| Concept | Description / Formula | Details |
| BODMAS Rule | Sequence of operations to solve expressions. | B – Bracket ( ), { }, [ ]O – of D – Division M – Multiplication A – Addition S – Subtraction |
| Modulus | The absolute value of a real number $a$. | $ |
| Virnaculum (Bar) | A horizontal line over an expression. | Simplify the expression under the bar before applying the BODMAS rule. |
1. ‘BODMAS’ Rule
This rule depicts the correct sequence in which the operations are to be executed, so as to find out the value of given expression.
| Letter | Meaning | Operation |
| B | Bracket | Remove in order: (), { }, [ ] |
| O | of | Multiplication (as “of”) |
| D | Division | / |
| M | Multiplication | * |
| A | Addition | + |
| S | Subtraction | - |
Note: In simplifying an expression, first of all the brackets must be removed, strictly in the order
(),{ }and[ ]. After removing the brackets, operations must follow the order: (i) of (ii) Division (iii) Multiplication (iv) Addition (v) Subtraction.
2. Modulus of a Real Number
Modulus of a real number $a$ is defined as:
$$|a| = \begin{cases} a, & \text{if } a > 0 \\ -a, & \text{if } a < 0 \end{cases}$$
Examples:
- $|5| = 5$
- $|-5| = -(-5) = 5$
3. Virnaculum (or Bar)
When an expression contains Virnaculum, before applying the ‘BODMAS’ rule, we simplify the expression under the Virnaculum.
| Property Number | Formula |
| 1. | $\sqrt{xy} = \sqrt{x} \times \sqrt{y}$ |
| 2. | $\sqrt{\frac{x}{y}} = \frac{\sqrt{x}}{\sqrt{y}} = \frac{\sqrt{x}}{\sqrt{y}} \times \frac{\sqrt{y}}{\sqrt{y}} = \frac{\sqrt{xy}}{y}$ |
