Ordering Fractions Worksheets - Math Monks - Free Printable

To solve the problem of ordering fractions from least to greatest, we need to compare the values of the fractions in each set. Here's a step-by-step explanation for each set:

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Set 1:

Fractions: \( \frac{3}{10}, \frac{4}{5}, \frac{1}{4}, \frac{6}{11}, \frac{8}{9} \)

1. Convert each fraction to a decimal:
- \( \frac{3}{10} = 0.3 \)
- \( \frac{4}{5} = 0.8 \)
- \( \frac{1}{4} = 0.25 \)
- \( \frac{6}{11} \approx 0.545 \)
- \( \frac{8}{9} \approx 0.889 \)

2. Order the decimals from least to greatest:
- \( 0.25, 0.3, 0.545, 0.8, 0.889 \)

3. Match the decimals back to the fractions:
- \( \frac{1}{4}, \frac{3}{10}, \frac{6}{11}, \frac{4}{5}, \frac{8}{9} \)

Answer for Set 1: \( \frac{1}{4}, \frac{3}{10}, \frac{6}{11}, \frac{4}{5}, \frac{8}{9} \)

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Set 2:

Fractions: \( \frac{1}{10}, \frac{2}{5}, \frac{9}{40}, \frac{7}{20}, \frac{5}{12} \)

1. Convert each fraction to a decimal:
- \( \frac{1}{10} = 0.1 \)
- \( \frac{2}{5} = 0.4 \)
- \( \frac{9}{40} = 0.225 \)
- \( \frac{7}{20} = 0.35 \)
- \( \frac{5}{12} \approx 0.4167 \)

2. Order the decimals from least to greatest:
- \( 0.1, 0.225, 0.35, 0.4, 0.4167 \)

3. Match the decimals back to the fractions:
- \( \frac{1}{10}, \frac{9}{40}, \frac{7}{20}, \frac{2}{5}, \frac{5}{12} \)

Answer for Set 2: \( \frac{1}{10}, \frac{9}{40}, \frac{7}{20}, \frac{2}{5}, \frac{5}{12} \)

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Set 3:

Fractions: \( \frac{5}{14}, \frac{6}{11}, \frac{1}{5}, \frac{7}{13}, \frac{9}{16} \)

1. Convert each fraction to a decimal:
- \( \frac{5}{14} \approx 0.357 \)
- \( \frac{6}{11} \approx 0.545 \)
- \( \frac{1}{5} = 0.2 \)
- \( \frac{7}{13} \approx 0.538 \)
- \( \frac{9}{16} = 0.5625 \)

2. Order the decimals from least to greatest:
- \( 0.2, 0.357, 0.538, 0.545, 0.5625 \)

3. Match the decimals back to the fractions:
- \( \frac{1}{5}, \frac{5}{14}, \frac{7}{13}, \frac{6}{11}, \frac{9}{16} \)

Answer for Set 3: \( \frac{1}{5}, \frac{5}{14}, \frac{7}{13}, \frac{6}{11}, \frac{9}{16} \)

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Set 4:

Fractions: \( \frac{27}{40}, \frac{3}{8}, \frac{7}{18}, \frac{11}{20}, \frac{10}{17} \)

1. Convert each fraction to a decimal:
- \( \frac{27}{40} = 0.675 \)
- \( \frac{3}{8} = 0.375 \)
- \( \frac{7}{18} \approx 0.389 \)
- \( \frac{11}{20} = 0.55 \)
- \( \frac{10}{17} \approx 0.588 \)

2. Order the decimals from least to greatest:
- \( 0.375, 0.389, 0.55, 0.588, 0.675 \)

3. Match the decimals back to the fractions:
- \( \frac{3}{8}, \frac{7}{18}, \frac{11}{20}, \frac{10}{17}, \frac{27}{40} \)

Answer for Set 4: \( \frac{3}{8}, \frac{7}{18}, \frac{11}{20}, \frac{10}{17}, \frac{27}{40} \)

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Set 5:

Fractions: \( \frac{5}{16}, \frac{2}{5}, \frac{1}{2}, \frac{21}{32}, \frac{3}{8} \)

1. Convert each fraction to a decimal:
- \( \frac{5}{16} = 0.3125 \)
- \( \frac{2}{5} = 0.4 \)
- \( \frac{1}{2} = 0.5 \)
- \( \frac{21}{32} = 0.65625 \)
- \( \frac{3}{8} = 0.375 \)

2. Order the decimals from least to greatest:
- \( 0.3125, 0.375, 0.4, 0.5, 0.65625 \)

3. Match the decimals back to the fractions:
- \( \frac{5}{16}, \frac{3}{8}, \frac{2}{5}, \frac{1}{2}, \frac{21}{32} \)

Answer for Set 5: \( \frac{5}{16}, \frac{3}{8}, \frac{2}{5}, \frac{1}{2}, \frac{21}{32} \)

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Set 6:

Fractions: \( \frac{26}{41}, \frac{4}{11}, \frac{6}{19}, \frac{12}{27}, \frac{9}{30} \)

