# 4.10: Division of Decimals by Whole Numbers

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

**Practice**Division of Decimals by Whole Numbers

Have you ever tried to divide change up between two or more people? Take a look at what happened at the science museum.

When the students in Mrs. Andersen’s class came out of the dinosaur exhibit, Sara, one of the people who works at the museum, came rushing up to her. “Hello Mrs. Andersen, we have some change for you. You gave us too much money, because today we have a discount for all students. Here is $35.20 for your change,” Sara handed Mrs. Andersen the money and walked away. Mrs. Andersen looked at the change in her hand. Each student is due to receive some change given the student discount. Mrs. Andersen tells Kyle about the change. Kyle takes out a piece of paper and begins to work.

If 22 students are on the trip, how much change should each student receive?

**In this Concept you will learn about dividing decimals by whole numbers. When finished with this Concept, you will know how much change each student should receive.**

### Guidance

To ** divide** means to split up into equal parts.

You have learned how to divide whole numbers in an earlier Concept.

Now we are going to learn how to divide decimals by whole numbers.

When we divide a decimal by a whole number, we are looking at taking that decimal and splitting it up into sections.

4.64 \begin{align*}\div\end{align*} 2 \begin{align*}=\end{align*} ______

The first thing that we need to figure out when working with a problem like this is which number is being divided by which number. In this problem, the two is the ** divisor**. Remember that the divisor goes outside of the division box. The

**is the value that goes inside the division box. It is the number that you are actually dividing.**

*dividend*\begin{align*}2 \overline{)4.64 \;}\end{align*}

We want to divide this decimal into two parts. We can complete this division by thinking of this problem as whole number division. We divide the two into each number and then we will insert the decimal point when finished. Here is our problem.

\begin{align*}& \overset{232}{2\overline{ ) 4.64 \;}}\end{align*}

Finally, we can insert the decimal point into the ** quotient**. We do this by bringing up the decimal point from its place in the division box right into the quotient. See the arrow in this example to understand it better, and here are the numbers for each step of the division.

\begin{align*}& \overset{\overset{ \ 2.32} {\uparrow}}{2 \overline{ ) 4.64 \;}}\\ & \quad \underline{4 \quad }\\ & \quad \ 0 6\\ & \quad \ \underline{ \ \ 6 \ }\\ & \qquad 04 \end{align*}

**Our answer is 2.32.**

**As long as you think of dividing decimals by whole numbers as the same thing as dividing by whole numbers it becomes a lot less complicated.**

Here are a few for you to try. Find each quotient.

#### Example A

36.48 \begin{align*}\div\end{align*} 12

**Solution: 3.04**

#### Example B

2.46 \begin{align*}\div\end{align*} 3

**Solution: .82**

#### Example C

11.5 \begin{align*}\div\end{align*} 5

**Solution: 2.3**

**Always remember to notice the position of the decimal point in the dividend and bring it up into the quotient.**

Now that you have learned about dividing decimals by whole numbers, we are ready to help Kyle figure out the change from the science museum. Here is the original problem once again.

When the students in Mrs. Andersen’s class came out of the dinosaur exhibit, Sara, one of the people who works at the museum, came rushing up to her. “Hello Mrs. Andersen, we have some change for you. You gave us too much money because today we have a discount for all students. Here is $35.20 for your change,” Sara handed Mrs. Andersen the money and walked away. Mrs. Andersen looked at the change in her hand. Each student is due to receive some change given the student discount. Mrs. Andersen tells Kyle about the change. Kyle takes out a piece of paper and begins to work. **If 22 students are on the trip, how much change should each student receive?**

**Now that we know about dividing decimals and whole numbers, this problem becomes a lot easier to solve.**

**Our divisor is the number of students, that is 22.**

**Our dividend is the amount of change = 35.20.**

\begin{align*}& \overset{ \quad \ 1.60}{22 \overline{ ) {35.20 \;}}}\\ & \ \ \underline{-22 \ \ }\\ & \quad \ \ 132\\ & \ \ \ \underline{-132 \ }\\ & \qquad \ \ \ 0 \end{align*}

**Our answer is $1.60.**

**Kyle shows his work to Mrs. Andersen, who then hands out $1.60 to each student.**

### Vocabulary

Here are the vocabulary words found in this Concept.

- Divide
- to split up into groups evenly.

- Divisor
- a number that is doing the dividing. It is found outside of the division box.

- Dividend
- the number that is being divided. It is found inside the division box.

- Quotient
- the answer to a division problem

### Guided Practice

Here is one for you to try on your own.

66.3 \begin{align*}\div\end{align*} 3

**Answer**

\begin{align*}22.1\end{align*}

**This is our answer.**

### Video Review

Here is a video for review.

James Sousa Example of Dividing a Decimal by a Whole Number

### Practice

Directions: Divide each decimal by each whole number.

1. 36.48 \begin{align*}\div\end{align*} 2

2. 5.4 \begin{align*}\div\end{align*} 3

3. 14.16 \begin{align*}\div\end{align*} 6

4. 18.63 \begin{align*}\div\end{align*} 3

5. 11.6 \begin{align*}\div\end{align*} 4

6. 11.26 \begin{align*}\div\end{align*} 2

7. 27.6 \begin{align*}\div\end{align*} 4

8. 18.5 \begin{align*}\div\end{align*} 5

9. 49.2 \begin{align*}\div\end{align*} 4

10. 27.09 \begin{align*}\div\end{align*} 7

11. 114.4 \begin{align*}\div\end{align*} 8

12. 325.8 \begin{align*}\div\end{align*} 9

13. 107.6 \begin{align*}\div\end{align*} 8

14. 115.7 \begin{align*}\div\end{align*} 5

15. 192.6 \begin{align*}\div\end{align*} 6

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Divide

To divide is split evenly into groups. The result of a division operation is a quotient.Dividend

In a division problem, the dividend is the number or expression that is being divided.divisor

In a division problem, the divisor is the number or expression that is being divided into the dividend. For example: In the expression , 6 is the divisor and 152 is the dividend.Quotient

The quotient is the result after two amounts have been divided.### Image Attributions

Here you'll learn to divide decimals by whole numbers.