The Four Operations

O Level and IGCSE Mathematics Cheat Sheet – 1.6 The Four Operations

The Four Operations

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course

Order of Operations (BODMAS)

• Brackets → Orders (powers, roots) → Division → Multiplication → Addition → Subtraction
• Work left to right for operations of the same priority.
• Example: 5 + 3 × 2 = 5 + 6 = 11 (not 16)
• Example: (5 + 3) × 2 = 8 × 2 = 16

Integers (Including Negatives)

• Adding a negative = subtraction
  Example: 5 + (−3) = 2
• Subtracting a negative = addition
  Example: 4 − (−2) = 4 + 2 = 6
• Multiplication & Division Rules:
  (+) × (+) = +, (+) × (−) = −, (−) × (+) = −, (−) × (−) = +

Fractions

• Addition/Subtraction: Find common denominator.
  Example: 2/3 + 1/6 = 4/6 + 1/6 = 5/6
• Multiplication: Multiply numerators & denominators.
  Example: 3/4 × 2/5 = 6/20 = 3/10
• Division: Multiply by reciprocal of the second fraction.
  Example: 5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12 = 5/4

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course

Improper Fractions & Mixed Numbers

• Mixed → Improper: (Whole × Denominator + Numerator)/Denominator
  Example: 2 ¹/₂ = (2×2+1)/2 = 5/2
• Improper → Mixed: Divide numerator by denominator.
  Example: 11/4 = 2 ³/₄

Decimals

• Line up decimal points when adding/subtracting.
• Ignore decimal points for multiplication, then place in result.
• For division, shift decimal points in both numbers to make divisor a whole number.

Practical Situations – Temperature Changes

• Example: If temperature drops from 5°C to −3°C:
  Change = −3 − 5 = −8°C
• Example: If temperature rises from −4°C to 3°C:
  Change = 3 − (−4) = 7°C rise.

Exam Special Tips

• Always apply BODMAS in all calculations, especially with negatives.
• In non-calculator papers, keep fractions until the final answer for accuracy.
• Brackets change priority—deal with them first.
• Double-check sign changes in subtraction involving negatives.

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course

Common Mistakes & Confusions

• Forgetting to multiply by reciprocal in fraction division.
• Adding/subtracting fractions without common denominator.
• Wrongly doing multiplication before division when they’re at the same step (must go left to right).
• Sign errors with negative numbers.