# 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.

**Ratio - Proportion**

• Ratio and Proportion

• Ratio in the simplest form

• Comparison of ratios

• Equivalent ratios

• Proportion

• Continued Proportion

• Ratio and Proportion

• Ratio in the simplest form

• Comparison of ratios

• Equivalent ratios

• Proportion

• Continued Proportion

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