# 3.18: Decimal Subtraction

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

**Practice**Decimal Subtraction

In the last Concept, Julie figured out the sum of the ice cream cone. Can you imagine being in the same situation? Well, that would be a lot of math that you would need to figure out. However, the dilemma didn't stop there. You see, when Julie was figuring out the sum, the customer handed Julie a $10.00 bill and two quarters.

“I am so glad that I have the change,” she said to Julie.

Julie frantically began to work out the math on her piece of paper.

**Pay attention in this Concept. To help Julie figure out the correct change, you will need to know how to subtract decimals.**

### Guidance

In the last Concept, you learned to add decimals. Well, subtracting decimals is very similar to adding them. While the operation is different, the way of working is the same.

To add or subtract decimals, we are going to be working with the wholes and parts of the numbers separately.

**We want to add or subtract the parts and then add or subtract the wholes.**

**How can we do this?**

The best way to do this is to keep the parts together and keep the wholes together.

**To do this, we simply line up the decimal points in each number that we are adding or subtracting.**

6.78 - 2.31 = _____

First, we line up the problem vertically.

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

Next, we subtract each digit vertically.

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

**Our answer is 4.47.**

**Sometimes, the values in a subtraction problem can have a different number of digits. We add zeros to help hold places where there are not digits. That way each number has the same number of places.**

67.89 - 18.4 = _____

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

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

**Our answer is 49.49.**

Now it is time for you to try a few on your own. Subtract the following decimals.

#### Example A

**16 - 12.22 = _____**

**Solution: 3.78**

#### Example B

**18.86 - 13.45 = _____**

**Solution: 5.41**

#### Example C

**19.2 - 13.211 = _____**

**Solution: 5.989**

Now let's think about Julie. Do you know how to figure out the customer's change?

**The cost of the ice cream cone is $3.50.** Julie took the ten dollar bill and the two quarters from the customer.

\begin{align*}\$10.50 - 3.50 & = \underline{\;\;\;\;\;\;\;\;\;\;}\\ .50 - .50 & = 0\\ 10 - 3 & = 7\end{align*}

**Julie confidently handed the customer $7.00 in change. The customer smiled, thanked Julie and left eating her delicious ice cream cone.**

### 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.

\begin{align*}34.08 - 12.99\end{align*} = _____

**Answer**

To begin, we line up the digits according to place value and subtract.

**Our answer is 21.09.**

### Interactive Practice

### Video Review

Here are videos for review.

Khan Academy Subtracting Decimals

James Sousa, Adding and Subtracting Decimals

### Practice

Directions: Subtract the following decimals.

1. 17.65 - 4 = _____

2. 18.97 - 3.4 = _____

3. 22.50 - .78 = _____

4. 27.99 - 1.99 = _____

5. 33.11 - 3.4 = _____

6. 44.59 - 11.34 = _____

7. 78.89 - 5 = _____

8. 222.56 - 11.2 = _____

9. 567.09 - 23.4 = _____

10. 657.80 - 3.04 = _____

11. 345.01 - 123.90 = _____

12. 567.08 - 111.89 = _____

13. 378.99 - 345.12 = _____

14. 786.01 - 123.10 = _____

15. 504.32 - 345.89 = _____

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

Here you'll learn how to subtract decimals.

## Concept Nodes:

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.