Page 180 - Maths Class 06

Simplest or Lowest Form of a Ratio
In general, the ratio is expressed in its simplest or lowest form. A ratio whose terms do not have any
common factor other than ‘1’ is said to be in the ‘simplest form’. A ratio in the simplest form is also called
the ratio in lowest terms.
For example : 25 : 30 can be written as 5 : 6.
18 : 24 can be written as 3 : 4.

To express the ratio of two numbers in the simplest form, we find the HCF of two terms and divide each
term by the HCF.
For example : Express ratio 250 : 450 in its simplest form.
HCF of 250 and 450 is 50.

Now, Antecedent = 250 ÷ 50 = 5
Consequent = 450 ÷ 50 = 9
5
\ Simplest form = 5 : 9 =
9

Equivalent Ratios
Consider, 3 : 4 = 6 : 8 = 12 : 16 (multiplying antecedent and consequent by 2 every time.)
And, 56 : 24 = 28 : 12 = 14 : 6 = 7 : 3 (dividing antecedent and consequent by 2 every time.)

We observe the simplest form of the given ratios remain same on dividing or multiplying both numerator
and denominator by same number.
Thus, equivalent ratios can be obtained by multiplying or dividing the numerator and denominator by
same number.

Dividing a Number in the Given Ratio

If the number p is to be divided in the ratio a b: ,
æ a ö æ b ö
then the first part = ç ÷ ´ p and the second part = ç ÷ ´ p.
è a b è a b
+ ø
+ ø
For ex am ple, let’s di vide 35 in the ra tio 2 : 3.
æ 2 ö 2
First part = ç ÷ ´35 = ´35 = 14 ;
è 2 3 5
+ ø
æ 3 ö 3
Second part = ç ÷ ´35 = ´35 = 21.
è 2 3 5
+ ø
EXAMPLE 1. Give four equivalent ratios of 3 : 5.
3
SOLUTION : Ratio 3 : 5 =
5
We know that, equivalent ratios can be obtained by multiplying or dividing the numerator
and denominator by the same number.
3 3 2´ 6 3 3 3´ 9 3 3 4´ 12 3 3 5´ 15
= = ; = = ; = = ; = =
5 5 2´ 10 5 5 3´ 15 5 5 4´ 20 5 5 5´ 25

Mathematics-6 180