Ordering
O Level and IGCSE Mathematics Cheat Sheet – 1.5 Ordering
Key Comparison Symbols
| Symbol | Meaning | Example |
|---|---|---|
| = | Equal to | 7 = 7 |
| ≠| Not equal to | 5 ≠8 |
| > | Greater than | 9 > 3 |
| < | Less than | 2 < 5 |
| ≥ (⩾) | Greater than or equal to | x ≥ 4 means x = 4 or x > 4 |
| ≤ (⩽) | Less than or equal to | y ≤ 7 means y = 7 or y < 7 |
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
Ordering Numbers
- Arrange from smallest to largest (ascending) or largest to smallest (descending).
- Compare place value for whole numbers.
- For decimals: Compare digits from left to right after the decimal point.
- For negative numbers: More negative = smaller.
Examples:
- Ascending: 3, 5, 12, 19
- Descending: 0.8, 0.7, 0.65, 0.6
- Negative order: −8, −3, 0, 2
Ordering Fractions
- Convert all to common denominator before comparing.
- Example: Order 2/3, 3/4, 5/6
- LCM of denominators (3, 4, 6) = 12
- 2/3 = 8/12, 3/4 = 9/12, 5/6 = 10/12
Order: 2/3 < 3/4 < 5/6
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
Ordering Decimals
- Compare whole number part first, then decimal part digit-by-digit.
- Example: 0.58, 0.6, 0.59 → Order: 0.58 < 0.59 < 0.6
Ordering Percentages
- Convert percentages to decimals or fractions for comparison.
- Example: 40%, 0.38, 39%
- 40% = 0.40, 39% = 0.39
Order: 0.38 < 39% < 40%
- 40% = 0.40, 39% = 0.39
Mixed Forms Ordering
- Convert all to the same form (decimal/fraction/percentage) before comparing.
- Example: 3/5, 62%, 0.65
- 3/5 = 0.6, 62% = 0.62
Order: 3/5 < 62% < 0.65
- 3/5 = 0.6, 62% = 0.62
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
Exam Special Tips
- Always convert recurring decimals to fractions for exact comparison in non-calculator questions.
- Watch for negative values—the one with the higher magnitude but negative sign is smaller.
- Use a number line for clarity in tricky ordering questions.
Common Mistakes & Confusions
- Forgetting to compare whole number first in decimals (e.g., thinking 0.58 > 0.6).
- Misplacing numbers when converting mixed forms.
- Treating −2 as larger than −1 (wrong — −1 is larger).