Ordering Fractions – Smallest to Largest and Back
Ordering fractions means arranging a set of fractions from smallest to largest (ascending) or from largest to smallest (descending). The two most reliable methods are finding a common denominator and converting to decimals.
Method 1 – Common Denominator
- Find the LCM of all the denominators.
- Convert every fraction to an equivalent fraction with that denominator.
- Order by numerator.
- Rewrite in the original form.
Order 1/2, 2/3, 3/8 from smallest to largest
LCM(2,3,8) = 24. Convert: 1/2 = 12/24, 2/3 = 16/24, 3/8 = 9/24.
Order of numerators: 9, 12, 16 → order: 3/8, 1/2, 2/3.
Method 2 – Decimal Conversion
Order 5/6, 3/4, 7/10, 2/3
5/6 ≈ 0.833, 3/4 = 0.75, 7/10 = 0.7, 2/3 ≈ 0.667.
Ascending: 0.667, 0.7, 0.75, 0.833 → 2/3, 7/10, 3/4, 5/6.
Mixed Sets – Including Improper Fractions and Mixed Numbers
Order 2½, 7/3, 8/4, 1¾
Convert to decimals: 2.5, 2.333, 2.0, 1.75.
Ascending: 1¾, 8/4, 7/3, 2½
Ordering on a Number Line
Once fractions are converted to decimals, they slot naturally onto a number line. Mark each value as a point, read left to right for ascending, right to left for descending.
Key Takeaways
- Common denominator method: find LCM, convert, compare numerators.
- Decimal method: divide numerator by denominator, then order.
- Always check your final order by confirming each consecutive pair.
- Mixed numbers and improper fractions can be included by converting to decimals first.
Practice Questions
- Order 3/4, 2/5, 7/10 in ascending order.
- Order 5/6, 11/12, 3/4, 2/3 in descending order.
- Order 1⅓, 4/3, 7/6 in ascending order.
- A recipe calls for 2/3 cup A, 3/4 cup B, and 5/8 cup C. Which ingredient requires the most?
- Insert in ascending order: 7/8, 5/6, 11/15, 4/5.