# EQUIVALENT FRACTIONS

The fractions which are equivalent 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.

## Understanding Equivalent Fractions

Let us divide a rectangle into two equal parts and shade one of the parts. 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 Find Equivalent Fractions

Change both numerator and denominator using multiplication or division by the same number.

Example :

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

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

## Practice Problems

Problem 1 :

Write 4 fractions which are equivalent to 5/6.

Solution :

5/6 = (5 ⋅ 2)/(6 ⋅ 2) = 10/12

5/6 = (5 ⋅ 3)/(6 ⋅ 3) = 15/18

5/6 = (5 ⋅ 4)/(6 ⋅ 4) = 20/24

5/6 = (5 ⋅ 5)/(6 ⋅ 5) = 25/30

The four fractions which are equivalent to 5/6 are

10/12, 15/18, 20/24 and 25/30

Problem 2 :

Write 3 fractions which are equivalent to 3/7.

Solution :

3/7 = (3 ⋅ 2)/(7 ⋅ 2) = 6/14

3/7 = (3 ⋅ 3)/(7 ⋅ 3) = 9/21

3/7 = (3 ⋅ 4)/(7 ⋅ 4) = 12/28

The four fractions which are equivalent to 5/6 are

6/14, 9/21 and 12/28

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  =  (2 ⋅ 8) / (5 ⋅ 8)  =  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  =  (1 ⋅ 5) / (3 ⋅ 5)  =  5/15

Problem 4 :

Find the missing numbers : Solution :

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. Problem 5 :

Find the missing numbers : Solution :

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.  Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here. Kindly mail your feedback to v4formath@gmail.com

## Recent Articles 1. ### Word Problems Involving Linear Equations

Aug 14, 22 09:31 PM

Word Problems Involving Linear Equations

2. ### Solving System of Linear Equations Word Problems Worksheet

Aug 14, 22 09:17 PM

Solving System of Linear Equations Word Problems Worksheet