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Division of Decimals by Whole Numbers

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Division of Decimals by Whole Numbers
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Introduction

Have you ever tried to divide change up between two or more people? 

When the students in Mrs. Williams’s class came out of the dinosaur exhibit, Angie, one of the people who works at the museum, came rushing up to her. “Hello Mrs. Williams, we have some change for you. You gave us too much money. The chaperones are free for each class. Here is $45.36 for your change,” Angie said. Mrs. Williams looked at the change in her hand. Each class is due to receive some change given the chaperone discount. Mrs. Williams tells Kyle about the change. Kyle takes out a piece of paper and begins to work.

If 8 chaperones are on the trip, how much change should each class 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.

Guided Learning

To divide means to split up into equal parts.

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.

8.46  \div 2 = ______

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

2 \overline{)8.46 \;}

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.

& \overset{423}{2\overline{ ) 8.64 \;}}

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.

& \overset{\overset{ \ 4.23} {\uparrow}}{2 \overline{ ) 8.46 \;}}\\& \quad \underline{8 \quad }\\& \quad \ 0 4\\& \quad \ \underline{ \ \ 4 \ }\\& \qquad 06

Our answer is 4.23.

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 \div  2

Solution: 

Example B

6.42  \div 3

Solution: 

Example C

10.5 \div 5

Solution: 

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. Williams’s class came out of the dinosaur exhibit, Angie, one of the people who works at the museum, came rushing up to her. “Hello Mrs. Williams, we have some change for you. You gave us too much money. The chaperones are free for each class. Here is $45.36 for your change,” Angie said. Mrs. Williams looked at the change in her hand. Each class is due to receive some change given the chaperone discount. Mrs. Williams tells Kyle about the change. Kyle takes out a piece of paper and begins to work.

If 8 chaperones are on the trip, how much change should each class 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 chaperones, is 8.

Our dividend is the amount of change = 45.36.

& \overset{ \quad \ 5.67}{8 \overline{ ) {45.36 \;}}}\\& \ \ \underline{-40 \ \ }\\& \quad \ \ 53\\& \ \ \ \underline{-48 \ }\\& \quad \ \ \ 56& \ \ \ \ \ \underline{-56 \ }\\

Our answer is $5.67

Kyle shows his work to Mrs. Williams who then hands out $5.67 to each chaperone.

Here is one for you to try on your own.

96.3 \div 3

Answer

Video Review

Here is a video for review.

James Sousa Example of Dividing a Decimal by a Whole Number

Practice Set

Directions: Divide each decimal by each whole number.

1. 63.28 \div 2

2. 6.6  \div 3

3. 12.10  \div  5

4. 19.62  \div 3

5. 15.6 \div 4

6. 19.24  \div 2

7. 27.6 \div  3

8. 17.5 \div 5

9. 49.2 \div  3

10. 47.04  \div 7

11. 108.8 \div 8

12. 523.8 \div 9

13. 107.6 \div  2

14. 115.5  \div 5

15. 122.7  \div 6

16. 

Lori, Ann, Mary, and
Kim are splitting their dinner bill.
After tip, the total is $40.08. How much
does each owe if they split the bill four
ways?

17. 

There are 73 servings in a
44 ounce bottle of ketchup. How many
ounces are in a serving?(Round to the .00)

18. 

Grade A B C

D

F
Average Score 90-100 80-89 70-79 60-69 50-59

Alex wants to figure out
what grade he is getting in science. His
test scores were 84.5, 88.5, 72.5, 64,
and 94.7. What was his average
test score? What grade will he receive?

Review

  • When we  divide  a decimal by a whole number, we are looking at taking that decimal and splitting it up into sections.
  • Think of dividing decimals by whole numbers as the same thing as dividing by whole numbers.

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