Fractions, decimals and percentsGrades 4–5
Ordering fractions worksheets
Every line lists four different fractions in scrambled order, and the student writes them from least to greatest on a blank. Choose the largest denominator and the number of lines, and print an answer key with the sorted sets.
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On this page
From comparing two to sorting four
Comparing two fractions needs one decision. Ordering four needs several, and a student must keep all of them in mind at once. That makes ordering a strong check on whether fraction sense has taken hold. It follows comparing fractions, and it is the fraction version of putting whole numbers on a number line.
The sheet suits fourth and fifth graders. Each line has four fractions followed by a long blank labeled "least to greatest", so the finished answer is a row of four fractions separated by commas.
What the generator does
Each set contains four proper fractions, all in simplest form, and no two of them are equal. That means there are never ties to explain, and a student never needs to decide whether 2/4 and 1/2 belong side by side. Fractions are scrambled on the page and sorted on the key.
Settings
- Largest denominator takes values from 4 to 20 and is the one setting that matters here. At 6 or 8, denominators such as 2, 3, 4 and 6 let a student find a common denominator quickly. At 12, sets like halves, thirds, fourths and twelfths appear. At 20, comparing without a plan is nearly impossible.
- Number of problems can be 8 to 30 lines. This page opens at 12, and each takes a full line, so a page holds plenty of work.
- Denominators within a set are drawn independently, so some sets have a shared denominator and many do not.
Worked example: 2/3, 3/5, 5/8 and 7/12
Imagine the line reads 2/3, 3/5, 5/8, 7/12.
- Find a denominator that all four divide into. The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120. 120 is the first one that 3, 5, 8 and 12 all divide into evenly.
- Rename each fraction with 120 as the denominator. 2/3 = 80/120 (multiply by 40). 3/5 = 72/120 (multiply by 24). 5/8 = 75/120 (multiply by 15). 7/12 = 70/120 (multiply by 10).
- Order the numerators: 70, 72, 75, 80.
- Translate back to the original fractions: 7/12, 3/5, 5/8, 2/3.
Not every set needs this much work. A student who notices that 7/12 is just above one half, while 2/3 is clearly larger than 5/8, can reason much of the order without finding 120. Encourage both approaches. Neither is wrong, as long as the answer matches the key.
Common errors
- Ordering by denominator. Writing the fractions according to denominator size, small to large, is the classic whole-number habit applied to fractions. Check whether the sorted line shows the same denominators in order.
- Ordering by numerator. A student who sorts 3/5, 5/8, 7/12 and 2/3 as 2, 3, 5, 7 has ignored the denominators.
- Right order, reversed. The sheet asks for least to greatest. Students who get the order backward are often rushing, not confused. Circle the label before they start.
- One fraction out of place. This usually points to an arithmetic slip while renaming. Have the student redo the common denominator for just the misplaced fraction.
Next steps
If the renaming step feels shaky, return to simplifying fractions, which strengthens equivalent fractions in the other direction. Subtraction is the next place a common denominator is required, and the unlike denominators subtraction sheet is a direct continuation.