The Four Operations

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Use the four operations for calculations with integers, fractions and decimals, including correct ordering of operations and use of brackets.
  2. Work with negative numbers, improper fractions, mixed numbers, and apply these skills to practical situations like temperature changes.

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What Are The Four Operations?

The four operations are the basic calculations we use in mathematics:

  • Addition (+): Adding numbers together (also called finding the sum or total)
  • Subtraction (−): Taking one number away from another (also called finding the difference)
  • Multiplication (×): Repeated addition or finding the product of numbers (also called "times")
  • Division (÷): Sharing or splitting a number into equal parts (also called finding the quotient)

These operations work with all types of numbers: whole numbers (integers), fractions, decimals, and negative numbers.

Order of Operations: BODMAS/BIDMAS

When a calculation has more than one operation, you must do them in a specific order. If you don't follow this order, you'll get the wrong answer.

BODMAS (or BIDMAS) helps you remember the correct order:

  • Brackets — Do anything inside brackets first
  • Orders or Indices — Powers (like 5²), roots (like √25), and other indices
  • Division and Multiplication — Work from left to right
  • Addition and Subtraction — Work from left to right

Important notes:

  • Division and multiplication have equal priority — do whichever comes first when reading left to right
  • Addition and subtraction have equal priority — do whichever comes first when reading left to right
  • Operators also include trigonometric functions (sin, cos, tan) and should be calculated before multiplication

Example 1: Simple BODMAS

Calculate: 18 − 2 × 3 + 4

Solution:

  1. No brackets or powers, so start with multiplication: 2 × 3 = 6
  2. The calculation becomes: 18 − 6 + 4
  3. Now work left to right: 18 − 6 = 12
  4. Then: 12 + 4 = 16

Answer: 16

Common mistake: Don't add 6 + 4 first to get 10, then do 18 − 10 = 8. This is wrong because you must work left to right for addition and subtraction.

Example 2: With Powers

Calculate: 3 × 2³

Solution:

  1. Powers come before multiplication (remember BODMAS)
  2. First calculate: 2³ = 2 × 2 × 2 = 8
  3. Then multiply: 3 × 8 = 24

Answer: 24

Common mistake: Don't multiply first (3 × 2 = 6) then cube it (6³ = 216). Powers must be calculated before multiplication.

Example 3: With Brackets

Calculate: (5 − 3) + 2 × 7²

Solution:

  1. Brackets first: 5 − 3 = 2, so the calculation becomes: 2 + 2 × 7²
  2. Powers next: 7² = 49, giving us: 2 + 2 × 49
  3. Multiplication: 2 × 49 = 98, giving us: 2 + 98
  4. Addition: 2 + 98 = 100

Answer: 100

Invisible Brackets

Sometimes brackets are "invisible" but still apply:

With fractions: The fraction line acts like brackets around the top (numerator) and bottom (denominator).

Example: (2 + 5)/(7 − 2) means (2 + 5) ÷ (7 − 2)

  • Calculate top: 2 + 5 = 7
  • Calculate bottom: 7 − 2 = 5
  • Then divide: 7 ÷ 5 = 1.4

With roots: The line over the root symbol acts like brackets.

Example: √(9 + 16) means find the square root of the entire sum

  • Calculate inside: 9 + 16 = 25
  • Then find the root: √25 = 5

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