DIVIDING FRACTIONS WORKSHEET

Problem 1 : 

Simplify :

2/5 ÷ 6/7 

Solution :

2/5 ÷ 6/7 

In the division of above two fractions, change the division as multiplication and take reciprocal of the second fraction. 

2/5 ÷ 6/7  =  2/5 ⋅ 7/6

Simplify.

2/5 ÷ 6/7  =  (2 ⋅ 7)/(5 ⋅ 6)

2/5 ÷ 6/7  =  (1 ⋅ 7)/(5 ⋅ 3)

2/5 ÷ 6/7  =  7/15

Problem 2 :

Simplify :

7/5 ÷ 3/2

Solution :

7/5 ÷ 3/2

In the division of above two fractions, change the division as multiplication and take reciprocal of the second fraction. 

7/5 ÷ 3/2  =  7/5 ⋅ 2/3

Simplify.

7/5 ÷ 3/2  =  (7 ⋅ 2)/(5 ⋅ 3)

7/5 ÷ 3/2  =  (7 ⋅ 2)/(5 ⋅ 3)

7/5 ÷ 3/2  =  14/15

Problem 3 :

Simplify :

5/12 ÷ 20/13

Solution :

5/12 ÷ 20/13

In the division of above two fractions, change the division as multiplication and take reciprocal of the second fraction. 

5/12 ÷ 20/13  =  5/12 ⋅ 13/20

Simplify.

5/12 ÷ 20/13  =  (5 ⋅ 13)/(12 ⋅ 20)

5/12 ÷ 20/13  =  (1 ⋅ 13)/(12 ⋅ 4)

5/12 ÷ 20/13  =  13/48

Problem 4 :

Simplify :

2/19 ÷ 6 1/2

Solution :

2/19 ÷ 6½

2/19 ÷ 6½ = 2/19 ÷ 13/2

In the division of above two fractions, change the division as multiplication and take reciprocal of the second fraction. 

2/19 ÷ 6½  =  2/19 ⋅ 2/13

Simplify.

2/19 ÷ 6½  =  (2 ⋅ 2)/(19 ⋅ 13)

2/19 ÷ 6½  =  4/247

Problem 5 :

David can make one pizza in 1/2 hour. How many pizzas can he make in 5/2 hours ?

Solution :

Time taken to make one pizza is 1/2 hour.   

No. of pizzas made in 5/2 hours is

=  5/2 ÷ 1/2

In the division of above two fractions, change the division as multiplication and take reciprocal of the second fraction. 

=  5/2 ⋅ 2/1

=  (5 ⋅ 2)/(2 ⋅ 1)

=  10/2

=  5

So, David can make 5 pizzas in 5/2 hours.

Problem 6 :

If a fraction is multiplied by itself and then divided by the reciprocal of the same fraction, the result is 18  26/27. Find the fraction.

Solution :

Let x be the fraction and its reciprocal is 1/x.

(x · x)  ÷ 1/x = 18  26/27

x²  ÷ (1/x) = 512/27

x² · x = 512/27

x³ = 512/27

x³ = (8/3)³

x = 8/3

So, the required fraction is 8/3.

Problem 7 :

How many 1/8's are there in 37  1/2 ?

Solution :

Total number of 1/8's are = 37  1/2 ÷ 1/8

= 75/2 ÷ 1/8

= 75/2 · (8/1)

= 75(4)

= 300

So, there are three hundred 1/8's are there.

Problem 8 :

3/8 is what part of 1/12 ?

a)  3/7     b)  1/12    c)  4/3     d)  none

Solution :

Let x of 1/12 = 3/8

x/12 = 3/8

x = (3/8) (12)

= 9/2

Problem 9 :

Workout the missing number

9/11 · ____ = 3/4

Solution :

9/11 · ____ = 3/4

Let x be the unknown.

9/11 · x = 3/4

x = 3/4 ÷ (9/11)

= (3/4) · (11/9)

= 11/12

So, the required fraction is 11/12.

Problem 10 :

Workout (4/5) ÷ (3/10) ÷ (1/8)

Solution :

= (4/5) ÷ (3/10) ÷ (1/8)

= (4/5) · (10/3) · 8

= 64/3

= 21   1/3

So, the answer is 21  1/3.

Problem 10 :

Workout (7/9) + (1/2) ÷ (3/5)

Solution :

=  (7/9) + (1/2) ÷ (3/5)

First we have to perform division.

=  (7/9) + (1/2) · (5/3)

=  (7/9) + (5/6)

= (14 + 15)/18

= 29/18

= 1  11/18

So, the answer is 1  11/18.

Problem 11 :

James shares 5/8 of a cake between 6 people. What fraction of the cake do they each receive ?

Solution :

Quantity of cake = 5/8 of cake

Number of people who are sharing = 6

Fraction of cake each receive = 5/8 ÷ 6

= 5/8 · 1/6

= 5/48

Problem 12 :

John has 12 cans of dog food. He has two dogs and he gives each dog 2/3 of can of dog food each day.

Does he have enough dog food to last one week ?

Solution :

Quantity of dog food available = 12 cans

Number of dogs in the house = 2

Quantity of food given on each day = 2 x 2/3 of can food.

Quantity of food last in one week = 7 (4/3)

= 28/3

= 9  1/3

Since the amount of food serving is less than amount of food which is available. So, it is enough.

Problem 13 :

Alisha has 7/8 liters of lemonade. She is pouring glasses that each contains 1/5 liters. How many full glasses can she pour ?

Solution :

Quantity of lemonade = 7/8 liters

Capacity of glass = 1/5 liters

Number of glasses = 7/8 ÷ (1/5)

= (7/8) · (5/1)

= 35/8

= 4.375

So, the required number of glasses is 4.

Problem 13 :

Helen is cutting lengths of string from a roll that is 9  1/3 meters long. Each length of string is 1/9 meters long. How many lengths of string can Helen cut from the roll?

Solution :

Length of roll = 9  1/3 meter

= 28/3

Length of each string to cut = 1/9

Number of pieces cut from the roll = 28/3 ÷ (1/9)

= 28/3 · (9/1)

= 28(3)

= 84

So, the required number of pieces is 84.

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