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# Mental Math to Add and Subtract Decimals

## Group decimal and whole number parts to make mental addition and subtraction easier.

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Mental Math to Add and Subtract Decimals

Marlo is having a party. He needs to buy the party snacks and drinks from different stores. Marlo spends $21.60 at the first store and$19.40 at the second store. He's wondering if he can afford to go to a third store for more snacks. He doesn't have a calculator but wants to quickly figure out how much he's spent so far so. How can mental math help calculate how much Marlo has already spent on snacks?

In this concept, you will learn how to use mental math to add and subtract decimals.

### Sums and Differences Using Mental Math

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 the sum of two decimals.

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 0.30 + 0.70, you know that 3 + 7 is 10, therefore you know that 0.30 + 0.70 is 1.00.

Let’s look at an example.

5.30+6.70\begin{align*}5.30 + 6.70\end{align*}

Start by looking at the decimals. 0.30 + 0.70 is 1, then combine the whole numbers and add the total of the decimals to get an answer:

5+611+1=11=12\begin{align*}5 + 6 &= 11\\ 11 + 1 &= 12\end{align*}

Sometimes you can use mental math to figure out the difference of two decimals.

Look for which decimals add up to a whole and go from there.

Let's look at an example.

25.0022.50\begin{align*}25.00 - 22.50\end{align*}

First, notice that 0.50 can easily be paired with 0.50 to equal one whole.

Next, round 22.50 to the nearest whole number and subtract that value from 25.

2523=2\begin{align*}25 - 23 = 2\end{align*}

Then, combine the decimal and the whole number.

2+0.50=2.50\begin{align*}2 + 0.50 = 2.50 \end{align*}

The answer is 25.00 - 22.50 = 2.50

### Examples

#### Example 1

Earlier, you were given a problem about Marlo shopping for party snacks.

He spends $21.60 at one store and$19.40 at a second store. Marlo wants to quickly combine these totals. Can you use use mental math to find the sum of $21.60 and$19.40?

0.60+0.40=1\begin{align*}0.60 + 0.40 = 1\end{align*}

12+19=31\begin{align*}12 + 19 = 31\end{align*}

Then, combine the two sums.

31+1=32\begin{align*}31 + 1 = 32\end{align*}

The answer is that $21.60 +$19.40 = $32.00. Marlo spent a combined total of$32.00 at the two stores.

#### Example 2

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

First, what decimal added to 0.60 makes it a whole number?

0.40\begin{align*}0.40\end{align*}

Next, round 5.60 to the nearest whole number and subtract that from 10

106=4\begin{align*}10 - 6 = 4\end{align*}

Then, combine the decimal and the whole number.

4+0.40=4.40\begin{align*}4 + 0.40 = 4.40\end{align*}

The answer is 10 - 5.60 = 4.40.

#### Example 3

33.50+5.50\begin{align*}33.50 + 5.50\end{align*}

First, look at the decimals.

The decimals easily add up to one whole.

Next, combine the decimals and the whole numbers separately.

0.50+0.5033+5=1=38\begin{align*}0.50 + 0.50 &= 1\\ 33 + 5 &= 38\end{align*}

Then, add the two sums together.

38+1=39\begin{align*}38 + 1 = 39\end{align*}

The answer is 33.50 + 5.50 = 39.

Example 4

Subtract using mental math.103.75\begin{align*}10 - 3.75\end{align*}

First, what decimal added to 0.75 makes it a whole number?

0.25\begin{align*}0.25\end{align*}

Next, round 3.75 to the nearest whole number and subtract that from 10

104=6\begin{align*}10 - 4 = 6\end{align*}

Then, combine the decimal and the whole number.

6+0.25=6.25\begin{align*}6 + 0.25 = 6.25\end{align*}

The answer is 10 - 3.75 = 6.25

Example 5

18.25+2.25\begin{align*}18.25 + 2.25\end{align*}

0.25+0.25=0.50\begin{align*}0.25 + 0.25 = 0.50\end{align*}

18+2=20\begin{align*}18 + 2 = 20\end{align*}

Then, combine the two sums.

20+0.50=20.50\begin{align*}20 + 0.50 = 20.50\end{align*}

The answer is that 18.25 + 2.25 = 20.50.

### Review

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 = _____

To see the Review answers, open this PDF file and look for section 3.19.

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes

### Vocabulary Language: English

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.