Ordering (Copy)

IGCSE CORE Mathematics Cheat Sheet: Ordering Quantities & Inequality Symbols

1. Ordering Quantities by Magnitude

• Magnitude refers to the size or value of a number, regardless of sign.
• To order quantities, arrange numbers from smallest to largest or largest to smallest.
• Be careful when comparing:
  • Negative numbers (the number closer to zero is greater).
  • Fractions, decimals, percentages (convert to the same form for easy comparison).

Examples of Ordering:

• Order these numbers in ascending order:
  -3, 0, 2, -1, 4
  Answer: -3, -1, 0, 2, 4
• Order 0.5, ⅓, 45%, 0.25 from smallest to largest:
  Convert all to decimals:
  0.5 = 0.5
  ⅓ ≈ 0.333
  45% = 0.45
  0.25 = 0.25
  Order: 0.25, ⅓, 45%, 0.5

2. Inequality Symbols and Their Meanings

3. Using Inequalities in Context

• Example 1:
  Write using symbols:
  “5 is greater than 2” → 5 > 2
• Example 2:
  If x must be at least 7 → x ⩾ 7
• Example 3:
  If y is less than or equal to 12 → y ⩽ 12

4. Common Mistakes to Avoid

• Remember that -2 > -5 (closer to zero is greater for negative numbers).
• Always convert fractions, decimals, and percentages into the same form before comparing.
• Do not confuse > (greater than) with ⩾ (greater than or equal to).

5. Examples

• Compare using <, >, or =:
  a) 0.6 ___ ⅗
  Convert ⅗ = 0.6 → 0.6 = 0.6
• Insert the correct symbol:
  a) 7 ___ 10 → 7 < 10
  b) -4 ___ -6 → -4 > -6
• Write the inequality:
  A number x is greater than 3 → x > 3

6. Quick Reference Table

7. Tips for Exams

• When ordering mixed numbers (fractions, decimals, percentages), convert everything to decimals.
• Always double-check inequality directions:
  • The wide side opens towards the bigger number.
• Negative numbers can be tricky—remember -1 > -5.
• Practice rewriting word statements as inequalities for better understanding.