# EQUIVALENT FRACTIONS

## About "Equivalent fractions"

Equivalent Fractions have the same value, even though they may look different. These fractions are really the same.

For example,

3/4  =  6/8  =  12/16

Why are they the same ?

Because when we multiply or divide both the numerator and denominator by the same number, the fraction keeps it's value.

## Equivalent fractions

Let us divide a rectangle into two equal parts and shade one part. In the above rectangle, the shaded part is 1/2.

That is, in total of 2 parts, one part is shaded.

Let us divide the same rectangle into four equal parts and shade 2 parts. In the above rectangle, the shaded part is 2/4.

That is, in total of 4 parts, two parts are shaded.

Let us divide the same rectangle into six equal parts and shade 3 parts. In the above rectangle, the shaded part is 3/6.

That is, in total of 6 parts, three parts are shaded.

In all the above figures, the shaded portion are equal but they can be represented by different fractions.

1/2  =  2/4  =  3//6

When two or more fractions represent the same part of a whole, the fractions are called equivalent.

Rule to get equivalent fractions :

Change both numerator and denominator using multiplication or division.

Examples :

Using multiplication 1/2, 2/4 and 4/8 are equivalent fractions.

Using division 18/36, 6/12 and 1/2 are equivalent fractions.

## Equivalent fractions - Practice problems

Problem 1 :

Write 4 fractions which are equivalent to 5/6.

Solution :

5/6  =  (5x2)/(6x2)  =  10/12

10/12  =  (10x2)/(12x2)  =  20/24

20/24  =  (20x2)/(24x2)  =  40/48

40/48  =  (40x2)/(48x2)  =  80/96

The four fractions which are equivalent to 5/6 are

10/12, 20/24, 40/48 and 80/96

Problem 2 :

Write 3 fractions which are equivalent to 3/7.

Solution :

3/7  =  (3x2)/(7x2)  =  6/14

6/14  =  (6x2)/(14x2)  =  12/28

12/28  =  (12x2)/(28x2)  =  24/56

The three fractions which are equivalent to 3/7 are

6/14, 12/28 and 24/56

Problem 3 :

Pick out the fractions which are equivalent :

2/5, 12/16, 1/3, 5/15, 16/40, 3/4, 9/12

Solution :

The fractions 2/5 and 16/40 are equivalent.

Because, 2/5  =  (2x8) / (5x8)  =  16/40

The fractions 12/16, 3/4 and 9/12 are equivalent.

Because, 12/16  =  (12÷4) / (16÷4)  =  3/4

and 9/12  =  (9÷3) / (12÷3)  =  3/4

The fractions 1/3 and 5/15 are equivalent.

Because, 1/3  =  (1x5) / (3x5)  =  5/15

Problem 4 :

Find the missing number : The numerator of the first two fractions are 5 and 35. And 5 will become 35, when we multiply by 7.

So, we have to multiply the denominator of the first fraction 9 by 7 in order to get the denominator of the second fraction.

Hence, the denominator of the second fraction is 63.

The denominator of the first and third fraction are 9 and 72. And 9 will become 72, when we multiply by 8.

So, we have to multiply the numerator of the first fraction 5 by 8 in order to get the numerator of the third fraction.

Hence, the numerator of the third fraction is 40.

That is, Problem 5 :

Find the missing number : The numerator of the first two fractions are 3 and 21. And 3 will become 21, when we multiply by 7.

So, we have to multiply the denominator of the first fraction 5 by 7 in order to get the denominator of the second fraction.

Hence, the denominator of the second fraction is 35.

The denominator of the first and third fraction are 5 and 20. And 5 will become 20, when we multiply by 4.

So, we have to multiply the numerator of the first fraction 3 by 4 in order to get the numerator of the third fraction.

Hence, the numerator of the third fraction is 12.

That is, After having gone through the stuff given above, we hope that the students would have understood "Equivalent-fractions".

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