Examples on Simplification

Examples on simplification are discussed, in order to simplify expressions involving more than one bracket by using the steps of removal of brackets. Different types of questions on simplifications are explained here step by step.

1. Simplify: 37 - [5 + {28 - (19 - 7)}]

Solution:

37 - [5 + {28 - (19 - 7)}]

= 37 - [5 + {28 - 12}] [Removing the innermost bracket ( )]

= 37 - [5 + 16] [Removing braces { }]

= 37 - 21

= 16.

2. Simplify: 78 - [24 - {16 (5 - 4 - 1)}]

Solution:

78 - [24 - {16 - (5 – 4 - 1)}]

= 78 - [24 - {16 - (5 - 3)}]       [Removing vinculum]

= 78 -[24 - {16 - 2}]               [Removing parentheses]

= 78 - [24 – 14]                      [Removing braces]

= 78 - 10

= 68.

3. Simplify: 197 - [1/9{42 + (56 - 8 + 9)} +108]

Solution:

197 - [1/9 {42 + (56 - 8 + 9)} +108]

= 197 – [1/9 {42 + (56 – 17)} + 108]       [Removing vinculum]

= 197 - [1/9 {42 + 39} + 108]                [Removing parentheses]

= 197 - [(81/9) + 108]                          [Removing braces]

= 197 - [9 + 108]

= 197 - 117

= 80

4. Simplify: 39 – [23 – {29 – (17 – 9 – 3)}]

Solution:

39 - [23 - {29 – (17 – 9 – 3)}]

= 39 - [23 - {29 - (17 - 6)} ]      [Removing vinculum]

= 39 - [23 - {29 - 11}]              [Removing parentheses]

= 39 - [23—18]                         [Removing braces]

= 39 – 5

= 34

5. Simplify:

(i) 15 - (-5) {4 - 7 - 3} ÷ [3{5 + (-3) x (-6)}]

Solution:

15 - (-5) {4 - 7 - 3} ÷ [3{5 + (-3) x (-6)}]

= 15 - (-5) {4 - 4} ÷ [3 {5 + 18}]

= 15 - (-5) x 0 ÷ 3 x 23

= 15 - (-5) x 0 ÷ 69

= 15 - (-5) x 0       [Performing division 0 ÷ 69 = 01]

= 15

(ii) 95 - [144 ÷ (12 x 12) - (-4) - {3 – 17 - 10}]

Solution:

95 - [144 ÷ (12 x 12) - (-4) - {3 - 17 - 10}]

= 95 - [144 ÷ (12 x 12) - (-4) - {3 -7}]

= 95 - [144 ÷ 144 - (-4) - {3-7)]

= 95 - [1 - (-4) - (-4)] [Performing division]

= 95 - [1 + 4 + 4]

= 95 - 9

= 86

Students can practice these examples on simplification which are discussed here step by step and then proceed to the worksheet for more practice.