Equivalent Fractions

Equivalent fractions are discussed here.

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.

So, 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.