Brackets are symbols used in mathematics to group numbers or algebraic expressions together. They tell us which operations to do first when solving a problem.

• Round brackets ( ) – also called parentheses.


• Square brackets [ ] – used to group expressions within round brackets.


• Curly brackets { } – used for larger grouping when multiple brackets are involved.

• To indicate the order of operations.


• To clarify which part of the expression should be simplified first.


• To avoid ambiguity in expressions.

When brackets are present, always solve the expression inside the brackets first, then follow the normal order of operations (BODMAS):

• B – Brackets


• O – Orders (powers, roots)


• D – Division


• M – Multiplication


• A – Addition


• S – Subtraction

Examples

Example 1: Evaluate 5 + (3 + 2)

Step 1: Solve inside the bracket first: 3 + 2 = 5

Step 2: Add the result to 5: 5 + 5 = 10

Example 2: Evaluate (8 − 3) × 2

Step 1: Brackets first: 8 − 3 = 5

Step 2: Multiply: 5 × 2 = 10

Example 3: Evaluate 12 ÷ (2 + 4)

Step 1: Brackets: 2 + 4 = 6

Step 2: Division: 12 ÷ 6 = 2

Example 4: Evaluate 7 + [3 × (4 − 2)]

Step 1: Inner brackets: 4 − 2 = 2

Step 2: Multiply: 3 × 2 = 6

Step 3: Add 7: 7 + 6 = 13

Example 5: Evaluate [8 + (5 − 3)] × 2

Step 1: Inner brackets: 5 − 3 = 2

Step 2: Add: 8 + 2 = 10

Step 3: Multiply by 2: 10 × 2 = 20

Example 6: Evaluate 15 − [2 × (3 + 4)]

Step 1: Inner brackets: 3 + 4 = 7

Step 2: Multiply by 2: 2 × 7 = 14

Step 3: Subtract from 15: 15 − 14 = 1

Important Notes

• Always solve the innermost brackets first if there are multiple layers.


• Brackets do not change the numbers; they only indicate which operations to perform first.


• Use brackets to avoid mistakes in complex calculations.