Equivalent fractions

In this article, we will understand the concept of Equivalent Fraction from cutting a paper!

Let us start with a piece of paper, a pair of scissors, a pencil and notebook





Figure 1: The 'whole'





The entire piece of paper is what we will call 'one whole' or just 1.
Let us cut this paper into two equal pieces now.

Figure 2: The 'whole' cut into two equal pieces. Each piece is 1/2


Each of the cut pieces is now called as 'one out of two' or 'half' or just 1/2.

Let us cut each of these pieces, i.e halves into two equal pieces. By doing that, the entire piece of paper will be divided into 4equal pieces.




Figure 3: The 'whole' cut into four equal pieces. Each piece is 1/4




Each of the cut pieces is now called as 'one out of four' or 'one fourth' or just 1/4.

Let us now glue two of the smaller pieces together and compare the glued piece with a bigger piece that we had cut initially.


 2 x 1/4 = 2/4  --------- A

 2/4 = 1/2 -------------- B


It is clear from the picture that two of the 'one fourth's added together will be same as one 'half'.

We call 2/4 and 1/2 as Equivalent Fractions.

We could further cut each of the 1/4th pieces to two equal pieces and make 1/8th. The equivalent fractions will look like this:

4 x 1/8 = 4/8  --------- A

2 x 1/4 = 2/4 ---------- B
4/8 = 2/4 = 1/2 ------- C


Extending this further, 16/32, 8/16, 4/8, 2/4 and 1/2 are equivalent fractions.
As a rule, we need to multiply or divide the numerator and denominator of a fraction by the same integer to get its equivalent fraction.