SIMPLIFYING FRACTIONS

Examples 1-11 : Simplify each fraction to its simplest form.

Example 1 : 

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 : 

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 : 

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 : 

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 : 

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 : 

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

Example 7 : 

300/500

Solution :

300/500

In the above fraction, the greatest common divisor for both numerator 300 and denominator 500 is 100. 

So, we can divide both 300 and 500 by 100. 

300/500  =  (300 ÷ 100)/(500 ÷ 100)

300/500  =  3/5

Example 8 : 

145/225

Solution :

145/225

In the above fraction, the greatest common divisor for both numerator 145 and denominator 225 is 5. 

So, we can divide both 145 and 225 by 5. 

145/225  =  (145 ÷ 5)/(225 ÷ 5)

145/225  =  29/45

Example 9 : 

190/570

Solution :

190/570

In the above fraction, the greatest common divisor for both numerator 190 and denominator 570 is 10. 

So, we can divide both 190 and 570 by 10. 

190/570  =  (190 ÷ 10)/(570 ÷ 10)

190/570  =  19/57

In the fraction 19/57, the greatest common divisor for both numerator 19 and denominator 57 is 19. 

So, we can divide both 19 and 57 by 19.

190/570  =  (19 ÷ 19)/(57 ÷ 19)

190/570  =  1/3

Example 10 : 

230/495

Solution :

230/495

In the above fraction, the greatest common divisor for both numerator 230 and denominator 495 is 5. 

So, we can divide both 230 and 495 by 5. 

230/495  =  (230 ÷ 5)/(495 ÷ 5)

230/495  =  46/99

Example 11 : 

54/333

Solution :

54/333

In the above fraction, the greatest common divisor for both numerator 54 and denominator 333 is 3. 

So, we can divide both 54 and 333 by 3.

54/333  =  (54 ÷ 3)/(333 ÷ 3)

54/333  =  27/111

Example 12 : 

Which fractions below are equivalent to 2/3?

Solution :

4/6  =  (4 ÷ 2)/(6 ÷ 2)  =  2/3

6/8  =  (6 ÷ 3)/(8 ÷ 3)  =  2/4

8/12  =  (8 ÷ 4)/(12 ÷ 4)  =  2/3

6/8  =  (6 ÷ 3)/(8 ÷ 3)  =  2/4

10/15  =  (10 ÷ 5)/(15 ÷ 5)  =  2/3

The fractions 4/6, /12 and 10/15 are equivalent to 2/3.

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