Adding decimals

Here you will learn about adding decimals including how to add decimals with models and with the standard algorithm.

Students will first learn about adding decimals as part of numbers and operations in base 10 in 5th grade. They will build on this knowledge and use the standard algorithm to add as a part of the number system in 6th grade.

What is adding decimals?

Adding decimals is when you add numbers involving decimals.

Let’s look at the strategies for adding decimals.

Adding a decimal number and a decimal number
Modeling with a Hundredths Grid

Adding Decimals table image 1

Just like with multi-digit whole numbers, combine each place value.


Adding Decimals table image 2


Adding Decimals table image 3


Adding Decimals table image 4

Then write the answer in standard form:


Adding Decimals table image 5
Using the Algorithm

Adding Decimals table image 7

Adding Decimals table image 6

1. Stack the numbers, lining up the decimal
points (and place value).
2. Add each column from right to left and
regroup the numbers when necessary.
3. Write your final answer with the decimal
point and check to make sure your answer
is reasonable.

Is the answer reasonable?
1.4 rounds to 1 and 2.06 rounds to 2.
The answer should be close to 1 + 2 = 3.
It is, so 3.46 is reasonable.

What is adding decimals?

What is adding decimals?

Common Core State Standards

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

  • Grade 5 – Numbers and Operations in Base 10 (5.NBT.B.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.

  • Grade 6 – The Number System (6.NS.B.3)
    Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

How to add decimals

In order to add decimals with models:

  1. Show each number using decimal models.
  2. Combine each place value.
  3. Write your final answer with the decimal point.

In order to add decimals with the algorithm:

  1. Stack the numbers and line up the decimal points (and place value).
  2. Add each column from right to left and regroup the numbers when necessary.
  3. Write your final answer with the decimal point and check to make sure your answer is reasonable.

[FREE] Adding Decimals Worksheets (Grade 5 to 6)

[FREE] Adding Decimals Worksheets (Grade 5 to 6)

[FREE] Adding Decimals Worksheets (Grade 5 to 6)

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

DOWNLOAD FREE
x
[FREE] Adding Decimals Worksheets (Grade 5 to 6)

[FREE] Adding Decimals Worksheets (Grade 5 to 6)

[FREE] Adding Decimals Worksheets (Grade 5 to 6)

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

DOWNLOAD FREE

Adding decimals examples

Example 1: Adding decimals with models

Solve 3.5 + 4.9 = \; ?

  1. Show each number using decimal models.

Adding Decimals image 2 US

2Combine each place value.

3 ones + \; 4 ones = 7 ones

Adding Decimals image 3 US

5 tenths + \; 9 tenths = \; 14 tenths

Adding Decimals image 4 US

3Write your final answer with the decimal point.

3.5 + 4.9 = 8.4

Adding Decimals image 5 US

Example 2: Adding decimals with models

Solve 1.12 + 2.3 = \; ?

Show each number using decimal models.

Combine each place value.

Write your final answer with the decimal point.

Example 3: Adding numbers with one decimal place

Solve 5.8 + 3.7 = \; ?

Stack the numbers and line up the decimal points (and place value).

Add each column from right to left and regroup the numbers when necessary.

Write your final answer with the decimal point and check to make sure your answer is reasonable.

Example 4: Adding numbers with two decimal places

Solve 9.18 + 7.35 = \; ?

Stack the numbers and line up the decimal points (and place value).

Add each column from right to left and regroup the numbers when necessary.

Write your final answer with the decimal point and check to make sure your answer is reasonable.

Example 5: Adding more than two decimal numbers

Solve 3.79 + 2.18 + 14.6 = \; ?

Stack the numbers and line up the decimal points (and place value).

Add each column from right to left and regroup the numbers when necessary.

Write your final answer with the decimal point and check to make sure your answer is reasonable.

Example 6: Adding more than two decimal numbers

Solve 34.3 + 22.91 + 56.07 = \; ?

Stack the numbers and line up the decimal points (and place value).

Add each column from right to left and regroup the numbers when necessary.

Write your final answer with the decimal point and check to make sure your answer is reasonable.

Teaching tips for adding decimals

  • Decimal work in 4th grade centers around understanding through models, particularly area models, number lines and connections to fractions with the denominators 10 and 100. To build on this in 5th grade and 6th grade, always have physical or digital models available for students to use when necessary.

  • To introduce this topic, give students a decimal addition problem and give them time to solve in a way that makes sense to them. Then go over the different solving strategies as a whole group.

  • In the beginning, you may want to stick to smaller decimals or problems that do not involve regrouping. However, at some point it is important to transition to showing students all kinds of decimal addition problems mixed together. This gives them an opportunity to identify which solving strategy to use.

  • Math worksheets may have their place when students are still developing understanding around decimal addition, but once students have a successful strategy and can flexibly operate, incorporate math games or real-life projects that involve addition of decimals.

Our favorite mistakes

  • Not lining up the decimal point
    A common error when adding decimals occurs when the decimal points are not lined up but instead the last digits are lined up.
    For example,

    Adding Decimals image 19 US

  • Forgetting to include the number regrouped
    Always add in any numbers that are regrouped. Forgetting to include these values will cause your sum to be incorrect.

