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)  {37)]
= 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
Properties of Multiplication of Integers
Examples on Multiplication of Integers
Properties of Division of Integers
Examples on Division of Integers
Examples on Fundamental Operations
● Numbers  Worksheets
Worksheet on Multiplication of Integers
Worksheet on Division of Integers
Worksheet on Fundamental Operation
7th Grade Math Problems
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