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.

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