multiply the following and write their products inthe lowest terms 1/4×3/4
Answers
In multiplication of fractions to multiply a fraction by one or more natural numbers or fractions, proceed as follows:
(i) Convert the natural numbers (if any) to improper fractions.
(ii) Convert the mixed numbers (if any) to improper fractions.
(iii) Multiply numerator with numerator and denominator with denominator and cancel the common factors of the numerator and denominator and place the product of the numerator over the denominator.
(iv) Convert into mixed fraction if needed.
Product of two fractions = Product of their numerators
Product of their denominators
[Place the product of the numerators over the product of the denominators]
i.e., a/b × c/d = (a × c)/(b × d)
There are three steps to multiply fractions are:
1. Multiply the numerators of the fractions (the top numbers).
2. Multiply the denominators of the fractions (the bottom numbers).
3. Simplify the fraction if needed to the lowest terms.
For example:
(i) 3/7 × 4/5
= (3 × 4)/(7 × 5)
= 12/35
(ii) 7/3 × 5/2
= (7 × 5)/(3 × 2)
= 35/6
(iii) 5 × 3/7
= 5/1 × 3/7
= (5 × 3)/(1 × 7)
= 15/7
(iv) 5/12 × 9
= 5/12 × 9/1
= (5 × 9)/(12 × 1)
= (5 × 3)/(4 × 1)
= 15/4
Sometimes for indicating multiplication of two fractions, we use the word ‘of ‘as follows:
(i) 1/2 of 8
= 1/2 × 8
= 1/2 × 8/1
= (1 × 8)/(2 × 1)
= 8/2
= 4
(ii) 1/5 of 20
= 1/5 × 20
= 1/5 × 20/1
= 20/5
= 4
(iii) 2/5 of 25
= 2/5 × 25
= 2/5 × 25/1
= (2 × 25)/(5 × 1)
= 50/5
= 10
(iv) 2/3 of 5/7
= 2/3 × 5/7
= (2 ×5)/(3 × 7)
= 10/21.
Examples on multiplication of fractions:
1. Multiply the fractions:
(i) 2/9 by 4/5
(ii) 3/5 by 12
(iii) 2¹/₃ by 2/5
(iv) 5³/₄ by 2³/₇
(i) 2/9 by 4/5
= 2/9 × 4/5
= (2 × 4)/(9 × 5)
= 8/45
(ii) 3/5 by 12
= 3/5 × 12
= 3/5 × 12/1
= (3 × 12)/(5 × 1)
= 36/5
= 7¹/₅
(iii) 2¹/₃ by 2/5
= 2¹/₃ × 2/5
= 7/3 × 2/5
= (7 × 2)/(3 × 5)
= 14/15
(iv) 5³/₄ by 2³/₇
= 5³/₄ × 2³/₇
= 23/4 × 17/7
= (23 × 17)/(4 × 7)
= 391/28
= 13²⁷/₂₈
2. Multiply and reduce to lowest form (if possible) :
(i) 2/5 × 5/4
(ii) 1/3 × 15/8
(iii) 4/5 × 12/7
(iv) 15/16 × 10/12
Solution:
(i) 2/3 × 5/4
= (2 × 5)/(3 × 4)
= (1 × 5)/(3 × 2)
= 5/6
(ii) 1/3 × 15/8
= (1 × 15)/(3 × 8)
= (1 × 5)/(1 × 8)
= 5/8
(iii) 4/5 × 12/7
= (4 × 12)/(5 × 7)
= 48/35
= 1¹³/₃₅
(iv) 15/16 × 10/12
= (15 × 10)/(16 × 12)
= (5 × 5)/(8 × 4)
= 25/32