Page 2 - 10-Math-3 VARIATIONS

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In this unit, students will learn how to

• Define ratio, proportions and variations (direct and inverse).
• Find 3 rd, 4 th, mean and continued proportion.
• Apply theorems of invertendo, alternendo, componendo,

dividendo and componendo & dividendo to find proportions.
• Define joint variation.
• Solve problems related to joint variation.
• Use k-method to prove conditional equalities involving

proportions.
• Solve real life problems based on variations.

3.1 Ratio, Proportions and Variations

3.1(i) Define (a) ratio, (b) proportion (c) variations (direct
and inverse)

(a) Ratio
A relation between two quantities of the same kind (measured in
same unit) is called ratio. If a and b are two quantities of the same
kind and b is not zero, then the ratio of a and b is written as a : b or
in fraction e.g., if a hockey team wins 4 games and losses 5, then
the ratio of the games won to games lost is 4 : 5 or in fraction

Remember that:
(i) The order of the elements in a ratio is important.
(ii) In ratio a : b, the first term a is called antecedent and
the second term b is called consequent.
(iii) A ratio has no units.

Example 1: Find the ratio of (ii) 1km to 600m
(i) 200gm to 700 gm

Solution: (i) Ratio of 200gm to 700 gm

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