Equivalent Ratios

Equivalent ratios : A ratio obtained by multiplying or dividing the numerator and denominator of a given ratio by the same number is called an equivalent-ratios.



Example : Consider the ratio 6 : 4,
6/4 = (6 x2)/(4 x 2) = 12/8
6/4 = (6 x3)/(4 x 3) = 18/12
6/4 = (6 x4)/(4 x 4) = 24/16
And so on.
All these are equivalent-ratio of 6/4.
If a : b and c : d are two equivalent-ratios, we write a/b = c/d

Solved examples :
1) Find two equivalent-ratios of 6 : 15.
Solution :
6/15 = (6 x2)/(15 x 2) = 12/30
6/15 = (6 ÷ 3)/(15 ÷ 3) = 2/5
So, 12 : 30 and 2 : 5 are the two equivalent-ratios of 6 : 15.
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2) Fill in the blank.

Solution :
In order to find the first missing number, consider the denominator 21 and 3.
Think of a number in such a way that when we divide 21 with that number we will get 3.
21 ÷ ( ) = 3 So that number must be 7. So divide 14 with 7 that gives us the 1st missing number.
∴ 1st missing number = 14 ÷ 7 = 2
So the 2nd ratio is 2/3.
For 2nd missing number, consider

As we know that when we multiply 2 with 3 we get 6 so with that same number multiply 3 we will get the 2nd missing number.
∴ 2nd missing number = 3 x 3 = 9
So the 3rd ratio is 6/9.
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3) Find the value of ‘a’ and ‘b’ in
Solution :
Consider the 1st two ratios,
12/20 = a/5 ⇒ 12 x 5 = 20 x a
60 = 20a
∴ a = 60/20
∴ a = 3
For finding b, consider 1st and 3rd ratio.
12/20 = 9/b ⇒ 12 x b = 20 x 9
12b = 180
∴ b = 180/12
∴ b = 15.

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Ratio - Proportion

• Ratio and Proportion
• Ratio in the simplest form
• Comparison of ratios
• Equivalent ratios
• Proportion
• Continued Proportion

From equivalent-ratios to number system

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