Practice Ordering Fractions in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Ordering fractions means arranging a set of fractions from least to greatest (or greatest to least) by converting them to a common denominator or to decimals so their sizes can be directly compared.

Convert all fractions to a common denominator and then read off the order from the numerators.

Showing a random 20 of 50 problems.

Example 1

challenge
Five fractions all lie between 12\frac{1}{2} and 23\frac{2}{3}. Could 712\frac{7}{12} be one of them? Justify.

Example 2

easy
Order using the benchmark 12\frac{1}{2}: 13\frac{1}{3} and 23\frac{2}{3}.

Example 3

easy
Order 12\frac{1}{2}, 13\frac{1}{3}, and 14\frac{1}{4} from least to greatest.

Example 4

easy
Order least to greatest: 210,25,23\frac{2}{10}, \frac{2}{5}, \frac{2}{3}.

Example 5

hard
Four students reported they had completed 38,25,720\frac{3}{8}, \frac{2}{5}, \frac{7}{20}, and 925\frac{9}{25} of their reading. Order least to greatest.

Example 6

hard
Order least to greatest using cross-multiplication: 57,710\frac{5}{7}, \frac{7}{10}.

Example 7

medium
Use the benchmark 12\frac{1}{2} to order 49,611,37\frac{4}{9}, \frac{6}{11}, \frac{3}{7} least to greatest.

Example 8

easy
Which is largest: 12,16,13\frac{1}{2}, \frac{1}{6}, \frac{1}{3}?

Example 9

hard
Order least to greatest: 1720,45,910\frac{17}{20}, \frac{4}{5}, \frac{9}{10}.

Example 10

medium
Order least to greatest: 35\frac{3}{5}, 58\frac{5}{8}, 12\frac{1}{2}.

Example 11

medium
Order least to greatest: 23\frac{2}{3}, 34\frac{3}{4}, 58\frac{5}{8}.

Example 12

easy
Order least to greatest: 15,18,12\frac{1}{5}, \frac{1}{8}, \frac{1}{2}.

Example 13

hard
Order greatest to least: 920,49,1125\frac{9}{20}, \frac{4}{9}, \frac{11}{25}.

Example 14

medium
Order least to greatest: 12\frac{1}{2}, 49\frac{4}{9}, 59\frac{5}{9}.

Example 15

medium
Order greatest to least: 78\frac{7}{8}, 56\frac{5}{6}, 1112\frac{11}{12}.

Example 16

easy
Which is the smallest of 38,34,35\frac{3}{8}, \frac{3}{4}, \frac{3}{5}?

Example 17

challenge
Arrange least to greatest and identify the median: 14\frac{1}{4}, 25\frac{2}{5}, 12\frac{1}{2}, 35\frac{3}{5}, 710\frac{7}{10}.

Example 18

easy
Order from least to greatest: 15\frac{1}{5}, 35\frac{3}{5}, 25\frac{2}{5}.

Example 19

medium
Order greatest to least: 35,710,1320\frac{3}{5}, \frac{7}{10}, \frac{13}{20}.

Example 20

medium
Order least to greatest using a common denominator: 14,23,512\frac{1}{4}, \frac{2}{3}, \frac{5}{12}.
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