Ivana goes to the thrift store with $20 in her pocket. She purchases a shirt and a necklace that total $12.42. Ivana hands the cashier her $20 bill and watches as the cashier enters the number. Ivana tries to predict the amount of change that she will receive from the cashier, but she can't decide what to do since $12.42 and $20 have a different number of digits. Can you find the difference between $20 and $12.42 and figure out much change the cashier should give Ivana?

In this concept, you will learn how to subtract decimals.

### Subtracting Decimals

To subtract decimals, you will work with the wholes and parts of the numbers separately. First, you subtract the parts and then you subtract the wholes. The best way to do this is to keep the parts together and keep the wholes together. To do this, simply line up the decimal points in each number that you are subtracting.

Let's look at an example.

6.78 - 2.31 = _____

First, line up the problem vertically.

\begin{align*}6.78 \\ \underline{-\ 2.31} \end{align*}

Then, subtract each digit vertically.

\begin{align*}6.78 \\ \underline{-\ 2.31} \\ 4.47\end{align*}

The answer is 4.47.

Sometimes, the values in a subtraction problem can have a different number of digits. Add zeros to help hold places where there are no digits. That way each number has the same number of places.

Let's look at an example.

67.89 - 18.4 = _____

First, line up the problem vertically with the decimal point.

\begin{align*}67.89 \\ \underline{-\ 18.40} \\ 49.49 \end{align*}

Then, subtract each digit vertically.

49.49

The answer is 49.49.

### Examples

#### Example 1

Earlier, you were given a problem about Ivana and her purchases at the thrift store.

She has $20 and she spends $12.42. How can she subtract her total and calculate her change?

First, add zeros to the 20 so that both numbers have the same number of places.

Next, line up the numbers vertically.

Then, subtract the numbers

The answer is $7.58. Ivana should receive $7.58 from the cashier.

#### Example 2

Subtract the decimals.

12.5 - 10.38 = _____

First, add a zero to the 12.5 so that both numbers have the same number of places.

Next, line up the numbers vertically.

\begin{align*} 12.50\\ \underline {- 10.38}\end{align*}

Then, subtract the numbers.

The answer is 2.12.

#### Example 3

Subtract the decimals.

16 - 12.22 = _____

First, add zeros to the 16 so that both numbers have the same number of places.

Next, line up the numbers vertically.

Then, subtract the numbers

The answer is 3.78.

#### Example 4

Subtract the decimals.

18.86 - 13.45 = _____

First, line up the numbers vertically.

Then, subtract the numbers.

The answer is 5.41

#### Example 5

Subtract the decimals.

19.2 - 13.211 = _____

First, add zeros to the 19.2 so that both numbers have the same number of places.

Next, line up the numbers vertically.

Then, subtract the numbers.

The answer is 5.989.

### Review

Subtract the following decimals.

- 17.65 - 4 = _____
- 18.97 - 3.4 = _____
- 22.50 - .78 = _____
- 27.99 - 1.99 = _____
- 33.11 - 3.4 = _____
- 44.59 - 11.34 = _____
- 78.89 - 5 = _____
- 222.56 - 11.2 = _____
- 567.09 - 23.4 = _____
- 657.80 - 3.04 = _____
- 345.01 - 123.90 = _____
- 567.08 - 111.89 = _____
- 378.99 - 345.12 = _____
- 786.01 - 123.10 = _____
- 504.32 - 345.89 = _____

### Review (Answers)

To see the Review answers, open this PDF file and look for section 3.18.