whole Number European Format Divide Ten Thousandths by a Whole Number European Format Divide Various Decimals by a Whole Number
• European Format Dividing Decimals by Decimals European Format Decimal Tenth (0,1 to 9,9) Divided by Decimal Tenth (1,1 to 9,9) European Format Decimal Hundredth (0,01 to 9,99) Divided by Decimal Tenth (1,1 to 9,9) European Format Decimal Thousandth (0,001 to 9,999) Divided by Decimal Tenth (1,1 to 9,9) European Format Decimal Ten Thousandth (0,0001 to 9,9999) Divided by Decimal Tenth (1,1 to 9,9) European Format Various Decimal Places (0,1 to 9,9999) Divided by Decimal Tenth (1,1 to 9,9) European Format Various Decimal Places (0,1 to 9,9999) Divided by Various Decimal Places (1,1 to 9,9999)

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Decimal Worksheets Hub Page

Welcome to our Decimal Worksheets area.

On this page, there are links to all of our decimal math worksheets, including decimal place value, decimal money worksheets and our adding, subtracting, multiplying and dividing decimals pages.

We also have some decimal resources including decimal place value charts to support teaching and learning of decimals.

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• This page contains links to other Math webpages where you will find a range of activities and resources.
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Decimal Worksheets

On this page you will find link to our range of decimal math worksheets.

Quicklinks to...

• Decimal Place Value Charts

Decimal Place Value Worksheets

Rounding decimals.

• Couting in decimals

Decimal Addition

• Decimal Subtraction
• Decimal Multiplication
• Decimal Division

Converting Decimals

These decimal place value charts are designed to help children understand decimal place value.

They are especially useful in learning how to multiply and divide decimals by 10 or 100.

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Here you will find our selection of Place Value involving Decimals with up to 2 decimal places (2dp).

Using these sheets will help your child learn to:

• learn their place value with decimals up to 3dp;
• understand the value of each digit in a decimal number;
• learn to read and write numbers with up to 3dp.
• Decimal Place Value Worksheets to 2dp
• Decimal Place Value to 3dp
• Ordering Decimals Worksheets
• Decimal Number Line Worksheets
• Rounding to the nearest tenth
• Rounding Decimal Places Sheets to 2dp
• Rounding Decimals Worksheet Challenges

Decimal Counting Worksheets

Using these sheets will support you child to:

• count on and back by multiples of 0.1;
• fill in the missing numbers in sequences;
• finding number bonds to 1 with numbers to 1dp, 2dp or 3dp.
• Counting By Decimals
• Decimal Number Bonds to 1
• Decimal Money Column Addition 4th Grade
• Decimal Column Addition 5th Grade

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Decimal Subtraction Worksheets

• Money Subtraction Worksheets ($)
• Decimal Subtraction Worksheets (columns)

Decimal Multiplication Worksheets

These sheets are designed for 4th and 5th graders.

• Multiplying Decimals by 10 and 100
• Multiply and Divide by 10 100 (decimals)

These sheets are designed for 5th graders to develop mental multiplication skills.

• Multiplying Decimals by Whole Numbers
• Decimal Long Multiplication Worksheets to 1dp
• Decimal Long Multiplication Worksheets to 2dp

Decimal Division Worksheets

• Decimal Division Facts
• Long Division of Decimal Numbers
• Convert Fractions to Decimal Sheets
• Convert Decimal to Fraction Support
• Converting Decimals to Fractions Worksheets
• Fractions Decimals Percents Worksheets

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Decimals  - Adding and Subtracting Decimals

Decimals  -, adding and subtracting decimals, decimals adding and subtracting decimals.

Decimals: Adding and Subtracting Decimals

Lesson 2: adding and subtracting decimals.

/en/decimals/introduction-to-decimals/content/

Adding and subtracting with decimals

Adding and subtracting decimals happens a lot in real life. You may find that you need to add up the cost of your groceries to see if you have enough money to pay for them. Or perhaps you need to subtract the cost of a bill from your bank account.

