Use this worksheet to practice ordering sets of four fractions from smallest to largest value.

Let's solve each problem step by step. The goal is to arrange the given fractions in ascending order (from smallest to largest). To compare fractions, we can:

1. Convert them to decimals, or
2. Find a common denominator and compare numerators.

We'll use decimal conversion for simplicity and accuracy.

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Problem 1:

Fractions: $ \frac{2}{3}, \frac{1}{2}, \frac{3}{4}, \frac{4}{5} $

Convert to decimals:
- $ \frac{2}{3} \approx 0.6667 $
- $ \frac{1}{2} = 0.5 $
- $ \frac{3}{4} = 0.75 $
- $ \frac{4}{5} = 0.8 $

Order:
$ 0.5 < 0.6667 < 0.75 < 0.8 $
So:
$ \frac{1}{2} < \frac{2}{3} < \frac{3}{4} < \frac{4}{5} $

✔ Answer: $ \boxed{\frac{1}{2} < \frac{2}{3} < \frac{3}{4} < \frac{4}{5}} $

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Problem 2:

$ \frac{1}{6}, \frac{4}{9}, \frac{5}{12}, \frac{1}{3} $

Decimals:
- $ \frac{1}{6} \approx 0.1667 $
- $ \frac{4}{9} \approx 0.4444 $
- $ \frac{5}{12} \approx 0.4167 $
- $ \frac{1}{3} \approx 0.3333 $

Order:
$ 0.1667 < 0.3333 < 0.4167 < 0.4444 $
So:
$ \frac{1}{6} < \frac{1}{3} < \frac{5}{12} < \frac{4}{9} $

✔ Answer: $ \boxed{\frac{1}{6} < \frac{1}{3} < \frac{5}{12} < \frac{4}{9}} $

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Problem 3:

$ \frac{5}{6}, \frac{9}{16}, \frac{7}{12}, \frac{3}{8} $

Decimals:
- $ \frac{5}{6} \approx 0.8333 $
- $ \frac{9}{16} = 0.5625 $
- $ \frac{7}{12} \approx 0.5833 $
- $ \frac{3}{8} = 0.375 $

Order:
$ 0.375 < 0.5625 < 0.5833 < 0.8333 $
So:
$ \frac{3}{8} < \frac{9}{16} < \frac{7}{12} < \frac{5}{6} $

✔ Answer: $ \boxed{\frac{3}{8} < \frac{9}{16} < \frac{7}{12} < \frac{5}{6}} $

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Problem 4:

$ \frac{7}{10}, \frac{4}{5}, \frac{4}{15}, \frac{9}{20} $

Decimals:
- $ \frac{7}{10} = 0.7 $
- $ \frac{4}{5} = 0.8 $
- $ \frac{4}{15} \approx 0.2667 $
- $ \frac{9}{20} = 0.45 $

Order:
$ 0.2667 < 0.45 < 0.7 < 0.8 $
So:
$ \frac{4}{15} < \frac{9}{20} < \frac{7}{10} < \frac{4}{5} $

✔ Answer: $ \boxed{\frac{4}{15} < \frac{9}{20} < \frac{7}{10} < \frac{4}{5}} $

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Problem 5:

$ \frac{11}{21}, \frac{5}{6}, \frac{5}{2}, \frac{9}{14} $

Decimals:
- $ \frac{11}{21} \approx 0.5238 $
- $ \frac{5}{6} \approx 0.8333 $
- $ \frac{5}{2} = 2.5 $
- $ \frac{9}{14} \approx 0.6429 $

Order:
$ 0.5238 < 0.6429 < 0.8333 < 2.5 $
So:
$ \frac{11}{21} < \frac{9}{14} < \frac{5}{6} < \frac{5}{2} $

✔ Answer: $ \boxed{\frac{11}{21} < \frac{9}{14} < \frac{5}{6} < \frac{5}{2}} $

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Problem 6:

$ \frac{7}{8}, \frac{3}{4}, \frac{15}{16}, \frac{1}{2} $

Decimals:
- $ \frac{7}{8} = 0.875 $
- $ \frac{3}{4} = 0.75 $
- $ \frac{15}{16} = 0.9375 $
- $ \frac{1}{2} = 0.5 $

Order:
$ 0.5 < 0.75 < 0.875 < 0.9375 $
So:
$ \frac{1}{2} < \frac{3}{4} < \frac{7}{8} < \frac{15}{16} $

✔ Answer: $ \boxed{\frac{1}{2} < \frac{3}{4} < \frac{7}{8} < \frac{15}{16}} $

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Problem 7:

$ \frac{7}{4}, \frac{8}{3}, \frac{7}{6}, \frac{9}{8} $

Decimals:
- $ \frac{7}{4} = 1.75 $
- $ \frac{8}{3} \approx 2.6667 $
- $ \frac{7}{6} \approx 1.1667 $
- $ \frac{9}{8} = 1.125 $

Order:
$ 1.125 < 1.1667 < 1.75 < 2.6667 $
So:
$ \frac{9}{8} < \frac{7}{6} < \frac{7}{4} < \frac{8}{3} $

