# Finding Fractional Parts with Division

In this 4th grade lesson, students learn the connection between division and finding a fractional part of a quantity. For example, to find 2/3 of 9 apples, we first find 1/3 of 9 apples using division, and then double our result. These 8 hearts are divided into four equal parts.
Each part is
 1 4
(one-fourth) of the whole.

We can use division: 8 ÷ 4 = 2. Each group
 has 2 hearts. So, 1 4 of 8 hearts is 2 hearts. Mom's 24 brownies are divided into 6 equal
parts. Each part is 1/6th of the whole. How
many pieces are in each part?

Divide to find out:  24 ÷ 6 = 4. Four pieces.
 So, 1 6 of 24 brownies is 4 brownies.

To find
 1 2
,
 1 3
,
 1 4
,
 1 5
etc. part of something, divide by 2, 3, 4, 5, etc. (respectively).

1. Write a division sentence and a fractional part sentence.

a. _____ ÷ 5 = ____

 1 5 of ____ is ____.

b. _____ ÷ ____ = ____

 1 3 of ____ is ____.

c. _____ ÷ ____ = ____ of ____ is ____.

d. _____ ÷ ____ = ____ of ____ is ____.

2. Write a fractional part sentence for each division sentence.

a.  30 ÷ 5 = _____ of 30 is ______.

b.  48 ÷ 6 = _____ of ____ is ____.

c.  25 ÷ 5 = _____ of ____ is ____.

d.  50 ÷ 5 = _____ of ____ is ____.

3. Find a part. Also write a division sentence.

 a. 1 6 of 30 is _______.

3 0    ÷   6    =    5

 b. 1 7 of 49 is _______.

_______ ÷_____ = _____

 c. 1 10 of 250 is _______.

_______ ÷_____ = _____

 d. 1 2 of 480 is _______.

_______ ÷_____ = _____

 e. 1 9 of 1,800 is _______.

_______ ÷_____ = _____

 f. 1 5 of 400 is _______.

_______ ÷_____ = _____

Divide these ten
fish into 5 groups. 1/5 of 10 fish is 2 fish. 1 5 of 10 is 2. 2/5 of 10 fish is TWICE as much, or 4 fish. 2 5 of 10 is 4. 3/5 of 10 fish is THREE TIMES as much, or 6 fish. 3 5 of 10 is 6. What about 4/5 of 10? Can you tell? 4 5 of 10 is _____.

4. Fill in the blanks.

a. 1 3 of 9 apples is _____ apples. 2 3 of 9 apples is _____ apples. 3 3 of 9 apples is _____ apples.

b. 1 4 of 12 flowers is _____. 2 4 of 12 flowers is _____. 3 4 of 12 flowers is _____. 4 4 of 12 flowers is _____.

c. 1 5 of _____ fish is ____ fish. 2 5 of _____ fish is ____ fish. 3 5 of _____ fish is ____ fish. 4 5 of _____ fish is ____ fish. 5 5 of _____ fish is ____ fish.

5. Calculate.

 a. 1 5 of 20 is _______. 2 5 of 20 is _______. 3 5 of 20 is _______.
 b. 1 8 of 32 is _______. 3 8 of 32 is _______. 5 8 of 32 is _______.
 c. 1 10 of 500 is __________. 3 10 of 500 is __________. 7 10 of 500 is __________.
 d. 1 6 of 420 is __________. 2 6 of 420 is __________. 5 6 of 420 is __________.
 e. 1 20 of 600 is __________. 7 20 of 600 is __________. 11 20 of 600 is __________.
 f. 1 100 of 700 is __________. 9 100 of 700 is __________. 50 100 of 700 is __________.

6. Fill in.

 a. Marsha got \$18 from her mom. She put into her savings \$6, which was one-__________ part of it.     Division sentence: _______ ÷_____ = _____ b. Mariana spent one-fourth of her \$80 savings, or \$________.     Division sentence: _______ ÷_____ = _____ c. One-fifth  (which was 5 boys) of all the boys went jogging. So, in total there were _____ boys.     Division sentence: _______ ÷_____ = _____

7. An 8-lb bag of potatoes costs \$3.20.

a. One pound is one-___________________ part of the bag. How much does it cost?

b. How much does 5/8 of the bag cost?

8. A shepherd's pie is divided into 10 equal-size pieces. The whole pie weighs 1,200 g.

a. What does 1/10 of the pie weigh?

b. What does 9/10 of the pie weigh?

9. Four backpacks cost \$28. How much would three cost?

10. A new fan for the clubhouse costs \$24.40. Mark paid half of it, Judy paid 1/4 of it,
and Art and Grace paid 1/8 of it each. Find how much each child paid.

Mark: ______________     Judy: ______________

Art: ______________      Grace: ______________ 11. Erica and James had 28 balloons each to sell.

By the evening, Erica had sold 1/2 of her balloons.
James had sold 3/4 of his.
How many balloons had they sold in total?

If one balloon costs \$1.20, how much money did they take in?

This lesson is taken from Maria Miller's book Math Mammoth Division 2, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.

#### Math Mammoth Division 2

A self-teaching worktext for 4th grade that covers long division, finding fractional parts with division, word problems, remainder, average, and divisibility.