Equivalent Fractions

What are called equivalent fractions?

A given fraction and various fractions obtained by multiplying (or dividing) its numerator and denominator both by the same non-zero number, are called equivalent fractions.

In other-words:

If two or more fraction have the same value, then they are called the equivalent or equal fractions

The value of the fraction does not change if both the numerator and the denominator are multiplied by the same natural number.

(i) ^{(3 × 2)}/_{(4 × 2)} = ⁶/₈, ^{(3 × 3)}/_{(4 × 3)} = ⁹/₁₂, ^{(3 × 4)}/_{(4 × 4)} = ¹²/₁₆ etc. are equivalent fractions equivalent to the fraction ³/₄.

(ii) ¹/₃ = ^{(1 × 3)}/_{(3 × 3)} = ³/₉;

¹/₃ = ^{(1 × 6)}/_{(3 × 6)} = ⁶/₁₈;

¹/₃ = ^{(1 × 9)}/_{(3 × 9)} = ⁹/₂₇ and so on.

So, ¹/₃, ³/₉, ⁶/₁₈, ⁹/₂₇, etc., are equivalent fractions.

(iii) ⁴⁵/₂₇ = ^{(45 ÷ 3)}/_{(27 ÷ 3)} = ¹⁵/₉;

⁴⁵/₂₇ = ^{(45 ÷ 9)}/_{(27 ÷ 9)} = 5/3

So, ⁴⁵/₂₇, ¹⁵/₉, ⁵/₃, etc., are equivalent fractions.

We have,

⁸/₂₈ = ^{(8 ÷ 4)}/_{(28 ÷ 4)} = ²/₇ , ¹⁰/₃₅ = ^{( 10 ÷ 5)}/_{(35 ÷ 5)} = ²/₇

⁸/₂₈ and ¹⁰/₃₅ are equivalent fractions equivalent to the fraction ²/₇

If ^a/_b and ^c/_d are two equivalent fractions, then

a × d = b × c