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Common denominator and ordering fractions
Lesson: Common Denominator & Ordering Fractions
Year 7 — common denominators and ordering fractions (UK curriculum).
1. Why we need a common denominator
To compare, add or subtract fractions we must write them with the same denominator. A common denominator makes the fractions easier to work with.
Example:
Compare 2/5 and 3/8 — use a common denominator first.
2. How to find a common denominator
Method A — Use the Lowest Common Multiple (LCM)
Find the LCM of the denominators. This gives the least common denominator (LCD).
For 2/5 and 3/8: denominators 5 and 8 → LCM = 40. Convert:
2/5 = (2×8)/(5×8) = 16/40
3/8 = (3×5)/(8×5) = 15/40
Method B — Multiply the denominators (quick but not always smallest)
Multiply denominators when LCM is hard to spot: 5×8 = 40. This also works but may not give the smallest numbers.
3. Ordering fractions (steps)
- Find a common denominator (LCM of the denominators).
- Convert each fraction to have that denominator.
- Compare the numerators — the larger numerator means the larger fraction.
Example: Order 2/5, 3/8 and 7/20 from smallest to largest.
Denominators: 5, 8, 20 → LCM = 40.
2/5 = 16/40, 3/8 = 15/40, 7/20 = 14/40
Numerators: 16, 15, 14 → order: 7/20 < 3/8 < 2/5.
4. Quick checks and tips
- If one denominator is a multiple of another (e.g. 4 and 12), use the larger denominator as common denominator.
- Always simplify at the end if needed.
- Use number lines for a visual check — place fractions on the number line to compare.
5. Practice
- Order these from smallest to largest:
3/4,5/6,7/8. - Order these:
2/3,5/9,3/6. - Put in order:
1/2,3/10,4/7. - Compare and state which is greater:
5/12or2/5(show working). - Find a common denominator and write equivalents:
3/8and5/12.
Answers (teacher)
3/4 < 5/6 < 7/8- Denominators 3, 9, 6 → LCM = 18.
2/3=12/18, 5/9=10/18, 3/6=9/18→3/6 < 5/9 < 2/3. - Denominators 2, 10, 7 → LCM = 70.
1/2=35/70, 3/10=21/70, 4/7=40/70→3/10 < 1/2 < 4/7. - Compare
5/12and2/5: LCM 60 →5/12=25/60, 2/5=24/60→5/12 > 2/5. - LCM of 8 and 12 is 24:
3/8=9/24, 5/12=10/24.