Simplification of Numerical Expressions

We will discuss here about the simplification of numerical expressions. We know how to perform the four fundamental operations, that is namely, addition, subtraction, multiplication and division involving whole numbers, fractional numbers and decimals. We perform only one operation at a time. Now we will learn how to perform two or more operations together.

To simplify a numerical expression having two or more operations, we perform operation like: Division first, followed by Multiplication, Addition and then Subtraction. A standard result called BODMAS is applied for simplification of these operations.

The word BODMAS stands for:

B → Brackets

O → of means (Multiplication ×)

D → Division

M → Multiplication

A → Addition

S → Subtraction

If the brackets are present in the problem, we first simplify the brackets. There are four kind of brackets.

1. ( ) → simple brackets or round brackets or parenthesis.

2. { } → Braces or Curly brackets.

3. [ ] → Square brackets.

4. ______ → This is a line called bar, vinculum. If two or more types of brackets are involved in the problem, then they are removed in this order ‘_________’, ( ), { }, [ ].

Solved examples to simplify the numerical expressions:

Simplify the following:

(i) [12 + {7 - (8 ÷ 2)}] × 3

= [12 + {7 - 4}] × 3 (Round brackets removed)

= [12 + 3] × 3 (Curly brackets removed)

= 15 × 3 (Square brackets removed)

= 45

(ii) 14 + [22 - {8 + (6 ÷ 2)}]

= 14 + [22 - {8 + 3}] (Round brackets removed)

= 14 + [22 - 11] (Curly brackets removed)

= 14 + 11 (Square brackets removed)

= 25