1. BODMAS Rule : This rule depicts the correct sequence in which the operation are to be executed, so as to find out the value of a given expression.

BODMAS is a short form for Bracket, Of, Division, Multiplication, Addition and Subtraction. In some regions, PEDMAS (Parentheses, Exponents, Division, Multiplication, Addition and Subtraction) is the synonym of BODMAS.

It explains the order of operations to solve an expression. According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (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.

Thus, in simplifying an expression, first of all the brackets must be removed, strictly in the order :

(i) of (ii) Division (iii) Multiplication (iv) Addition (v) Subtraction.

Note: The “of” 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.

2. Modulus of a Real Number : Modulus of a real number a is defined as

Thus, | 5 | = 5 and | -5 | = -(-5) = 5

The modulus of a positive number is simply the number.

The modulus of a negative number is found by ignoring the minus sign.

The modulus of a number is denoted by writing vertical lines around the number.

Note also that the modulus of a negative number can be found by multiplying it by −1 since, for example, −(−8) = 8.

3. Virnaculum (or Bar) : When an expression contains Virnaculum, before applying the ‘BODMAS’ rule, we simplify the expression under the Virnaculum.