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\\October 8, 2025 12:09 PM Bharat Arora P-9 Reader _________________________ Date: ___________________74

bodMaS

Sometimes, in numerical expressions, we need to group the operations. To do this, we
use various symbols called brackets. So, we can say, brackets are grouping symbols. We
generally use the following brackets for grouping.
( a) ( ): Parentheses or round brackets Knowledge Desk

( b) { }: Braces or curly brackets In English, parentheses are

( c) [ ]: Square brackets or box brackets used to show an alternative
or option, but in Maths,
( d) : Line brackets or bar brackets or vinculum parentheses are used to group
When there are nested brackets, we always solve them numbers.
in the following order:
Bar brackets Parentheses ( ) Curly brackets { } Square brackets [ ]

In the order of simplification of numerical expressions along with brackets, we use the
BOdMAS rule, where B stands for brackets.
B Brackets [{( )}]
O Of
d Division (÷)

M Multiplication (×)
Solve Solve Solve Solve A Addition (+)
1st 2nd 3rd last S Subtraction (–)

example 1: Simplify the following.
( a) 87 – [46 – {14 ÷ (8 – 1)}] (b) {59 + (16 × 3 – 14)} + 99 ÷ 9

Solution: (a) 87 – [46 – {14 ÷ (8 – 1)}]
= 87 – [46 – {14 ÷ 7}] (Subtraction: 8 – 1, in the parentheses)

= 87 – [46 – 2] (Division: 14 ÷ 7, in the curly brackets)

= 87 – 44 (Subtraction: 46 – 2, in the square brackets)
= 43 (Subtraction: 87 – 44)

(b) {59 + (16 × 3 – 14)} + 99 ÷ 9
= {59 + (48 – 14)} + 99 ÷ 9 (Multiplication: 16 × 3 in the parentheses)

= {59 + 34} + 99 ÷ 9 (Subtraction: 48 – 14 in the parentheses)

= 93 + 99 ÷ 9 (Addition: 59 + 34 in the curly brackets)
= 93 + 11 (Division: 99 ÷ 9)

= 104 (Addition: 93 + 11)

teacher’s Explain to the students by taking an example that if there is an ‘of’ operation in a numerical expression, it is
tip the same as the multiplication of two numbers.

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