ORDER OF OPERATIONS WITH FRACTIONS

Perform operations within the Bracket or Parenthesis first.

Calculate Exponents.

Starting from left to right perform division or multiplication, whichever comes first.

Finally from left to right perform addition or subtraction whichever comes first.

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 1

Solution :

= (2/3)– 3/4 x 1

=  4/9 – 3/4 x 5/3

= 4/9 – 5/4

= (16 - 45)/36

= -29/36

Example 6 :

4 x 1 – 5 x 2/7

Solution :

= 4 x 1 – 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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