Least To Greatest Worksheet Collection For Teaching & Learning - Free Printable

Let's solve each problem step by step, ordering the fractions from least to greatest. We'll use a consistent method: convert fractions to decimals (or find a common denominator) for easier comparison.

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🔢 Problem 1:

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

Convert to decimals:
- $ \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 $

Order:
$ 0.25 < 0.3 < 0.545 < 0.8 < 0.889 $

So, order is:
$ \frac{1}{4}, \frac{3}{10}, \frac{6}{11}, \frac{4}{5}, \frac{8}{9} $

✔ Answer: $ \boxed{\frac{1}{4}, \frac{3}{10}, \frac{6}{11}, \frac{4}{5}, \frac{8}{9}} $

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🔢 Problem 2:

$$
\frac{1}{10}, \frac{2}{5}, \frac{9}{40}, \frac{7}{20}, \frac{5}{12}
$$

Convert to decimals:
- $ \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 $

Order:
$ 0.1 < 0.225 < 0.35 < 0.4 < 0.4167 $

So:
$ \frac{1}{10}, \frac{9}{40}, \frac{7}{20}, \frac{2}{5}, \frac{5}{12} $

✔ Answer: $ \boxed{\frac{1}{10}, \frac{9}{40}, \frac{7}{20}, \frac{2}{5}, \frac{5}{12}} $

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🔢 Problem 3:

$$
\frac{5}{14}, \frac{6}{11}, \frac{1}{5}, \frac{7}{13}, \frac{9}{16}
$$

Decimals:
- $ \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 $

Order:
$ 0.2 < 0.357 < 0.538 < 0.545 < 0.5625 $

So:
$ \frac{1}{5}, \frac{5}{14}, \frac{7}{13}, \frac{6}{11}, \frac{9}{16} $

✔ Answer: $ \boxed{\frac{1}{5}, \frac{5}{14}, \frac{7}{13}, \frac{6}{11}, \frac{9}{16}} $

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🔢 Problem 4:

$$
\frac{27}{40}, \frac{3}{8}, \frac{7}{18}, \frac{11}{20}, \frac{10}{17}
$$

Decimals:
- $ \frac{27}{40} = 0.675 $
- $ \frac{3}{8} = 0.375 $
- $ \frac{7}{18} \approx 0.3889 $
- $ \frac{11}{20} = 0.55 $
- $ \frac{10}{17} \approx 0.5882 $

Order:
$ 0.375 < 0.3889 < 0.55 < 0.5882 < 0.675 $

So:
$ \frac{3}{8}, \frac{7}{18}, \frac{11}{20}, \frac{10}{17}, \frac{27}{40} $

✔ Answer: $ \boxed{\frac{3}{8}, \frac{7}{18}, \frac{11}{20}, \frac{10}{17}, \frac{27}{40}} $

---

🔢 Problem 5:

$$
\frac{5}{16}, \frac{2}{5}, \frac{1}{2}, \frac{21}{32}, \frac{3}{8}
$$

Decimals:
- $ \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 $

Order:
$ 0.3125 < 0.375 < 0.4 < 0.5 < 0.65625 $

So:
$ \frac{5}{16}, \frac{3}{8}, \frac{2}{5}, \frac{1}{2}, \frac{21}{32} $

✔ Answer: $ \boxed{\frac{5}{16}, \frac{3}{8}, \frac{2}{5}, \frac{1}{2}, \frac{21}{32}} $

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🔢 Problem 6:

$$
\frac{26}{41}, \frac{4}{11}, \frac{6}{19}, \frac{12}{27}, \frac{9}{30}
$$

Simplify and convert:
- $ \frac{26}{41} \approx 0.634 $
- $ \frac{4}{11} \approx 0.3636 $
- $ \frac{6}{19} \approx 0.3158 $
- $ \frac{12}{27} = \frac{4}{9} \approx 0.4444 $
- $ \frac{9}{30} = \frac{3}{10} = 0.3 $

Order:
$ 0.3 < 0.3158 < 0.3636 < 0.4444 < 0.634 $

So:
$ \frac{9}{30}, \frac{6}{19}, \frac{4}{11}, \frac{12}{27}, \frac{26}{41} $

✔ Answer: $ \boxed{\frac{9}{30}, \frac{6}{19}, \frac{4}{11}, \frac{12}{27}, \frac{26}{41}} $

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🔢 Problem 7:

$$
\frac{3}{20}, \frac{23}{25}, \frac{1}{4}, \frac{7}{50}, \frac{2}{7}
$$

Decimals:
- $ \frac{3}{20} = 0.15 $
- $ \frac{23}{25} = 0.92 $
- $ \frac{1}{4} = 0.25 $
- $ \frac{7}{50} = 0.14 $
- $ \frac{2}{7} \approx 0.2857 $

Order:
$ 0.14 < 0.15 < 0.25 < 0.2857 < 0.92 $

So:
$ \frac{7}{50}, \frac{3}{20}, \frac{1}{4}, \frac{2}{7}, \frac{23}{25} $

✔ Answer: $ \boxed{\frac{7}{50}, \frac{3}{20}, \frac{1}{4}, \frac{2}{7}, \frac{23}{25}} $

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🔢 Problem 8:

$$
\frac{13}{42}, \frac{8}{15}, \frac{7}{18}, \frac{11}{21}, \frac{4}{9}
$$

Decimals:
- $ \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 $

Order:
$ 0.3095 < 0.3889 < 0.4444 < 0.5238 < 0.5333 $

So:
$ \frac{13}{42}, \frac{7}{18}, \frac{4}{9}, \frac{11}{21}, \frac{8}{15} $

✔ Answer: $ \boxed{\frac{13}{42}, \frac{7}{18}, \frac{4}{9}, \frac{11}{21}, \frac{8}{15}} $

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✔ Final Answers Summary:

| Problem | Order (Least to Greatest) |
|--------|----------------------------|
| 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} $ |

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📌 Tips for Students:
- Always convert fractions to decimals if you're unsure.
- Use a calculator or long division for tricky ones.
- Simplify fractions first when possible.
- Compare decimal values carefully.

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