Page 93 - ICSE Math 7

Simplest form of ratio

A ratio is said to be in its simplest form when the terms of the ratio are co-prime, i.e., they have no
common factors other than 1. For example, the simplest form of the ratio 20 : 15 is 4 : 3.

Equivalent ratios
Equivalent ratios are obtained by multiplying or dividing the terms of the ratio by the same constant
non-zero number. For example, the ratio 1 : 2 is equivalent to 2 : 4 or 5 : 10.

Points to remember
• Ratio exists between two or more quantities of the same kind.

• To find the ratio between the same kind of quantities, quantities should be expressed in the same
unit.
• In a ratio, the order of terms is very important, i.e., the ratio 2 : 3 is different from the ratio 3 : 2.
• The ratio will remain unchanged if each term of the ratio is multiplied or divided by the same
non-zero number.

Example 1: Find the ratio between the following.
(a) 35 kg and 45 kg (b) 3 m 10 cm and 4 m 50 cm

35 7
Solution: (a) Ratio between 35 kg and 45 kg = = = 7 : 9
45 9
(b) 1 m = 100 cm, therefore 3 m 10 cm = 300 cm + 10 cm = 310 cm and
4 m 50 cm = 400 cm + 50 cm = 450 cm

310 cm 31
Ratio between 3 m 10 cm and 4 m 50 cm = = = 31 : 45
450 cm 45
Example 2: If x, y and z are three numbers such that x : y = 7 : 8 and y : z = 16 : 35, then find x : z.
x 7 y 16
Solution: = and =
y 8 z 35
x y 7 16 2
∴ × = × =
y z 8 35 5
x 2
⇒ =
z 5
⇒ x : z = 2 : 5

1 1
Example 3: Express the ratio : in its simplest form.
3 12
Solution: The LCM of the denominators 3 and 12 is 12.
Multiply both the terms by 12 to get:
 1   1 
  3 × 12 :  12 × 12 = 4 : 1





Comparison of ratios
Two ratios can be compared if they have the same consequent. However, if the ratios to be compared
do not have the same consequent, then we first convert the ratios into like fractions and then compare
them.

79