In this section, you will learn how to multiply a fraction by another fraction.
To multiply a proper or improper fraction by another proper or improper fraction, we have to multiply the numerators and denominators.
For example,
2/3 ⋅ 4/5 = (2 ⋅ 4)/(3 ⋅ 5) = 8/15
1/3 ⋅ 7/11 = (1 ⋅ 7)/(3 ⋅ 11) = 7/33
Problem 1 :
Find the value of :
1/5 of 3/8
Solution :
1/5 of 3/8 = 1/5 ⋅ 3/8
1/5 of 3/8 = (1 ⋅ 3)/(5 ⋅ 8)
1/5 of 3/8 = 3/40
Problem 2 :
Find the value of :
2/9 ⋅ 3/2
Solution :
2/9 ⋅ 3/2 = (2 ⋅ 3)/(9 ⋅ 2)
2/9 ⋅ 3/2 = 6/18
Problem 3 :
Find the value of :
2/5 ⋅ 5 2/3
Solution :
2/5 ⋅ 5⅔ = 2/5 ⋅ 17/3
2/5 ⋅ 5⅔ = (2 ⋅ 17)/(5 ⋅ 3)
2/5 ⋅ 5⅔ = 34/15
2/5 ⋅ 5⅔ = 2⁴⁄₁₅
Problem 4 :
Find the value of :
6 3/4 ⋅ 7/10
Solution :
6¾ ⋅ 7/10 = 27/4 ⋅ 7/10
6¾ ⋅ 7/10 = (27 ⋅ 7)/(4 ⋅ 10)
6¾ ⋅ 7/10 = 189/40
6¾ ⋅ 7/10 = 4²⁹⁄₄₀
Problem 5 :
Lily reads 1/4 th of a book in 1 hour. How much of the book will she read in 3½ hours ?
Solution :
The part of the book read by Lily in 1 hour is 1/4.
So, the part of the book read by Lily in 3½ hours is
= 3½ ⋅ 1/4
= 7/2 ⋅ 1/4
= (7 ⋅ 1)/(2 ⋅ 4)
= 7/8
Hence, Lily will read 7/8 part of the book in 3 1/2 hours.
Problem 6 :
David ate 1/3 of the pizza and gave 3/4 th of the remaining to his friend. What is the part of the pizza did David give his friend ?
Solution :
The part of the pizza eaten by David is 1/3.
So, the remaining pizza is 2/3.
The part of the pizza given to his friend is
= 3/4 of the remaining
= 3/4 of 2/3
= 3/4 ⋅ 2/3
= (3 ⋅ 2)/(4 ⋅ 3)
= (1 ⋅ 1)/(2 ⋅ 1)
= 1/2
Hence, David gave 1/2 of the pizza to his friend.
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