# 3.18: Decimal Subtraction

**At Grade**Created by: CK-12

**Practice**Decimal Subtraction

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?

\begin{align*}$20 - 12.42\end{align*}

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

\begin{align*}20.00\end{align*}

Next, line up the numbers vertically.

\begin{align*} 20.00\\
\underline {- 12.42}\end{align*}

Then, subtract the numbers

\begin{align*}7.58\end{align*}

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.

\begin{align*}12.5\end{align*}

Next, line up the numbers vertically.

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

Then, subtract the numbers.

\begin{align*}2.12\end{align*}

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.

\begin{align*}16.00\end{align*}

Next, line up the numbers vertically.

\begin{align*} 16.00\\
\underline {- 12.22}\end{align*}

Then, subtract the numbers

\begin{align*}3.78\end{align*}

The answer is 3.78.

#### Example 4

Subtract the decimals.

18.86 - 13.45 = _____

First, line up the numbers vertically.

\begin{align*} 18.86\\
\underline {- 13.45}\end{align*}

Then, subtract the numbers.

\begin{align*}5.41\end{align*}

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.

\begin{align*}19.200\end{align*}

Next, line up the numbers vertically.

\begin{align*} 19.200\\
\underline {- 13.211}\end{align*}

Then, subtract the numbers.

\begin{align*}5.989\end{align*}

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.

### Resources

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).Decimal point

A decimal point is a period that separates the complete units from the fractional parts in a decimal number.Difference

The result of a subtraction operation is called a difference.Magnitude

The magnitude of a number is the size of a number without respect to its sign. The number -35.6 has a magnitude of 35.6.Place Value

The value of given a digit in a multi-digit number that is indicated by the place or position of the digit.Sum

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

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

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