DIVIDING FRACTIONS BY WHOLE NUMBERS

We can divide a fraction by a whole using the steps explained below.

Step 1 :

Keep the fraction as it is and change the division as multiplication.

Step 2 :

Take reciprocal of the whole number.

Step 3 :

Multiply the two fractions and simplify.

Example 1 :

Divide 2/5 by 6.

Solution :

2/5 ÷ 6 

In the above division, change the division as multiplication and take reciprocal of the whole number 6. 

2/5 ÷ 6 = 2/5  1/6

= (2 ⋅ 1)/(5 ⋅ 6)

= (1 ⋅ 1)/(5 ⋅ 3)

= 1/15

Example 2 :

Divide 7/5 by 3.

Solution :

7/5 ÷ 3

In the above division, change the division as multiplication and take reciprocal of the whole number 3. 

7/5 ÷ 3 = 7/5  1/3

= (7 ⋅ 1)/(5 ⋅ 3)

= 7/15

Example 3 :

Divide 5/12 by 20.

Solution :

5/12 ÷ 20

In the above division, change the division as multiplication and take reciprocal of the whole number 20. 

5/12 ÷ 20 = 5/12  1/20

= (5 ⋅ 1)/(12 ⋅ 20)

= (1 ⋅ 1)/(12 ⋅ 4)

= 1/48

Example 4 :

Divide 2/19 by 6.

Solution :

2/19 ÷ 6

In the above division, change the division as multiplication and take reciprocal of the whole number 6. 

= 2/19  1/6

= (2 ⋅ 1)/(19 ⋅ 6)

= (1 ⋅ 1)/(19 ⋅ 3)

1/57

Example 5 :

David eats 1/4 of a pizza and divides the remaining in to two equal parts for his two kids. What is the part of the pizza will each kid receive ?

Solution :

Part of the pizza eaten by David is 1/4.

Remaining pizza is 3/4.

Given : Remaining pizza is divided in to equal parts for his two kids.

Then, the part of the pizza received by each kid is

= 3/4 ÷ 2

= 3/4 ⋅ 1/2

= (3 ⋅ 1)/(4 ⋅ 2)

= 3/8

So, each kid will receive 3/8 part of the pizza.

Example 6 :

David  donated one-fourth of his property to charity and divided the rest equally for his three sons. Find the share of each son.

Solution :

Given : One-fourth of the property donated to charity.

Then, 3/4th of the property is remaining and it divided equally for the three sons.

Share of each son :

= 3/4 ÷ 3

= 3/4  1/3

= (3 ⋅ 1)/(4 ⋅ 3)

= 3/12

= 1/4

So, each son will get one-fourth of the property as share.

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