Page 111 - ICSE Math 6

Example 1: Find the ratio between 2.75 kg and 750 g.
Solution: We know that, 2.75 kg = 2.75 × 1,000 g = 2,750 g

2750 11
Thus, the ratio between 2,750 g and 750 g = = = 11 : 3
750 3

Example 2: In a class of 50 students, 17 are boys and the rest are girls. Find the ratio between the
number of boys and girls.
Solution: Number of girls in the class = 50 – 17 = 33
Number of boys 17
\ Ratio between number of boys and girls = = = 17 : 33
Number of girls 33

Example 3: The ratio of the number of balloons with Arun and Arpita is 3 : 7. If Arun has 15 balloons,
then find the number of balloons Arpita has.
Solution: We know that, Ratio = antecedent ÷ consequent

Arun’s balloons 3 15 3
Here, = ⇒ =
Arpita’s balloons 7 Arpita’s balloons 7

7 5
⇒ Arpita’s balloons = × 15 = 35
3

Example 4: The ratio of the length to the breadth of a rectangular sheet of paper is 7 : 5. If the
breadth is 15 cm, find its length.
Solution: Ratio of length to the breadth = 7 : 5

Length 7
\ =
Breadth 5

Length 7 7 3
⇒ = ⇒ Length = × 15 = 21
21 5 5
\ Length of the rectangular sheet of paper is 21 cm.

Simplification of ratios
A ratio is always expressed in its lowest (simplest) terms by cancelling Maths Info
out the common factors from the antecedent and consequent. If both A ratio does not change by
the terms of a ratio are fractions, then multiply the antecedent and multiplying or dividing its terms
consequent by the LCM of their denominators. by the same number.

Example 5: Simplify the given ratios.
Try These
3 1 5
(a) 35 : 75 (b) : (c) :2
1
20 40 9 1. Is the simplified form of 1
1
35 7 : 2 is 1 : 2? 3
3
Solution: (a) 35 : 75 = = = 7 : 15
1
75 15 2. If of a book is read. Find
3
(b) The LCM of the denominators 20 and 40 is 40. the simplified ratio between
Multiply both the terms by 40 to get: the fraction of book read and
 3   1  the fraction of book left to


 ×40 :  ×40 = (3 × 2) : (1) = 6 : 1 be read.
 20   40 
95