This worksheet provides twelve exercises for students to practice arranging fractions in ascending and descending order.

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 greater than 1 except possibly? Let’s convert to decimals:

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

Now order from largest to smallest (since it says $> > >$):

- $0.9 > 0.8667 > 0.8 > 0.64$

So:
$$
\frac{9}{10} > \frac{13}{15} > \frac{4}{5} > \frac{16}{25}
$$

✔ 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:

- $\frac{7}{9} \approx 0.7778$
- $\frac{5}{6} \approx 0.8333$
- $\frac{1}{3} \approx 0.3333$
- $\frac{2}{7} \approx 0.2857$

Order from largest to smallest:
- $0.8333 > 0.7778 > 0.3333 > 0.2857$

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

✔ 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:

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

Now order ascending: smallest to largest:

- $1.1429 < 1.1667 < 1.75 < 3.333$

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

✔ 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:
- $0.375 < 0.4 < 0.5714 < 0.8333$

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

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

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🔹 Problem 9:

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

Decimals:

- $\frac{5}{8} = 0.625$
- $\frac{3}{4} = 0.75$
- $\frac{2}{9} \approx 0.2222$
- $\frac{1}{7} \approx 0.1429$

Descending order:
- $0.75 > 0.625 > 0.2222 > 0.1429$

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

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

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🔹 Problem 10:

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

Decimals:

- $\frac{5}{6} \approx 0.8333$
- $\frac{5}{12} \approx 0.4167$
- $\frac{3}{2} = 1.5$
- $\frac{7}{4} = 1.75$

Descending order:
- $1.75 > 1.5 > 0.8333 > 0.4167$

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

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

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🔹 Problem 11:

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

Simplify and convert:

- $\frac{6}{10} = \frac{3}{5} = 0.6$
- $\frac{5}{6} \approx 0.8333$
- $\frac{2}{9} \approx 0.2222$
- $\frac{4}{15} \approx 0.2667$

Ascending order:
- $0.2222 < 0.2667 < 0.6 < 0.8333$

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

✔ 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:
- $0.1176 < 0.2143 < 0.3077 < 0.5333$

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

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

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✔ Final Answers Summary:

| # | 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 | $\frac{2}{17} < \frac{3}{14} < \frac{4}{13} < \frac{8}{15}$ |

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