Ordering Fractions Worksheets - Math Monks - Free Printable

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

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Set 1:

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

- Convert all fractions to have a common denominator (LCM of 6, 9, 12, and 3 is 36):
- $\frac{1}{6} = \frac{6}{36}$
- $\frac{4}{9} = \frac{16}{36}$
- $\frac{5}{12} = \frac{15}{36}$
- $\frac{1}{3} = \frac{12}{36}$

- Compare the numerators:
- $\frac{16}{36} > \frac{15}{36} > \frac{12}{36} > \frac{6}{36}$

- Original fractions in order:
- $\frac{4}{9} > \frac{5}{12} > \frac{1}{3} > \frac{1}{6}$

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

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Set 2:

Fractions: $\frac{5}{12}$, $\frac{7}{12}$, $\frac{13}{12}$, $\frac{9}{12}$

- All fractions have the same denominator (12), so compare the numerators directly:
- $13 > 9 > 7 > 5$

- Original fractions in order:
- $\frac{13}{12} > \frac{9}{12} > \frac{7}{12} > \frac{5}{12}$

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

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Set 3:

Fractions: $\frac{6}{14}$, $\frac{5}{14}$, $\frac{7}{14}$, $\frac{15}{14}$

- All fractions have the same denominator (14), so compare the numerators directly:
- $15 > 7 > 6 > 5$

- Original fractions in order:
- $\frac{15}{14} > \frac{7}{14} > \frac{6}{14} > \frac{5}{14}$

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

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Set 4:

Fractions: $\frac{19}{16}$, $\frac{12}{16}$, $\frac{14}{16}$, $\frac{10}{16}$

- All fractions have the same denominator (16), so compare the numerators directly:
- $19 > 14 > 12 > 10$

- Original fractions in order:
- $\frac{19}{16} > \frac{14}{16} > \frac{12}{16} > \frac{10}{16}$

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

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Set 5:

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

- Convert all fractions to have a common denominator (LCM of 25, 15, 5, and 10 is 150):
- $\frac{16}{25} = \frac{96}{150}$
- $\frac{13}{15} = \frac{130}{150}$
- $\frac{4}{5} = \frac{120}{150}$
- $\frac{9}{10} = \frac{135}{150}$

- Compare the numerators:
- $135 > 130 > 120 > 96$

- Original fractions in order:
- $\frac{9}{10} > \frac{13}{15} > \frac{4}{5} > \frac{16}{25}$

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

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Set 6:

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

- Convert all fractions to have a common denominator (LCM of 9, 6, 3, and 7 is 126):
- $\frac{7}{9} = \frac{98}{126}$
- $\frac{5}{6} = \frac{105}{126}$
- $\frac{1}{3} = \frac{42}{126}$
- $\frac{2}{7} = \frac{36}{126}$

- Compare the numerators:
- $105 > 98 > 42 > 36$

- Original fractions in 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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Set 7:

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

- Convert all fractions to decimals for easier comparison:
- $\frac{7}{4} = 1.75$
- $\frac{7}{6} \approx 1.167$
- $\frac{8}{7} \approx 1.143$
- $\frac{10}{3} \approx 3.333$

- Compare the decimal values:
- $3.333 > 1.75 > 1.167 > 1.143$

- Original fractions in order:
- $\frac{10}{3} > \frac{7}{4} > \frac{7}{6} > \frac{8}{7}$

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

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Set 8:

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

- Convert all fractions to have a common denominator (LCM of 5, 8, 7, and 6 is 840):
- $\frac{2}{5} = \frac{336}{840}$
- $\frac{3}{8} = \frac{315}{840}$
- $\frac{4}{7} = \frac{480}{840}$
- $\frac{5}{6} = \frac{700}{840}$

- Compare the numerators:
- $700 > 480 > 336 > 315$

- Original fractions in order:
- $\frac{5}{6} > \frac{4}{7} > \frac{2}{5} > \frac{3}{8}$

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

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Set 9:

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

- Convert all fractions to have a common denominator (LCM of 8, 4, 9, and 7 is 504):
- $\frac{5}{8} = \frac{315}{504}$
- $\frac{3}{4} = \frac{378}{504}$
- $\frac{2}{9} = \frac{112}{504}$
- $\frac{1}{7} = \frac{72}{504}$

- Compare the numerators:
- $378 > 315 > 112 > 72$

- Original fractions in order:
- $\frac{3}{4} > \frac{5}{8} > \frac{2}{9} > \frac{1}{7}$

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

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Set 10:

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

- Convert all fractions to have a common denominator (LCM of 6, 12, 2, and 4 is 12):
- $\frac{5}{6} = \frac{10}{12}$
- $\frac{5}{12} = \frac{5}{12}$
- $\frac{3}{2} = \frac{18}{12}$
- $\frac{7}{4} = \frac{21}{12}$

- Compare the numerators:
- $21 > 18 > 10 > 5$

- Original fractions in 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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Set 11:

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

- Convert all fractions to have a common denominator (LCM of 10, 6, 9, and 15 is 90):
- $\frac{6}{10} = \frac{54}{90}$
- $\frac{5}{6} = \frac{75}{90}$
- $\frac{2}{9} = \frac{20}{90}$
- $\frac{4}{15} = \frac{24}{90}$

- Compare the numerators:
- $75 > 54 > 24 > 20$

- Original fractions in order:
- $\frac{5}{6} > \frac{6}{10} > \frac{4}{15} > \frac{2}{9}$

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

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Set 12:

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

- Convert all fractions to have a common denominator (LCM of 17, 14, 13, and 15 is 46,890):
- $\frac{2}{17} = \frac{5460}{46890}$
- $\frac{3}{14} = \frac{9945}{46890}$
- $\frac{4}{13} = \frac{14040}{46890}$
- $\frac{8}{15} = \frac{25296}{46890}$

- Compare the numerators:
- $25296 > 14040 > 9945 > 5460$

- Original fractions in order:
- $\frac{8}{15} > \frac{4}{13} > \frac{3}{14} > \frac{2}{17}$

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

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Final Answers:

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