Equivalent Fractions

The fractions having the same value are called equivalent fractions. Their numerator and denominator can be different but, they represent the same part of a whole.

Consider the following:

(i)

$Equivalent Fractions$

1/2

(ii)

$Equivalent Fractions$

2/4

(iii)

$Equivalent Fractions$

4/8

(iv)

8/16

(v)

5/10

(vi)

$Equivalent Fractions$

10/20

(viii)

6/12

(viii)

$Equivalent Fractions$

3/6

We can see the shade portion with respect to the whole shape in the figures from (i) to (viii)

In; (i) Shaded to whole shape is half to whole i.e., ¹/₂

(ii) Shaded to whole shape is 2 to fourth i.e., ²/₄ = ¹/₂

(iii) Shaded to whole shape is 4 to eighth i.e., ⁴/₈ = ¹/₂

(iv) Shaded to whole shape is 8 to sixteenth i.e., ⁸/₁₆ = ¹/₂

(v) Shaded to whole shape is 5 to tenth i.e., ⁵/₁₀ = ¹/₂

(vi) Shaded to whole shape is 10 to 20th i.e., ¹⁰/₂₀ = ¹/₂

(vii) Shaded to whole shape is 6 to 12th i.e., ⁶/₁₂ = ¹/₂

(viii) Shaded to whole shape is 3 to 6th i.e., ³/₆ = ¹/₂

Thus, 1/2, 2/4, 4/8, 8/16, 5/10, 10/20, 6/12, 3/6, etc., each fraction represents half portion of the shape, which are all equal. All have different numerator and denominator but they all have the same value because they represent the same shaded area i.e., half of the rectangle.

So, 1/2, 2/4, 4/8, 8/16, 5/10, 10/20, 6/12, 3/6 are equivalent fractions.

We can express it as, 1/2 = 2/4 = 4/8 = 8/16 = 5/10 = 10/20 = 6/12 = 3/6 = 1/2.

The fractions having different numerators and denominators but representing equal value or magnitude are called equivalent fractions.

Note:

The fraction 1/2 and 2/4 and 4/8 show the same amount of shaded or colored parts. 1/2 and 2/4 and 4/8 are equivalent fractions.
Equivalent fractions are fractions that have different forms but the same value.

Building Equivalent Fractions:

1. Change 2/5 to an equivalent fraction with denominator 15.