Fractions, Decimals and Percentages (Copy)

IGCSE CORE Mathematics Cheat Sheet: Fractions, Decimals, and Percentages

1. Proper Fractions, Improper Fractions, and Mixed Numbers

• Proper Fraction:
  A fraction where the numerator is less than the denominator.
  Example: 3/5, 7/10
• Improper Fraction:
  A fraction where the numerator is greater than or equal to the denominator.
  Example: 9/4, 7/3
• Mixed Number:
  A whole number combined with a proper fraction.
  Example: 2 ¼, 5 ²⁄₃

2. Conversion Between Fractions and Mixed Numbers

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

3. Simplifying Fractions

• Divide numerator and denominator by their Highest Common Factor (HCF).
  Example:
  12/20 → divide by 4 → 3/5

4. Decimals

• Definition: A number with a decimal point separating the whole part from the fractional part.
  Example: 0.75, 3.4
• Common Fraction to Decimal Conversions:

• To Convert Fraction → Decimal:
  Divide numerator by denominator.
  Example: 3/4 = 3 ÷ 4 = 0.75

5. Percentages (%)

• Definition: A percentage is a fraction out of 100.
  Example: 25% = 25/100 = 0.25
• Key Conversions:

6. Conversion Rules

• Fraction → Percentage:
  Multiply by 100.
  Example: 3/5 × 100 = 60%
• Decimal → Percentage:
  Multiply by 100.
  Example: 0.4 × 100 = 40%
• Percentage → Decimal:
  Divide by 100.
  Example: 75% ÷ 100 = 0.75
• Percentage → Fraction:
  Write over 100 and simplify.
  Example: 40% = 40/100 = 2/5
• Decimal → Fraction:
  Place over 10, 100, etc., depending on decimal places, then simplify.
  Example: 0.2 = 2/10 = 1/5

7. Examples

• Convert 7/8 to a percentage:
  7 ÷ 8 = 0.875
  0.875 × 100 = 87.5%
• Convert 0.6 to a fraction:
  0.6 = 6/10 = 3/5
• Convert 65% to decimal:
  65 ÷ 100 = 0.65
• Convert 2 ¼ to an improper fraction:
  (2×4) + 1 = 9/4
• Simplify 18/24:
  Divide by 6 → 3/4

8. Quick Reference Table

9. Tips for Exams

• Always simplify fractions unless told otherwise.
• Convert to the form asked in the question.
• Remember:
  • % → ÷100,
  • Decimal to % → ×100.
• Be careful with mixed number conversions—practice both ways.
• No need to handle recurring decimals in Core syllabus.