1. Convert each fraction to a decimal:
- \( \frac{26}{41} \approx 0.634 \)
- \( \frac{4}{11} \approx 0.364 \)
- \( \frac{6}{19} \approx 0.316 \)
- \( \frac{12}{27} \approx 0.444 \)
- \( \frac{9}{30} = 0.3 \)

2. Order the decimals from least to greatest:
- \( 0.3, 0.316, 0.364, 0.444, 0.634 \)

3. Match the decimals back to the fractions:
- \( \frac{9}{30}, \frac{6}{19}, \frac{4}{11}, \frac{12}{27}, \frac{26}{41} \)

Answer for Set 6: \( \frac{9}{30}, \frac{6}{19}, \frac{4}{11}, \frac{12}{27}, \frac{26}{41} \)

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Set 7:

Fractions: \( \frac{3}{20}, \frac{23}{25}, \frac{1}{4}, \frac{7}{50}, \frac{2}{7} \)

1. Convert each fraction to a decimal:
- \( \frac{3}{20} = 0.15 \)
- \( \frac{23}{25} = 0.92 \)
- \( \frac{1}{4} = 0.25 \)
- \( \frac{7}{50} = 0.14 \)
- \( \frac{2}{7} \approx 0.286 \)

2. Order the decimals from least to greatest:
- \( 0.14, 0.15, 0.25, 0.286, 0.92 \)

3. Match the decimals back to the fractions:
- \( \frac{7}{50}, \frac{3}{20}, \frac{1}{4}, \frac{2}{7}, \frac{23}{25} \)

Answer for Set 7: \( \frac{7}{50}, \frac{3}{20}, \frac{1}{4}, \frac{2}{7}, \frac{23}{25} \)

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Set 8:

Fractions: \( \frac{13}{42}, \frac{8}{15}, \frac{7}{18}, \frac{11}{21}, \frac{4}{9} \)

1. Convert each fraction to a decimal:
- \( \frac{13}{42} \approx 0.3095 \)
- \( \frac{8}{15} \approx 0.5333 \)
- \( \frac{7}{18} \approx 0.3889 \)
- \( \frac{11}{21} \approx 0.5238 \)
- \( \frac{4}{9} \approx 0.4444 \)

2. Order the decimals from least to greatest:
- \( 0.3095, 0.3889, 0.4444, 0.5238, 0.5333 \)

3. Match the decimals back to the fractions:
- \( \frac{13}{42}, \frac{7}{18}, \frac{4}{9}, \frac{11}{21}, \frac{8}{15} \)

Answer for Set 8: \( \frac{13}{42}, \frac{7}{18}, \frac{4}{9}, \frac{11}{21}, \frac{8}{15} \)

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Final Answers:

1. \( \frac{1}{4}, \frac{3}{10}, \frac{6}{11}, \frac{4}{5}, \frac{8}{9} \)
2. \( \frac{1}{10}, \frac{9}{40}, \frac{7}{20}, \frac{2}{5}, \frac{5}{12} \)
3. \( \frac{1}{5}, \frac{5}{14}, \frac{7}{13}, \frac{6}{11}, \frac{9}{16} \)
4. \( \frac{3}{8}, \frac{7}{18}, \frac{11}{20}, \frac{10}{17}, \frac{27}{40} \)
5. \( \frac{5}{16}, \frac{3}{8}, \frac{2}{5}, \frac{1}{2}, \frac{21}{32} \)
6. \( \frac{9}{30}, \frac{6}{19}, \frac{4}{11}, \frac{12}{27}, \frac{26}{41} \)
7. \( \frac{7}{50}, \frac{3}{20}, \frac{1}{4}, \frac{2}{7}, \frac{23}{25} \)
8. \( \frac{13}{42}, \frac{7}{18}, \frac{4}{9}, \frac{11}{21}, \frac{8}{15} \)

\boxed{
\begin{aligned}
&1. \frac{1}{4}, \frac{3}{10}, \frac{6}{11}, \frac{4}{5}, \frac{8}{9} \\
&2. \frac{1}{10}, \frac{9}{40}, \frac{7}{20}, \frac{2}{5}, \frac{5}{12} \\
&3. \frac{1}{5}, \frac{5}{14}, \frac{7}{13}, \frac{6}{11}, \frac{9}{16} \\
&4. \frac{3}{8}, \frac{7}{18}, \frac{11}{20}, \frac{10}{17}, \frac{27}{40} \\
&5. \frac{5}{16}, \frac{3}{8}, \frac{2}{5}, \frac{1}{2}, \frac{21}{32} \\
&6. \frac{9}{30}, \frac{6}{19}, \frac{4}{11}, \frac{12}{27}, \frac{26}{41} \\
&7. \frac{7}{50}, \frac{3}{20}, \frac{1}{4}, \frac{2}{7}, \frac{23}{25} \\
&8. \frac{13}{42}, \frac{7}{18}, \frac{4}{9}, \frac{11}{21}, \frac{8}{15}
\end{aligned}
}