    Adding Decimals image 20 US

Practice adding decimals questions

1. Solve 3.7 + 5.6 = \; ?

9.3
GCSE Quiz True

8.13
GCSE Quiz False

8.3
GCSE Quiz False

9.13
GCSE Quiz False

Show each number using decimal models.

 

Adding Decimals image 21 US

 

Then, combine each place value.

 

3 ones + \; 5 ones = \; 8 ones

 

Adding Decimals image 22 US

 

7 tenths + \; 6 tenths = \; 13 tenths

 

Adding Decimals image 23 US

 

Write your final answer with a decimal point.

 

3.7 + 5.6 = 9.3

 

Adding Decimals image 24 US

 

You can also solve with the algorithm by lining up the decimal points and adding each column.

 

Adding Decimals image 25 US

2. Solve 2.84 + 6.19 = \; ?

8.93
GCSE Quiz False

8.913
GCSE Quiz False

9.03
GCSE Quiz True

9.3
GCSE Quiz False

Show each number using decimal models.

 

Adding Decimals image 26 US

 

Then, combine each place value.

 

2 ones + \; 6 ones = \; 8 ones

 

Adding Decimals image 27 US

 

84 hundredths + \; 19 hundredths = \; 103 hundredths

 

Adding Decimals image 28 US

 

Write your final answer with the decimal point.

 

2.84 + 6.19 = 9.03

 

Adding Decimals image 29 US

 

You can also solve with the algorithm by lining up the decimal points and adding each column.

 

Adding Decimals image 30 US

3. Solve 0.069 + 5.987 = \; ?

5.1056
GCSE Quiz False

6.677
GCSE Quiz False

6.056
GCSE Quiz True

6.56
GCSE Quiz False

You can solve with the algorithm by lining up the decimal points and adding each column. Regroup the numbers when necessary.

 

Adding Decimals image 31 US

 

Is this answer reasonable? Use rounding to estimate a reasonable answer. For smaller numbers, you can round to the nearest tenths:

 

0.069 rounds to 0.1

 

5.987 rounds to 6

 

6 + 0.1 = 6.1

 

The sum should be close to 6.1. Since 6.056 is close, it is a reasonable answer.

4. Solve 2.1 + 3.87 = \; ?

5.97
GCSE Quiz True

3.99
GCSE Quiz False

4.07
GCSE Quiz False

23.97
GCSE Quiz False

You can solve with the algorithm by lining up the decimal points and adding each column.

 

A zero can be added to 2.1 as a placeholder. It does not change the value because 2.1 = 2.10.

 

Adding Decimals image 32 US

 

Is this answer reasonable? Use rounding to estimate a reasonable answer. For smaller numbers, you can round to the nearest ones:

 

2.1 rounds to 2

 

3.87 rounds to 4

 

2 + 4 = 6

 

The sum should be close to 6. Since 5.97 is close, it is a reasonable answer.

5. Solve 9.04 + 17.381 = \; ?

18.285
GCSE Quiz False

107.781
GCSE Quiz False

26.385
GCSE Quiz False

26.421
GCSE Quiz True

You can solve with the algorithm by lining up the decimal points and adding each column. Regroup the numbers when necessary.

 

A zero can be added to 9.04 as a placeholder. It does not change the value because 9.04 = 9.040.

 

Adding Decimals image 33 US

 

Is this answer reasonable? Use rounding to estimate a reasonable answer. For smaller numbers, you can round to the nearest ones:

 

9.04 rounds to 9

 

17.381 rounds to 17

 

9 + 17 = 26

 

The sum should be close to 26. Since 26.421 is close, it is a reasonable answer.

6. Solve 20.3 + 13.67 + 0.998 = \; ?

2,568
GCSE Quiz False

4.395
GCSE Quiz False

34.068
GCSE Quiz False

34.968
GCSE Quiz True

You can solve with the algorithm by lining up the decimal points and adding each column. Regroup the numbers when necessary.

 

Zeros can be added to 20.3 and 13.67 as placeholders. It does not change the value because 20.3 = 20.300 and 13.67 = 13.670.

 

Adding Decimals image 34 US

 

Is this answer reasonable? Use rounding to estimate a reasonable answer. For smaller numbers, you can round to the nearest ones:

 

20.3 rounds to 20

 

13.67 rounds to 14

 

0.998 rounds to 1

 

20 + 14 + 1 = 35

 

The sum should be close to 35. Since 34.968 is close, it is a reasonable answer.

Adding decimals FAQs

Is addition of decimals similar to subtraction of decimals?

Yes, you follow the same steps to subtract decimals. The only difference is that you subtract each place value position instead of adding.

Do all addends need to be decimals to solve with these strategies?

No, these strategies will also work when adding whole numbers and numbers with decimals.

What decimals should students work with in 5th and 6th grade?

Following the Common Core recommendations, in 5th grade, students should work with tenths place, hundredths place and thousandths place. In 6th grade this is expanded to smaller numbers. Check your state’s specific standards for further clarification.

Still stuck?

At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.

Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence.

One on one math tuition

Find out how we can help your students achieve success with our math tutoring programs.

x

[FREE] Common Core Practice Tests (Grades 3 to 6)

Prepare for math tests in your state with these Grade 3 to Grade 6 practice assessments for Common Core and state equivalents.

40 multiple choice questions and detailed answers to support test prep, created by US math experts covering a range of topics!

Download free