✔ Answer: $ \boxed{\frac{9}{8} < \frac{7}{6} < \frac{7}{4} < \frac{8}{3}} $

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Problem 8:

$ \frac{13}{18}, \frac{1}{3}, \frac{5}{6}, \frac{7}{9} $

Decimals:
- $ \frac{13}{18} \approx 0.7222 $
- $ \frac{1}{3} \approx 0.3333 $
- $ \frac{5}{6} \approx 0.8333 $
- $ \frac{7}{9} \approx 0.7778 $

Order:
$ 0.3333 < 0.7222 < 0.7778 < 0.8333 $
So:
$ \frac{1}{3} < \frac{13}{18} < \frac{7}{9} < \frac{5}{6} $

✔ Answer: $ \boxed{\frac{1}{3} < \frac{13}{18} < \frac{7}{9} < \frac{5}{6}} $

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Problem 9:

$ \frac{5}{8}, \frac{13}{24}, \frac{7}{12}, \frac{1}{6} $

Decimals:
- $ \frac{5}{8} = 0.625 $
- $ \frac{13}{24} \approx 0.5417 $
- $ \frac{7}{12} \approx 0.5833 $
- $ \frac{1}{6} \approx 0.1667 $

Order:
$ 0.1667 < 0.5417 < 0.5833 < 0.625 $
So:
$ \frac{1}{6} < \frac{13}{24} < \frac{7}{12} < \frac{5}{8} $

✔ Answer: $ \boxed{\frac{1}{6} < \frac{13}{24} < \frac{7}{12} < \frac{5}{8}} $

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Problem 10:

$ \frac{16}{25}, \frac{4}{5}, \frac{9}{10}, \frac{13}{15} $

Decimals:
- $ \frac{16}{25} = 0.64 $
- $ \frac{4}{5} = 0.8 $
- $ \frac{9}{10} = 0.9 $
- $ \frac{13}{15} \approx 0.8667 $

Order:
$ 0.64 < 0.8 < 0.8667 < 0.9 $
So:
$ \frac{16}{25} < \frac{4}{5} < \frac{13}{15} < \frac{9}{10} $

✔ Answer: $ \boxed{\frac{16}{25} < \frac{4}{5} < \frac{13}{15} < \frac{9}{10}} $

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Problem 11:

$ \frac{4}{7}, \frac{2}{5}, \frac{1}{2}, \frac{3}{8} $

Decimals:
- $ \frac{4}{7} \approx 0.5714 $
- $ \frac{2}{5} = 0.4 $
- $ \frac{1}{2} = 0.5 $
- $ \frac{3}{8} = 0.375 $

Order:
$ 0.375 < 0.4 < 0.5 < 0.5714 $
So:
$ \frac{3}{8} < \frac{2}{5} < \frac{1}{2} < \frac{4}{7} $

✔ Answer: $ \boxed{\frac{3}{8} < \frac{2}{5} < \frac{1}{2} < \frac{4}{7}} $

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Problem 12:

$ \frac{5}{6}, \frac{3}{4}, \frac{2}{9}, \frac{1}{10} $

Decimals:
- $ \frac{5}{6} \approx 0.8333 $
- $ \frac{3}{4} = 0.75 $
- $ \frac{2}{9} \approx 0.2222 $
- $ \frac{1}{10} = 0.1 $

Order:
$ 0.1 < 0.2222 < 0.75 < 0.8333 $
So:
$ \frac{1}{10} < \frac{2}{9} < \frac{3}{4} < \frac{5}{6} $

✔ Answer: $ \boxed{\frac{1}{10} < \frac{2}{9} < \frac{3}{4} < \frac{5}{6}} $

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✔ Final Answers Summary:

1) $ \frac{1}{2} < \frac{2}{3} < \frac{3}{4} < \frac{4}{5} $
2) $ \frac{1}{6} < \frac{1}{3} < \frac{5}{12} < \frac{4}{9} $
3) $ \frac{3}{8} < \frac{9}{16} < \frac{7}{12} < \frac{5}{6} $
4) $ \frac{4}{15} < \frac{9}{20} < \frac{7}{10} < \frac{4}{5} $
5) $ \frac{11}{21} < \frac{9}{14} < \frac{5}{6} < \frac{5}{2} $
6) $ \frac{1}{2} < \frac{3}{4} < \frac{7}{8} < \frac{15}{16} $
7) $ \frac{9}{8} < \frac{7}{6} < \frac{7}{4} < \frac{8}{3} $
8) $ \frac{1}{3} < \frac{13}{18} < \frac{7}{9} < \frac{5}{6} $
9) $ \frac{1}{6} < \frac{13}{24} < \frac{7}{12} < \frac{5}{8} $
10) $ \frac{16}{25} < \frac{4}{5} < \frac{13}{15} < \frac{9}{10} $
11) $ \frac{3}{8} < \frac{2}{5} < \frac{1}{2} < \frac{4}{7} $
12) $ \frac{1}{10} < \frac{2}{9} < \frac{3}{4} < \frac{5}{6} $

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Let me know if you'd like this as a printable answer sheet!