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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.

Download ($5.10). Also available as a printed copy.

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