# Concept of Equivalent Ratios

## Definition

Equivalent Ratios: If two ratios have the same value when simplified, then they are called Equivalent Ratios. Thus, 3: 2 is equivalent to 6: 4 or 12: 8.

## Equivalent ratio:

• If two ratios have the same value when simplified, then they are called Equivalent Ratios.

• Two ratios are equivalent if the fractions corresponding to them are equivalent.
• Equivalent Ratios can be obtained by multiplying or dividing the numerator and denominator by the same number.

• For Example,
Give two equivalent ratios of 6: 4.

Ratio 6: 4 = 6/4 = (6 × 2)/(4 × 2) = 12/8.

Therefore, 12: 8 is an equivalent ratio of 6: 4

Similarly,
Ratio 6: 4 = 6/4 = (6 × 2)/(4 × 2) = 3/2

So, 3: 2 is another equivalent ratio of 6: 4.

## Example

Fill in the following blanks:

 14 = = 6 21 3

[Are these equivalent ratios?]

14/21 = (7 xx 2)/(7 xx 3) = 2/3.

2/3 = (2 xx 3)/(3 xx 3) = 6/9

Therefore, 2, 9 will come in the blanks respectively.

Yes, all these are equivalent ratios.

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