When you're adding or subtracting decimal numbers, it's important to set up the expression correctly . The numbers need to be in a certain place, and so do the decimals .

Click through the slideshow below to learn how to set up these expressions.

First, let's set up an addition expression: 21.4 plus 6.82 .

Just like with any addition example, we're going to stack one number on top of the other.

But instead of lining our numbers up on the right...

But instead of lining our numbers up on the right...we're going to line up the decimal points .

No matter how many numbers are on either side of the decimal point, we'll always line up the decimal points before adding.

Once we have the decimal points lined up, our decimals are ready to be added.

When we subtract decimals, we'll set up the decimals in the same way. Let's set up this example.

Instead of lining up our two numbers on the right, we'll line up the two decimal points.

And now our decimals are ready to be subtracted.

Adding decimal numbers

Now that we know how to set up problems with decimals, let's practice by solving a few. First, we'll work on adding . If you feel comfortable adding larger numbers , you're ready to add decimal numbers.

Click through the slideshow to learn how to add decimals.

Let's try solving this problem: 1.9 + 2.15 .

First, we'll make sure the decimals are lined up.

We'll start by adding the digits farthest to the right . In this case, we have nothing on top and 5 on the bottom.

Nothing plus 5 equals 5 . We'll write 5 beneath the line.

Now we'll add the next set of digits to the left : 9 and 1 .

9 + 1 equals 10 , but there's no room to write both digits in 10 underneath the 9 and 1 . We'll have to carry .

We learned how to carry numbers in the lesson on Adding Two- and Three-Digit Numbers .

We'll write the right digit, 0 , under the line...

We'll write the right digit, 0 , under the line...then we'll carry the left digit, 1 , up to the next set of digits in the problem.

Now we'll write the decimal point. We'll place it directly beneath the other two decimal points.

Next, we'll move left to add the next set of digits: 1 and 2 . Since we carried the 1 , we'll add it too.

1 + 1 + 2 equals 4 . We'll write 4 below the line.

We're done. 1.9 + 2.15 = 4.05 . We can read this answer as four and five-hundredths .

Let's try it with a money problem: $51.99 + $25.32 .

We'll make sure our decimal points are lined up properly.

As always, we'll start by adding the digits on the right. Here, that's 9 and 2 .

9 + 2 equals 11 , so it looks like we'll have to carry .

The 1 on the right stays underneath the 9 and the 2 .

We'll carry the 1 on the left and place it above the next set of digits to the left.

Now we'll move left to add the next set of digits. Since we carried the 1 , we'll add it too.

1 + 9 + 3 = 13 .

We'll put the 3 under the digits we added.

We'll carry the 1 and place it above the next column to the left.

Now it's time to write the decimal point. Remember to place it directly beneath the other two decimal points.

Next, we'll move left and add the next set of digits. We'll make sure to add the 1 we carried.

1 + 1 + 5 = 7 . We'll write 7 beneath the line.

To finish, we'll add the next column to the left: 5 and 2 .

5 + 2 equals 7 . We'll write 7 underneath the 2 .

We'll finish by writing the dollar sign ( $ ).

We're done. $51.99 + $25.32 = $77.31 . We can read this answer as seventy-seven dollars and thirty-one cents .

Try solving these problems to practice adding decimal numbers.

Subtracting Decimal Numbers

On the previous page, you saw that adding numbers with decimals is a lot like adding other numbers. The same is true for subtracting numbers with decimals. If you can subtract large numbers , you can subtract numbers with decimals too!

Click through the slideshow to learn how to subtract decimals.

Let's try to solve this problem: 41.2 - 3.09 .

First, we'll make sure the expression is set up correctly. Here, 41.2 is the larger number, so we'll put it on top.

The decimal points are lined up.

As always, we’ll begin with the digits farthest to the right . Here, we have nothing on top and 9 on the bottom.

We can’t take 9 away from nothing . We'll need to place a digit after 41.2 so we can subtract from it.

The value of our number won't change if we use the digit that means nothing: 0 . We'll place a 0 after 41.2 .

Now we can subtract the digits on the right. 0 is smaller than 9 , so we’ll need to borrow to make 0 larger.

