ORDER OF OPERATIONS WITH FRACTIONS AND DECIMALS

BODMAS is the rule that can be used to simplify or evaluate complicated numerical expressions with more than one  operation.

Example 1 :

1  1/4 x 6 - (1/2)²

Solution :

= 1  1/4 x 6 - (1/2)²

Converting the mixed fraction to improper, we get

Example 2 :

1.55 + (0.5)² - 4.9 ÷ 7

Solution :

Example 3 :

1  2/7 x (2/3)² - (6/7²) ÷ (1/7)

Solution :

= 1  2/7 x (2/3)² - (6/7²) ÷ (1/7)

Converting the improper fraction to mixed fraction, we get

= (9/7) x (2/3)² - (6/7²) ÷ (1/7)

Using exponents, we get

= (9/7) x (4/9) - (6/49) ÷ (1/7)

Multiplying the first two fractions, we get

= 4/7 - (6/49) ÷ (1/7)

Dividing 6/49 by 1/7, we get

= 4/7 - (6/7)

= (4 - 6)/7

= -2/7

Example 4 :

(2.4)² + 5.6 x 1.6

Solution :

= (2.4)² + 5.6 x 1.6

= 5.76 + 5.6 x 1.6

= 5.76 + 8.96

= 14.72

Example 5 :

(1/2)² x (4/5) - (6/5)

Solution :

= (1/2)² x (4/5) - (6/5)

By using exponent, we get

= (1/4) x (4/5) - (6/5)

= (1/5) - (6/5)

= (1-6)/5

= -5/5

= -1

Example 6 :

18.14 + (0.5)³ ÷ 2.5 - 21.13

Solution :

Example 7 :

1.9 - 3² x 0.3 + 16.1

Solution :

Example 8 :

(1/3)² ÷ 1/9 + 2/3 -15/2 x 2/5

Solution :

= (1/3)² ÷ 1/9 + 2/3 -15/2 x 2/5

= (1/9) ÷ 1/9 + 2/3 -15/2 x 2/5

= 1 + 2/3 -15/2 x 2/5

= 1 + 2/3 - 3

= (3 + 2 - 9)/3

= -4/3

Example 9 :

2.16 ÷ 6² - 13.06 + 1.2 x 0.5

Solution :

= 2.16 ÷ 6² - 13.06 + 1.2 x 0.5

= 2.16 ÷ 36 - 13.06 + 1.2 x 0.5

= 0.06 - 13.06 + 1.2 x 0.5

= 0.06 - 13.06 + 0.6

= -13 + 0.6

= -12.4

Example 10 :

(2/3) ÷ (2/3) x 2² + 1 1/2

Solution :

= (2/3) ÷ (2/3) x 2² + 1 1/2

= (2/3) ÷ (2/3) x 2² + 1 1/2

= 1 x 4 + 1 1/2

= 4 + 3/2

= (8 + 3)/2

= 11/2