What does it mean to order fractions?
Ordering fractions means arranging them from least to greatest or from greatest to least. To do this, we compare the size of different fractions.
- From least to greatest: 14, 12, 34
- From greatest to least: 56, 23, 13
A fraction represents a part of a whole. When ordering, you are finding which part is smaller or larger.
Compare fractions with the same denominator
When fractions have the same denominator (the bottom number), you look at the numerator (the top number). The fraction with the larger numerator is the larger fraction.
Compare 38 and 58.
- Denominators are the same (8).
- Compare numerators: 3 and 5.
- Since 3 < 5, then 38 < 58.
The denominator tells you how many equal parts the whole is split into. If the parts are the same size, more parts means a larger fraction.
Compare fractions with the same numerator
When fractions have the same numerator (the top number), you look at the denominator. The fraction with the smaller denominator is the larger fraction.
Compare 25 and 23.
- Numerators are the same (2).
- Compare denominators: 5 and 3.
- If you have the same number of parts (2), but the parts are bigger when the denominator is smaller (3).
- Therefore, 23 > 25.
Think of sharing a pizza. If you get 2 slices from a pizza cut into 3 big slices, that's more than 2 slices from a pizza cut into 5 smaller slices.
Use models and number lines to order fractions
Drawing pictures, using fraction strips, or placing points on a number line are powerful tools to see the size of fractions and order them correctly.
To order 14, 34, and 12:
- Mark each fraction on the same number line from 0 to 1.
- You will see: 14 comes first, then 12, then 34.
- Order from least to greatest: 14, 12, 34.
Visual models help you understand fractions as numbers with a specific place between 0 and 1, or beyond. Always draw your models accurately with equal parts.
Strategies for ordering any set of fractions
Follow these steps to successfully order fractions, especially when they have different numerators and denominators.
- Step 1: Look for benchmarks. Compare each to 0, 12, and 1. 13 is less than 12. Both 36 and 24 are equal to 12.
- Step 2: Use models or equivalence. Draw fraction strips. You'll see 13 is the smallest. The other two are the same size.
- Step 3: State the order. Least to greatest: 13, 24, 36 (or 36, 24).
Knowing that 12 is a useful benchmark is key. Also, remember that different fractions can represent the same amount, like 12 = 24 = 36.