We learned how to borrow in the lesson on Subtracting Two- and Three-Digit Numbers .

We'll borrow from the digit to the left of 0 . Here, it's 2 . We'll take 1 from it.

2 - 1 = 1 . To help us remember we subtracted 1, we'll cross out the 2 and write 1 above it.

Then we'll place the 1 we took next to the 0 .

0 becomes 10 .

10 is larger than 9 , which means we can subtract. We'll solve for 10 - 9 .

10 - 9 = 1 . We'll write 1 beneath the line.

Now we'll move left to subtract the next set of digits: 1 - 0 .

1 - 0 = 1 . We'll write 1 beneath the line.

Now it's time to write the decimal point . We'll place it directly beneath the other two decimal points.

Now we'll find the difference of the next set of digits to the left: 1 - 3 .

Because 1 is smaller than 3, it looks like we'll need to borrow again. We need to make the 1 larger.

We'll borrow from the digit to the left of 1 . Here, we'll borrow 1 from the 4 .

4 - 1 = 3 . We'll write 3 above the 4 .

Then we'll place the 1 we took next to the 1 .

1 becomes 11 .

11 is larger than 3 , which means we can subtract. We'll solve for 11 - 3 .

11 - 3 = 8 . We'll write 8 beneath the line.

Finally, we'll move to the left to subtract the last set of digits. The top digit is 3 , but there's nothing beneath it.

3 minus nothing equals 3 , so we'll write 3 beneath the line.

41.2 - 3.09 = 38.11 . We can read this as thirty-eight and eleven-hundredths .

Let's try subtracting money. Let's see if we can solve $14.76 - $3.86 .

First, let's make sure the expression is set up correctly. The larger number is on top , and the decimal points are lined up .

As always, let's start by finding the difference of the digits on the right. Here, that's 6 - 6 .

6 - 6 = 0 . We'll write 0 beneath the line.

We'll move left to the next set of digits: 7 and 8 . 7 is smaller than 8 , so we'll borrow to make 7 larger.

Let's look at the digit to the left of 7 . Here, it's 4 . We'll take 1 from it.

4 - 1 = 3 . We'll cross out the 4 and write 3 above it.

Then we'll place the 1 we took next to the 7 .

7 becomes 17 .

Now it's time to subtract. We'll solve for 17 - 8 .

17 - 8 = 9 . We'll write 9 beneath the line.

We'll put a decimal point directly beneath the other two decimal points.

Next, we'll move left to find the difference of the next set of digits. Here, that's 3 - 3 .

3 - 3 = 0 . We'll write 0 below the line.

Finally, we'll move left to subtract the last set of digits. The top digit is 1 , but there's nothing beneath it.

1 minus nothing equals 1 . We'll write 1 beneath the line.

Next, we'll write a dollar sign ( $ ) to the left of the 1 .

$14.76 - $3.86 = $10.90 . We can read this as ten dollars and ninety cents .

Try solving these problems to practice subtracting decimal numbers.

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• Math Article
• Addition And Subtraction In Decimals

Addition and Subtraction of Decimals

Addition and subtraction of decimals  are a bit complex as compared to performing the operations on natural numbers. Before we learn how to add or subtract any two or more than two given decimals, first, let us understand decimals. The decimal number is used to represent a number with greater precision than integers or whole numbers. It uses a dot in between numbers, which is said to be a decimal point. Decimals are nothing but the simplified version of fractions. Check problems based on  decimal fractions  here.

For example, when we have to divide three pies among 4 kids, we cannot represent the pies received by each kid in terms of integers alone, as each kid has received pies that lie between 0 and 1. To deal with other similar problems, the concept of decimal was introduced. Thus, the idea of addition, multiplication, division and subtraction of decimals is an important topic. Let us say two friends are contributing to buy a cricket ball that costs Rs. 20. One of them has Rs. 7.50, and the other has Rs. 18.50. To know how much money each will have to contribute and how much they will be left with, they must understand the concept of addition and subtraction of decimals.

