BODMAS And Simplification Of Brackets

As per BODMAS rule, we have to calculate the expressions given in the brackets first. The full form of BODMAS is Brackets, Orders, Division, Multiplication, Addition and Subtraction. Hence, second preference in BODMAS is given here to the orders or exponents (xⁿ).  Later we perform the arithmetic operations (÷, ×, +, -). We will solve examples based on this rule in the below sections.

An arithmetic expression that involves multiple operations such as addition, subtraction, multiplication, and division are not easy to solve as compared to operations involving two numbers. An operation on two numbers is easy, but how to solve an expression with brackets and multiple operations and how to simplify a bracket? Let’s recollect the BODMAS rule and learn about the simplification of brackets.

What is BODMAS RULE?

BODMAS is an acronym and it stands for Bracket, Order, Division, Multiplication, Addition, and Subtraction. In certain regions, PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction) is used, which is the synonym of BODMAS.

It explains the order of operations to be performed while solving an expression. According to BODMAS rule, if an expression contains brackets ((), {}, []) we have first to solve or simplify the bracket followed by ‘order’ (that means powers and roots, etc.), then division, multiplication, addition and subtraction from left to right. Solving the problem in the wrong order will result in a wrong answer.

Note: The “O” in the BODMAS full form is also called “Order”, which refers to the numbers which involve powers, square roots, etc. Check the examples below to have a better understanding of using the BODMAS rule.

SIMPLIFICATION OF BRACKETS

Simplification of terms inside the brackets can be done directly. That means we can perform the operations inside the bracket in the order of division, multiplication, addition and subtraction.

Note: The order of brackets to be simplified is (), {}, [].

Example 2: Simplify: 14 + (8 – 2 × 3)

Solution: 14 + (8 – 2 × 3)

= 14 + (8 – 6)

= 14 + 2

= 16

Therefore, 14 + (8 – 2 × 3) = 16.

Example 3: Simplify the following.

(i) 1800÷10{(12−6)+(24−12)}

(ii) 1/2[{−2(1+2)}10]

Solution:

(i) 1800÷10{(12−6)+(24−12)}

Step 1: Simplify the terms inside {}.

Step 2: Simplify {} and operate with terms outside the bracket.

1800÷10{(12−6)+(24−12)}

1800÷10{6+12}

⇒1800÷10{18}

= 1800÷10×18
= 180×18
= 3,240

(ii) 1/2[{−2(1+2)}10]

Step 1: Simplify the terms inside () followed by {}, then [].

Step 2: Operate terms with the terms outside the bracket.

1/2[{−2(1+2)}10]

= 1/2 [{-2(3)} 10]

= 1/2 [{-6} 10]

= 1/2 [-60]

= -30

Conditions and Rules

A few conditions and rules for general simplification are given below: