# 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.

Numbers - Integers

Integers

Multiplication of Integers

Properties of Multiplication of Integers

Examples on Multiplication of Integers

Division of Integers

Absolute Value of an Integer

Comparison of Integers

Properties of Division of Integers

Examples on Division of Integers

Fundamental Operation

Examples on Fundamental Operations

Uses of Brackets

Removal of Brackets

Examples on Simplification

Numbers - Worksheets

Worksheet on Multiplication of Integers

Worksheet on Division of Integers

Worksheet on Fundamental Operation