Addition of Decimals

As we know numbers can be added, subtracted, multiplied and divided. However, all these type of operations can be easily performed on natural numbers. In case of decimals, addition can be done in a specific way. The addition of decimals involves several steps. 

How to Add Decimals?

Addition of decimals is performed using the following steps:

Step 1: The numbers are first padded with zero depending upon the maximum digits present after the decimal for any of the numbers. 

For example, while adding 3.456 to 7.1, since the number 3.456 has the number of digits after the decimal, the padding is done according to 3.456. Since 3.456 has 3 digits after the decimal, we pad two zeros after 1. So, 7.1 to three places is 7.100.

Step 2: The numbers are lined up vertically along with each other as given in the below figure.

Step 3: Finally, add the decimal numbers similar to integers and place the decimal point accordingly.

Let us understand the concept more clearly with the help of the following examples:

Also, read:

Examples of Decimal Addition

Let us see some examples of adding decimals.

Example 1: Addition 1.091 + 1.33.

Example 2: Addition 0.0075 + 5.

Example 3: Add 9.1, 3.22, and 0.66.

Given, 9.1, 3.22 and 0.66.

As we can see, 9.1 has only one digit after the decimal but 3.22 and 0.66 have two digits.

Hence, we can write 9.1 as 9.10

Now add all the three decimals.

——–

——

Click here to know about multiplying decimals .

Subtraction of decimals

Subtraction of decimals involves the subtraction of the decimal number with a small whole number part from the decimal number with a greater whole number part. However, we need to follow certain rules while performing the subtraction on decimals.

How to Subtract Decimals?

Subtraction of decimals is performed using the following steps:

For example, while subtracting 3.456 from 7.1, since the number 3.456 has more digits after the decimal, the padding is done according to 3.456. Since 3.456 has 3 digits after the decimal, we pad 7.1 to three places as 7.100.

Step 2: The numbers are lined up vertically along with each other as shown below.

Step 3: Finally, subtract the decimal numbers similar to integers and place the decimal point accordingly.

Examples on Decimal Subtraction

Example 1: Subtraction: 7.304 – 1.15

Example 2: Subtraction 4.1 – 0.94

Practice Questions

Try solving the following practice problems to get a thorough understanding of the addition and subtraction of decimal numbers.

• Add the decimals: 84.956 and 210.28163.
• Subtract 54.12 from 64.2.
• Subtract 72.3261 from 80.

Frequently Asked Questions – FAQs

What is addition and subtraction of decimals, how to do the addition of decimals, how to do subtraction of decimals, how do you line up decimal numbers in addition and subtraction, how to subtract a decimal number from a whole number.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

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Add and subtract decimals up to 3 digits.

Our grade 5 addition and subtraction of decimals worksheets provide practice exercises in adding and subtracting numbers with up to 3 decimal digits .

Sample Grade 5 Decimal Subtraction Worksheet

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Addition and subtraction of decimals

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

10 March 2023

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Adding and Subtracting Decimals

Adding decimals is easy when you keep your work neat

To add decimals, follow these steps:

• Write down the numbers, one under the other, with the decimal points lined up
• Put in zeros so the numbers have the same length ( see below for why that is OK)
• Then add , using column addition , remembering to put the decimal point in the answer

Example: Add 1.452 to 1.3

Example: Add 3.25, 0.075 and 5

That's all there is to it: line up the decimal points, pad with zeros, then add normally.

Subtracting

To subtract, follow the same method: line up the decimal points, then subtract .

Example: What is 7.368 − 1.15 ?

To check we can add the answer to the number subtracted:

Example: Check that 7.368 minus 1.15 equals 6.218

Let us try adding 6.218 to 1.15

It matches the number we started with, so it checks out.

Putting In Zeros

Why can we put in extra zeros?

A zero is really saying "there is no value at this decimal place".

• In a number like 10, the zero is saying "no ones"
• In a number like 2.50 the zero is saying "no hundredths"

So it is safe to take a number like 2.5 and make it 2.50 or 2.500 etc

But DON'T take 2.5 and make it 20.5, that is plain wrong.