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Equivalent Ratio

We know that when the numerator and the denominator of a fraction are multiplied or divided by
the same non-zero number, the result remains the same and such fractions are called equivalent
fractions.
Since, the ratio can also be expressed in the form of fraction. So, in the same way, if the terms
(antecedent and consequent) of a ratio are multiplied or divided by the same non-zero number,
the value of the ratio remains the same and such ratios are called equivalent ratios.

Example 6: Find three equivalent ratios of 3 : 5.
Solution: The given ratio is 3 : 5.
3
Write it in the form of fraction, that is, 3 : 5 =
5
Multiply by the same non-zero numbers in both numerator and denominator to get the equivalent ratios.

3 32 6 33 9 34 12
×
×
×
Therefore, = = , = , =
×
×
×
5 52 10 53 15 54 20
Thus, the required equivalent ratios are 6 : 10, 9 : 15 and 12: 20.
Example 7: Fill the missing numbers in the given box. Quick Check
18 = = 12 Are the ratios 3 : 4 and
54 18 9 : 12 equivalent?

Solution: In order to get the first missing number, we consider the fact that 54 ÷ 18 = 3, i.e. when
we divide 54 by 18 we get 3. Therefore,
÷
18 18 3 6
= =
54 54 3 18
÷
Now, 6 × 2 = 12, therefore, to get the second missing number, multiply the terms of second fraction
62 12
×
by 2, =
18 2 36
×
18 6 12
Thus, = =
54 18 36

Example 8: A ratio in the simplest form is 3 : 7. If its consequent is 35, find its antecedent.

3
Solution: It is given that =
7 35
We know that 35 ÷ 7 = 5

3
So, we multiply both the numerator and denominator of by 5.
7
35 15
×
\ =
75 35
×
\ 3 : 7 = 15 : 35

Thus, the required antecedent is 15.

203 Ratio and Proportion