# Equivalent Fractions

Equivalent fractions are discussed here.

Consider the following:

(i)

1/2

(ii)

2/4

(iii)

4/8

(iv)

8/16

(v)

5/10

(vi)

10/20

(viii)

6/12

(viii)

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.

Note:
Multiply numerator and denominator by the same number to get the required denominator.

2. Change 9/12 to an equivalent fraction with denominator 4.

Note:
To find an equivalent fraction with smaller denominator, you can divide the numerator and denominator with the same number.

3. We can build equivalent fraction with multiples of numerator and denominator.
Write the next three equivalent fractions.

Note:
Equivalent fraction can be built to very large numbers.
Equivalent fraction can be reduced to the lowest term.

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