# SIMPLIFYING FRACTIONS

Simplifying Fractions :

In this section, you will learn, how to simplify a fraction and express to its lowest term.

## Simplifying Fractions - Steps

Step 1 :

Use the divisibility rules to find the greatest common divisor of both numerator and denominator.

Step 2 :

Divide both numerator and denominator by the greatest common divisor.

Note :

If you find it difficult to find the greatest common divisor for both numerator and denominator of the fraction, then find the possible common divisor and simplify the fraction step by step.

This is explained in detail in example 6.

## Simplifying Fractions - Examples

Example 1 :

Simplify the fraction and write it in its simplest form.

16/24

Solution :

In the above fraction, the greatest common divisor for both numerator 16 and denominator 24 is 8.

So, we can divide both 16 and 24 by 8.

16/24  =  (16 ÷ 8) / (24 ÷ 8)

16/24  =  2/3

Example 2 :

Simplify the fraction and write it in its simplest form.

15/18

Solution :

In the above fraction, the greatest common divisor for both numerator 15 and denominator 18 is 3.

So, we can divide both 15 and 18 by 3.

15/18  =  (15 ÷ 3) / (18 ÷ 3)

15/18  =  5/6

Example 3 :

Simplify the fraction and write it in its simplest form.

30/48

Solution :

In the above fraction, the greatest common divisor for both numerator 30 and denominator 48 is 6.

So, we can divide both 30 and 48 by 6.

30/48  =  (30 ÷ 6) / (48 ÷ 6)

30/48  =  5/8

Example 4 :

Simplify the fraction and write it in its simplest form.

12/40

Solution :

In the above fraction, the greatest common divisor for both numerator 12 and denominator 40 is 4.

So, we can divide both 12 and 40 by 4.

12/40  =  (12 ÷ 4) / (40 ÷ 4)

12/40  =  3/10

Example 5 :

Simplify the fraction and write it in its simplest form.

63/81

Solution :

In the above fraction, the greatest common divisor for both numerator 63 and denominator 81 is 9.

So, we can divide both 63 and 81 by 9.

63/81  =  (63 ÷ 9) / (81 ÷ 9)

63/81  =  7/9

Example 6 :

Simplify the fraction and write it in its simplest form.

48/72

Solution :

In the above fraction, the greatest common divisor for both numerator 48 and denominator 72 is 24.

So, we can divide both 48 and 72 by 24.

48/72  =  (48 ÷ 24) / (72 ÷ 24)

48/72  =  2/3

Alternative Method :

If you find it difficult to find the greatest common divisor 24, then find the possible common divisor and simplify the fraction as shown below.

48/72  =  (48 ÷ 2) / (72 ÷ 2)  =  24/36

24/36  =  (24 ÷ 2) / (36 ÷ 2)  =  12/18

12/18  =  (12 ÷ 2) / (18 ÷ 2)  =  6/9

6/9  =  (6 ÷ 3) / (9 ÷ 3)  =  2/3

Therefore, we have

48/72  =  2/3

After having gone through the stuff given above, we hope that the students would have understood, how to simplify a fraction and write to its lowest term.

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