Ordering Fractions Worksheets - Math Monks - Free Printable

Let's solve each problem step by step. The goal is to arrange the given fractions in the correct order — either ascending (from smallest to largest) or descending (from largest to smallest), as indicated by the inequality signs.

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🔹 Problem 1:

Given: $\frac{1}{6}, \frac{4}{9}, \frac{5}{12}, \frac{1}{3}$
Answer already provided: $\frac{4}{9} > \frac{5}{12} > \frac{1}{3} > \frac{1}{6}$

Let’s verify:
- Convert all to decimals:
- $\frac{1}{6} \approx 0.1667$
- $\frac{1}{3} \approx 0.3333$
- $\frac{5}{12} \approx 0.4167$
- $\frac{4}{9} \approx 0.4444$

So, descending order:
$\frac{4}{9} > \frac{5}{12} > \frac{1}{3} > \frac{1}{6}$ ✔

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🔹 Problem 2:

$\frac{5}{12}, \frac{7}{12}, \frac{13}{12}, \frac{9}{12}$
All have same denominator → compare numerators:

- $13 > 9 > 7 > 5$ → So:
$$
\frac{13}{12} > \frac{9}{12} > \frac{7}{12} > \frac{5}{12}
$$

✔ Answer: $\boxed{\frac{13}{12} > \frac{9}{12} > \frac{7}{12} > \frac{5}{12}}$

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🔹 Problem 3:

$\frac{6}{14}, \frac{5}{14}, \frac{7}{14}, \frac{15}{14}$
Same denominator → compare numerators:

- $15 > 7 > 6 > 5$ → So:
$$
\frac{5}{14} < \frac{6}{14} < \frac{7}{14} < \frac{15}{14}
$$

✔ Answer: $\boxed{\frac{5}{14} < \frac{6}{14} < \frac{7}{14} < \frac{15}{14}}$

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🔹 Problem 4:

$\frac{19}{16}, \frac{12}{16}, \frac{14}{16}, \frac{10}{16}$
Same denominator → compare numerators:

- $19 > 14 > 12 > 10$ → So:
$$
\frac{10}{16} < \frac{12}{16} < \frac{14}{16} < \frac{19}{16}
$$

✔ Answer: $\boxed{\frac{10}{16} < \frac{12}{16} < \frac{14}{16} < \frac{19}{16}}$

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🔹 Problem 5:

$\frac{16}{25}, \frac{13}{15}, \frac{4}{5}, \frac{9}{10}$
All are close to 1. Let's convert to decimals:

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

Order from largest to smallest:
$$
\frac{9}{10} > \frac{13}{15} > \frac{4}{5} > \frac{16}{25}
$$

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

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🔹 Problem 6:

$\frac{7}{9}, \frac{5}{6}, \frac{1}{3}, \frac{2}{7}$

Convert to decimals:

- $\frac{7}{9} \approx 0.777$
- $\frac{5}{6} \approx 0.833$
- $\frac{1}{3} \approx 0.333$
- $\frac{2}{7} \approx 0.2857$

Descending order:
$$
\frac{5}{6} > \frac{7}{9} > \frac{1}{3} > \frac{2}{7}
$$

✔ Answer: $\boxed{\frac{5}{6} > \frac{7}{9} > \frac{1}{3} > \frac{2}{7}}$

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🔹 Problem 7:

$\frac{7}{4}, \frac{7}{6}, \frac{8}{7}, \frac{10}{3}$

Convert to decimals:

- $\frac{7}{4} = 1.75$
- $\frac{7}{6} \approx 1.1667$
- $\frac{8}{7} \approx 1.1429$
- $\frac{10}{3} \approx 3.333$

Ascending order:
$$
\frac{8}{7} < \frac{7}{6} < \frac{7}{4} < \frac{10}{3}
$$

✔ Answer: $\boxed{\frac{8}{7} < \frac{7}{6} < \frac{7}{4} < \frac{10}{3}}$

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🔹 Problem 8:

$\frac{2}{5}, \frac{3}{8}, \frac{4}{7}, \frac{5}{6}$

Convert to decimals:

- $\frac{2}{5} = 0.4$
- $\frac{3}{8} = 0.375$
- $\frac{4}{7} \approx 0.5714$
- $\frac{5}{6} \approx 0.8333$

