Concept of Equivalent Ratios

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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.

Notes

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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