The four Operations (Copy)

IGCSE CORE Mathematics Cheat Sheet: Four Operations with Integers, Fractions, Decimals & Practical Applications

1. The Four Basic Operations

• Addition (+)
• Subtraction (−)
• Multiplication (×)
• Division (÷)

These operations apply to:

• Integers (positive & negative numbers)
• Fractions (proper, improper, mixed numbers)
• Decimals

2. Order of Operations (BIDMAS / PEMDAS)

When performing calculations, always follow this order:

1. Brackets
2. Indices (Powers, Squares, etc.)
3. Division and Multiplication (left to right)
4. Addition and Subtraction (left to right)

Example:
6 + 4 × (3 − 1)
= 6 + 4 × 2
= 6 + 8 = 14

3. Working with Negative Numbers

4. Fractions

• Addition & Subtraction:
  1. Find a common denominator.
  2. Add/Subtract numerators.
  3. Simplify if possible.

  Example:
  2/3 + 1/6 = (4/6) + (1/6) = 5/6

• Multiplication: Multiply top × top and bottom × bottom.
  Example:
  3/4 × 2/5 = 6/20 = 3/10
• Division: Multiply by the reciprocal of the second fraction.
  Example:
  5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12 = 5/4
• Mixed Numbers: Convert to improper fractions before multiplying or dividing.

  Example:
  1 ½ × 2 ⅓ = (3/2) × (7/3) = 7/2 = 3 ½

5. Decimals

• Addition/Subtraction:
  • Line up decimal points.
• Multiplication:
  • Ignore decimal points, multiply normally, then place the decimal back.

  Example:
  1.2 × 3.4 → 12 × 34 = 408 → 4.08

• Division:
  • Move decimal to make divisor whole, then divide.

  Example:
  4.8 ÷ 0.6 → 48 ÷ 6 = 8

6. Improper Fractions & Mixed Numbers

• Improper → Mixed:
  Divide numerator by denominator.
  Example: 11/4 = 2 ¾
• Mixed → Improper:
  Multiply whole number by denominator and add numerator.
  Example: 3 ²⁄₅ = (3×5)+2 = 17/5

7. Practical Situations (e.g., Temperature & Real-Life Contexts)

• Temperature Change Example:
  If temperature is 4°C and drops by 9°C:
  4 − 9 = −5°C
• Elevation Example:
  A submarine is at −200m and descends another 150m:
  −200 − 150 = −350m
• Bank Balance Example:
  You have $50, spend $70:
  50 − 70 = −$20 (overdraft)

8. Example Calculations

• Simplify:
  −3 + 5 × 2
  Apply BIDMAS: 5 × 2 = 10
  −3 + 10 = 7
• Calculate:
  2 ¼ + 1 ⅓
  Convert: 9/4 + 4/3 = (27/12) + (16/12) = 43/12 = 3 7/12
• Work out:
  3.5 × 0.4 = 1.40

9. Quick Rules Table

10. Tips for Exams

• Always apply BIDMAS—brackets first!
• For negative numbers, double-check signs after multiplying/dividing.
• Convert mixed numbers to improper fractions when calculating.
• With decimals, carefully count decimal places after multiplying.
• Simplify your final answers, especially with fractions.
• For word problems, translate the situation into mathematical operations correctly, especially for temperature, money, or distance problems involving negatives.