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, 3/4^{th} 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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