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3.19: Mental Math to Add and Subtract Decimals

Difficulty Level: At Grade Created by: CK-12
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Have you ever had to add decimals without a paper and a pencil? Well, there is an easy way to do it. Take a look.

Justin and Kiley went to the mall. At lunch, they stopped at the food court to get something to eat. Justin ordered a hamburger for $2.99 and a drink for $1.09. Kiley ordered the same thing.

How much did they spend in all?

This Concept will show you how to add decimals using mental math. At the end of the Concept, you will know how to figure out the total cost for lunch.

Guidance

Sometimes, you don’t need to go through all of the work of lining up decimal points and filling in the zeros. Sometimes you can use mental math to figure out a sum.

When is mental math most helpful with decimal sums and differences?

When you have a decimal where the decimal parts can easily add up to be one whole, you can use mental math to figure out the sum. Think about this. If you had .30 + .70, you know that 3 + 7 is 10, therefore you know that .30 + .70 is 1.00.

Let’s apply this information.

5.30 + 6.70 = _____

Here we can start by looking at the decimals, since .30 + .70 is 1. Then we combine the whole numbers and add the total of the decimals to get an answer:

5 + 6 = 11 + 1 = 12

Our answer is 12.

What about subtraction?

We can use mental math to complete subtraction problems too.

We just look for which decimals add up to be wholes and go from there.

25.00 - 22.50 = _____

We are subtracting 25.00 - 22.50, we can think about this problem in reverse to make the mental math simpler. “What plus 22.50 will give us 25.00?" Think: 2.50 plus what equals 5.00?

25.00 - 22.50 = 2.50

Our answer is 2.50.

Not all problems will be able to be solved mentally, but when we can mental math makes things a whole lot simpler!!

Here are few for you to work on. Add or subtract using mental math.

Example A

33.50 + 5.50 = _____

Solution: $39.00

Example B

10 - 3.75 = _____

Solution: 6.25

Example C

18.25 + 2.25 = _____

Solution: 18 + 2 = 20, .25 + .25 = .50. The total is 20.50.

Have you been paying attention? Let's go back to the problem from the beginning of the Concept.

Justin and Kiley went to the mall. At lunch, they stopped at the food court to get something to eat. Justin ordered a hamburger for $2.99 and a drink for $1.09. Kiley ordered the same thing.

How much did they spend in all?

First, we can add $3.00 instead of $2.99 and $1.00 instead of $1.09.

\begin{align*}3 + 3 + 1 + 1 = 8\end{align*}

But, there is change to consider too.

\begin{align*}.09 + .09 = .18\end{align*}

But the original hamburger was .01 less than $3.00, so we add .16 instead of .18

The total cost of lunch is $8.16.

Vocabulary

Here are the vocabulary words in this Concept.

Sum
the answer in an addition problem.
Difference
the answer in a subtraction problem.

Guided Practice

Here is one for you to try on your own.

Kiley went shopping and spent $5.60. She gave the clerk a ten dollar bill. What was her change?

Answer

To figure this out, we can write a subtraction problem.

\begin{align*}10 - 5.60\end{align*}

Then we can use mental math to solve it.

Our answer is $4.40.

Video Review

Here are videos for review.

Khan Academy Adding Decimals

Khan Academy Subtracting Decimals

James Sousa, Adding and Subtracting Decimals

Practice

Directions: Use mental math to compute each sum or difference.

1. .50 + 6.25 = _____

2. 1.75 + 2.25 = _____

3. 3.50 + 4.50 = _____

4. 7.25 + 1.25 = _____

5. 8.75 + 3.25 = _____

6. 8.50 + 2.50 = _____

7. 10 + 4.50 = _____

8. 12 + 3.75 = _____

9. 15.50 - 5.25 = _____

10. 20 - 15.50 = _____

11. 10 - 4.50 = _____

12. 30 - 15.50 = _____

13. 40 - 16.40 = _____

14. 75 - 50.50 = _____

15. 80 - 40.25 = _____

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Vocabulary

Decimal

In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).

Difference

The result of a subtraction operation is called a difference.

Sum

The sum is the result after two or more amounts have been added together.

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Date Created:
Oct 29, 2012
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