Ascending order:
$$
\frac{3}{8} < \frac{2}{5} < \frac{4}{7} < \frac{5}{6}
$$

✔ Answer: $\boxed{\frac{3}{8} < \frac{2}{5} < \frac{4}{7} < \frac{5}{6}}$

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🔹 Problem 9:

$\frac{5}{8}, \frac{3}{4}, \frac{2}{9}, \frac{1}{7}$

Convert to decimals:

- $\frac{5}{8} = 0.625$
- $\frac{3}{4} = 0.75$
- $\frac{2}{9} \approx 0.222$
- $\frac{1}{7} \approx 0.1429$

Descending order:
$$
\frac{3}{4} > \frac{5}{8} > \frac{2}{9} > \frac{1}{7}
$$

✔ Answer: $\boxed{\frac{3}{4} > \frac{5}{8} > \frac{2}{9} > \frac{1}{7}}$

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🔹 Problem 10:

$\frac{5}{6}, \frac{5}{12}, \frac{3}{2}, \frac{7}{4}$

Convert to decimals:

- $\frac{5}{6} \approx 0.833$
- $\frac{5}{12} \approx 0.4167$
- $\frac{3}{2} = 1.5$
- $\frac{7}{4} = 1.75$

Descending order:
$$
\frac{7}{4} > \frac{3}{2} > \frac{5}{6} > \frac{5}{12}
$$

✔ Answer: $\boxed{\frac{7}{4} > \frac{3}{2} > \frac{5}{6} > \frac{5}{12}}$

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🔹 Problem 11:

$\frac{6}{10}, \frac{5}{6}, \frac{2}{9}, \frac{4}{15}$

Convert to decimals:

- $\frac{6}{10} = 0.6$
- $\frac{5}{6} \approx 0.833$
- $\frac{2}{9} \approx 0.222$
- $\frac{4}{15} \approx 0.2667$

Ascending order:
$$
\frac{2}{9} < \frac{4}{15} < \frac{6}{10} < \frac{5}{6}
$$

✔ Answer: $\boxed{\frac{2}{9} < \frac{4}{15} < \frac{6}{10} < \frac{5}{6}}$

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🔹 Problem 12:

$\frac{2}{17}, \frac{3}{14}, \frac{4}{13}, \frac{8}{15}$

Convert to decimals:

- $\frac{2}{17} \approx 0.1176$
- $\frac{3}{14} \approx 0.2143$
- $\frac{4}{13} \approx 0.3077$
- $\frac{8}{15} \approx 0.5333$

Ascending order:
$$
\frac{2}{17} < \frac{3}{14} < \frac{4}{13} < \frac{8}{15}
$$

✔ Answer: $\boxed{\frac{2}{17} < \frac{3}{14} < \frac{4}{13} < \frac{8}{15}}$

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $\frac{4}{9} > \frac{5}{12} > \frac{1}{3} > \frac{1}{6}$ |
| 2 | $\frac{13}{12} > \frac{9}{12} > \frac{7}{12} > \frac{5}{12}$ |
| 3 | $\frac{5}{14} < \frac{6}{14} < \frac{7}{14} < \frac{15}{14}$ |
| 4 | $\frac{10}{16} < \frac{12}{16} < \frac{14}{16} < \frac{19}{16}$ |
| 5 | $\frac{9}{10} > \frac{13}{15} > \frac{4}{5} > \frac{16}{25}$ |
| 6 | $\frac{5}{6} > \frac{7}{9} > \frac{1}{3} > \frac{2}{7}$ |
| 7 | $\frac{8}{7} < \frac{7}{6} < \frac{7}{4} < \frac{10}{3}$ |
| 8 | $\frac{3}{8} < \frac{2}{5} < \frac{4}{7} < \frac{5}{6}$ |
| 9 | $\frac{3}{4} > \frac{5}{8} > \frac{2}{9} > \frac{1}{7}$ |
| 10 | $\frac{7}{4} > \frac{3}{2} > \frac{5}{6} > \frac{5}{12}$ |
| 11 | $\frac{2}{9} < \frac{4}{15} < \frac{6}{10} < \frac{5}{6}$ |
| 12 | $\frac{2}{17} < \frac{3}{14} < \frac{4}{13} < \frac{8}{15}$ |

> 📝 Tip: When comparing fractions, use decimals for ease, or find a common denominator if needed. For quick comparisons, estimating decimal values works well.

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