 ## Brackets | BODMAS Rule

Brackets are the symbols used to enclose a group of symbols or numbers that are to be taken together. Brackets can be nested so that the whole content of the inner bracket is treated as single term in the larger bracket. Brackets can be used to change the order in which operations are to be done. For example, 7×2+3 will be 14+3=17. If the sum intended is 7×5=35 then brackets can be put round 2+3 so that the sum is taken before the product, i.e. 7×(2+3).

### Types of brackets

(   )   Parenthesis or small brackets
{  }   Middle brackets or curly brackets
[   ]   Big brackets or square brackets

While simplifying integers under the relation of basic operations ÷, ×, +, - and with brackets, we need to follow the BODMAS rule.

The ways to simplify mathematical problems are as follows in the same order.

 1 V Vinculum ¯¯¯ 2 B Brackets [{()}] 3 O Of × 4 D Division ÷ 5 M Multiplication × 6 A Addition + 7 S Subtraction -

### Workout Examples

Example 1: Simplify: 54 ÷ [{16 – (3 – 2)} – 6]

Solution:             54 ÷ [{16 – (3 – 2)} – 6]
= 54 ÷ [{16 – 1} – 6]
= 54 ÷ [15 – 6]
= 54 ÷ 9
= 6 Ans.

Example 2: Simplify: 13 × 5 ÷ [{12 ÷ (4 – 2)} – 2]

Solution:             13 × 5 ÷ [{12 ÷ (4 – 2)} – 1]
= 13 × 5 ÷ [{12 ÷ 2} – 1]
= 13 × 5 ÷ [6 – 1]
= 13 × 5 ÷ 5
= 13 × 1
= 13 Ans.

Example 3: Simplify: 8 × 3 + [63 ÷ {18 ÷ 3 (9 – 17 + 5 × 2)}]

Solution:             8 × 3 + [63 ÷ {18 ÷ 3 (9 – 17 + 5 × 2)}]
= 8 × 3 + [63 ÷ {18 ÷ 3 (9 – 17 + 10)}]
= 8 × 3 + [63 ÷ {18 ÷ 3 of 2}]
= 8 × 3 + [63 ÷ {18 ÷ 6}]
= 8 × 3 + [63 ÷ 3]
= 8 × 3 + 21
= 24 + 21
= 45 Ans.

You can comment your questions or problems regarding simplification of integers here.