### GCSE Maths

Numbers
Algebra
Geometry and Measures
Probability
Statistics

# Order of Operations

To evaluate expressions with multiple operations, we need to perform these operations in the correct order. The order of operations can be remembered using the acronym BIDMAS:

Brackets, Indices, Division and Multiplication, Addition and Subtraction.

Let’s look at an expression: To evaluate this expression, we’ll follow the BIDMAS rule:

1. Brackets: , which gives us 2. Indices: , which is 3. Division: , which is 4. Multiplication: and 5. Addition: 6. Subtraction: Therefore, Let’s look at some more examples.

## Examples

Example 1:

Evaluate the following expressions:

a) b) a)    b)     Example 2:

Find the value of  , since is done first.  Example 3:

Find the value of First, Next, To simplify, multiply the numerator and denominator by 3: Example 4: First, evaluate the power: Next, perform the division and multiplication: Now, simplify the expression:   Example 5:

Evaluate    Example 6:

When there are more brackets within brackets, perform the innermost brackets first and move outwards. For example, to evaluate: 1. First, evaluate the innermost bracket: 2. Now, the expression becomes: 3. Evaluate the power: 4. Simplify the expression within the bracket: 5. The expression becomes: 6. Evaluate the power: 7. Finally, simplify the expression: 8. The result is: Example 7:

Evaluate 1. First, evaluate the power: 2. Next, perform the division: 3. Now, simplify the expression with multiplication: 4. Finally, simplify the expression with subtraction: 