# Finding Equivalent Fractions

We will discuss about finding equivalent fractions.

Equivalent fractions can be obtained by multiplying the numerator and the denominator of a fraction by the same non-zero number.

For example, look at the following rectangles.

 (i)
 (ii)
 (iii)

The shaded part of 1st rectangle can be denoted as ½. In the same way, 2nd and 3rd can be denoted as 2/4 and 3/6. Because all are showing same part of rectangle i.e., half of rectangle so they are equivalent fractions.

i.e., ½ = 2/4 = 3/6                or, ½ = 1 X 2/2 x 2 = 1 X 3/2 X 3

½ = 1 X 2/2 x 2 = 2/4    (We can get 2/4 from ½ by multiplying the numerator and the denominator of ½ by 2.)

½ = 1 X 3/2 X 3 = 3/6          (We can get 3/6 from ½ by multiplying the numerator and the denominator of ½ by 3.)

So, we can get equivalent fractions by multiplying the numerator and the denominator of a fraction by a non-zero number.

For example, 3/5 = 3 x 3/5 x 3 = 9/15

Or, 3/5 = 3 x 6/5 x 6 = 18/30

Or, 3/5 = 3 x 8/5 x 8 = 24/40

Here, 3/5, 9/15, 18/30 and 24/40 are equivalent fractions.

We can also obtain an equivalent fraction of a fraction by dividing the numerator and the denominator both by the same non-zero number.

For example, observe the shaded parts of these rectangles.

 (i)
 (ii)
 (iii)

The shaded parts in the 1st rectangle can be denoted as 8/16 in the same way, 2nd and 3rd can be denoted as 4/8 and 2/4. Because, all are shown same part i.e., half of the rectangle, so they are equivalent fractions.

i.e., 8/16 = 4/8 = 2/4

or

8/16 = 8 ÷ 2/16 ÷ 2 = 8 ÷ 4/16 ÷ 4

(We can obtain 4/8 and 2/4 from 8/16 by dividing their numerator and denominator from non-zero numbers 2 and 4 respectively.)

But it is easier to obtain an equivalent fraction by multiplying its numerator and denominator by the same non-zero number.

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