Page 110 - ICSE Math 6

8 Ratio, Proportion and Unitary

Method

Key Concepts

• Ratio • Comparison of Ratios
• Difference between Fraction and Ratio • Proportion
• Simplification of Ratio • Unitary Method
• Dividing a Quantity in a Given Ratio

In our daily life, we often compare two quantities in terms of their magnitudes. For example, suppose
in a test of 100 marks, Amit and Rahul scored 60 marks and 75 marks respectively. Since 75 – 60
= 15, we compare their marks by saying that Rahul scored 15 more marks than Amit. We can also
compare their marks by division as shown.
Amit’s marks 60 4 
4
Rahul’s marks = 75 = 5 ⇒ Amit’s marks =  times Rahul’s marks
5

This method of comparison by division is known as ratio.
Ratio

Ratio is the relation obtained between two quantities (of the comparable kind) by dividing one quantity
x
by the other. Ratio is denoted by a colon ( : ). The ratio between two non-zero numbers x and y is .
y
It is denoted by x : y, where x and y are called the terms of the ratio. Also, the first term x is known
as the antecedent and the second term y is known as the consequent.
For example, Maths Info
(a) The ratio between 6 balls and 5 balls is 6 : 5. There is no relation between
(b) The ratio between 15 rupees and 11 rupees is 15 : 11. two quantities which are not
of the same kind.
Points to remember
• A ratio does not have a unit of measurement. Try These
• Ratio = antecedent ÷ consequent.
• A ratio can be expressed as a fraction. 1. If a = 5 and b = 2, find:
(i) a : b (ii) (a – b) : b
• A ratio x : y is defined only if x and y are non-zero numbers. (iii) (a – b) : (a + b)
• The ratio x : y is not equal to y : x, unless x = y. 2. Find the ratio between first
two multiples of 3.
Difference between fraction and ratio
The table given below shows the difference between a fraction and a ratio.

Fraction Ratio
It is used to represent a part of whole. It is used to compare two quantities using division.
a
The fraction represents a parts out of b equal The ratio a : b represents that for a parts of the first
b
parts of a whole. quantity there are b parts of the second quantity.
In a fraction, denominator represents the total In a ratio, antecedent or consequent may or may
parts of the whole. not represent the total of the two quantities.

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