Simplification of Brackets

Brackets in mathematics work like “boxes within boxes”. They help us decide which calculation to perform first, ensuring that our answers are correct and the solution process is well organised.

1. If an expression contains a single set of brackets, evaluate that part first.
2. If an expression contains two or more sets of brackets, one inside the other, evaluate the innermost set first.
3. For simplifying a given expression involving various operations, the rule of BODMAS is used, where
   B = Brackets, O = Of, D = Division, M = Multiplication, A = Addition and S = Subtraction

24 − (6 + 8) − 3

= 24 − 14 − 3

= 10 − 3

= 7

[12 + (9 ÷ 3)] − 4²

= [12 + (`"9"/"3"`)] − 16

=  [12 + 3] − 16

= 15 − 16

= −1 

[21 − (4 + 5) + 2] × 2

= [21 − 9 + 2] × 2

= [12 + 2] × 2

= 14 × 2

= 28 

Simplify: 28 − [19 − {14 − (10 − 2)}]

Solution:

28 − [19 − {14 − (10 − 2)}]

= 28 − [19 − {14 − 8}]        [Simplifying small brackets, i.e., ( )]

= 28 − [19 − 6]                     [Simplifying curly brackets, i.e., { }]

= 28 − 13                              [Simplifying square brackets, i.e., [ ]]

= 15

Simplify: 14 − [7 − {8 + 28 ÷ (3 − `bar" 4 - 3"`)}]

= 14 − (7 − {8 + 28 ÷ (3 − 1)}]   [Simplifying bar bracket]

= 14 − [7 − {8 + 28 ÷ 2}]             [Simplifying ( )]

= 14 − (7 − {8 + 14}]                    [28 ÷ 2 = `28/2` = 14]

= 14 − (7 − 22)                              [Simplifying { }]

= 14 + 15                                       [− [7 − 22] = −7 + 22 = 15]

= 29

Story Problem: Priya has 50 colouring pencils. She packs them into [10 boxes]. In each box, she gives away {4 pencils and then (adds 3 pencils)}. How many pencils does Priya have in total?

Expression: $50+[10-\{4+(3)\; \}\; ]$

• (3) = 3

• {4 + 3} = 7

• [10 − 7] = 3

• 50 + 3 = 53

Priya has 53 pencils.

• Always follow the bracket order: Bar → ( ) → { } → [ ]

• Use BODMAS in every multi-operation problem.

• Work step by step and double-check each stage for sign or copying errors.