ORDER OF OPERATIONS WITH FRACTIONS

Example 1 :

2/3 + 3/4 x 2/3

Solution :

= 2/3 + 3/4 x 2/3

= 2/3 + 1/2

= (4 + 3)/6

= 7/6

Example 2 :

3/5 – 5/2 x 4/3

Solution :

= 3/5 – 5/2 x 4/3

= 3/5 – 10/3

= (9 - 50)/15

= -41/15

Example 3 :

3/5 x 1/3 + 2/3 x 1/4

Solution :

= 3/5 x 1/3 + 2/3 x 1/4

= 1/5 + 1/6

= (6 + 5)/30

= 11/30

Example 4 :

4/3 x 1/2 – 1/6 x 2/3

Solution :

= 4/3 x 1/2 – 1/6 x 2/3

= 2/3 – 1/9

= (6 - 1)/9

= 5/9

Example 5 :

(2/3)² – 3/4 x 1⅔

Solution :

= (2/3)² – 3/4 x 1⅔

=  4/9 – 3/4 x 5/3

= 4/9 – 5/4

= (16 - 45)/36

= -29/36

Example 6 :

4 x 1⅓ – 5 x 2/7

Solution :

= 4 x 1⅓ – 5 x 2/7

= 4 x 4/3 – 5 x 2/7

= 16/3 - 10/7

= (112 - 30)/21

= 82/21

Example 7 :

2/3 – 3/2 ÷ 4/5

Solution :

= 2/3 – 3/2 ÷ 4/5

= 2/3 – 3/2 x 5/4

= 2/3 – 15/8

= (16 - 45)/24

= -29/24

Example 8 :

5/3 ÷ 1/2 + 4/3

Solution :

= 5/3 ÷ 1/2 + 4/3

= 5/3 x 2/1 + 4/3

= 10/3 + 4/3

= (10 + 4)/3

= 14/3

Example 9 :

1/2 x 2/5 – 3/4 ÷ 6/5

Solution :

= 1/2 x 2/5 – 3/4 ÷ 6/5

1/2 x 2/5 – 3/4 x 5/6

= 1/5 – 5/8

= (8 - 25)/40

= -17/40

Example 10 :

2/5 ÷ (-1/2) + 3/4 x 2/5

Solution :

= 2/5 ÷ (-1/2) + 3/4 x 2/5

= 2/5 x (-2/1) + 3/4 x 2/5

= -4/5 + 6/20

= (-16 + 6)/20

= -10/20

= -1/2 

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