Ordering Fractions Worksheets - Math Monks - Free Printable

To solve the problem of arranging fractions in ascending order, 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: \( \frac{5}{6}, \frac{1}{2}, \frac{2}{3}, \frac{7}{9} \)

#### Step 1: Convert all fractions to a common denominator.
The denominators are 6, 2, 3, and 9. The least common multiple (LCM) of these numbers is 18.

- \( \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} \)
- \( \frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18} \)
- \( \frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18} \)
- \( \frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18} \)

#### Step 2: Compare the numerators.
The fractions in terms of the common denominator 18 are:
- \( \frac{15}{18}, \frac{9}{18}, \frac{12}{18}, \frac{14}{18} \)

Arranging these by their numerators:
- \( \frac{9}{18}, \frac{12}{18}, \frac{14}{18}, \frac{15}{18} \)

#### Step 3: Convert back to the original fractions.
- \( \frac{9}{18} = \frac{1}{2} \)
- \( \frac{12}{18} = \frac{2}{3} \)
- \( \frac{14}{18} = \frac{7}{9} \)
- \( \frac{15}{18} = \frac{5}{6} \)

Thus, the ascending order is:
\[ \boxed{\frac{1}{2}, \frac{2}{3}, \frac{7}{9}, \frac{5}{6}} \]

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Set 2:

Fractions: \( \frac{4}{7}, \frac{6}{11}, \frac{7}{12}, \frac{3}{17} \)

#### Step 1: Compare fractions using cross-multiplication or decimal approximations.
- \( \frac{4}{7} \approx 0.571 \)
- \( \frac{6}{11} \approx 0.545 \)
- \( \frac{7}{12} \approx 0.583 \)
- \( \frac{3}{17} \approx 0.176 \)

#### Step 2: Arrange the fractions based on their decimal values.
- \( \frac{3}{17} \approx 0.176 \)
- \( \frac{6}{11} \approx 0.545 \)
- \( \frac{4}{7} \approx 0.571 \)
- \( \frac{7}{12} \approx 0.583 \)

Thus, the ascending order is:
\[ \boxed{\frac{3}{17}, \frac{6}{11}, \frac{4}{7}, \frac{7}{12}} \]

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Set 3:

Fractions: \( \frac{6}{13}, \frac{1}{3}, \frac{3}{5}, \frac{9}{14} \)

#### Step 1: Compare fractions using cross-multiplication or decimal approximations.
- \( \frac{6}{13} \approx 0.462 \)
- \( \frac{1}{3} \approx 0.333 \)
- \( \frac{3}{5} = 0.6 \)
- \( \frac{9}{14} \approx 0.643 \)

#### Step 2: Arrange the fractions based on their decimal values.
- \( \frac{1}{3} \approx 0.333 \)
- \( \frac{6}{13} \approx 0.462 \)
- \( \frac{3}{5} = 0.6 \)
- \( \frac{9}{14} \approx 0.643 \)

Thus, the ascending order is:
\[ \boxed{\frac{1}{3}, \frac{6}{13}, \frac{3}{5}, \frac{9}{14}} \]

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Set 4:

Fractions: \( \frac{2}{5}, \frac{6}{7}, \frac{11}{12}, \frac{13}{15} \)

#### Step 1: Compare fractions using cross-multiplication or decimal approximations.
- \( \frac{2}{5} = 0.4 \)
- \( \frac{6}{7} \approx 0.857 \)
- \( \frac{11}{12} \approx 0.917 \)
- \( \frac{13}{15} \approx 0.867 \)

#### Step 2: Arrange the fractions based on their decimal values.
- \( \frac{2}{5} = 0.4 \)
- \( \frac{6}{7} \approx 0.857 \)
- \( \frac{13}{15} \approx 0.867 \)
- \( \frac{11}{12} \approx 0.917 \)

Thus, the ascending order is:
\[ \boxed{\frac{2}{5}, \frac{6}{7}, \frac{13}{15}, \frac{11}{12}} \]

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Set 5:

Fractions: \( \frac{5}{9}, \frac{2}{5}, \frac{9}{16}, \frac{15}{17} \)

#### Step 1: Compare fractions using cross-multiplication or decimal approximations.
- \( \frac{5}{9} \approx 0.556 \)
- \( \frac{2}{5} = 0.4 \)
- \( \frac{9}{16} = 0.5625 \)
- \( \frac{15}{17} \approx 0.882 \)

#### Step 2: Arrange the fractions based on their decimal values.
- \( \frac{2}{5} = 0.4 \)
- \( \frac{5}{9} \approx 0.556 \)
- \( \frac{9}{16} = 0.5625 \)
- \( \frac{15}{17} \approx 0.882 \)

Thus, the ascending order is:
\[ \boxed{\frac{2}{5}, \frac{5}{9}, \frac{9}{16}, \frac{15}{17}} \]

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Set 6:

Fractions: \( \frac{8}{9}, \frac{5}{16}, \frac{13}{18}, \frac{7}{19} \)

#### Step 1: Compare fractions using cross-multiplication or decimal approximations.
- \( \frac{8}{9} \approx 0.889 \)
- \( \frac{5}{16} = 0.3125 \)
- \( \frac{13}{18} \approx 0.722 \)
- \( \frac{7}{19} \approx 0.368 \)

#### Step 2: Arrange the fractions based on their decimal values.
- \( \frac{5}{16} = 0.3125 \)
- \( \frac{7}{19} \approx 0.368 \)
- \( \frac{13}{18} \approx 0.722 \)
- \( \frac{8}{9} \approx 0.889 \)

Thus, the ascending order is:
\[ \boxed{\frac{5}{16}, \frac{7}{19}, \frac{13}{18}, \frac{8}{9}} \]

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Final Answers:

1. \( \frac{1}{2}, \frac{2}{3}, \frac{7}{9}, \frac{5}{6} \)
2. \( \frac{3}{17}, \frac{6}{11}, \frac{4}{7}, \frac{7}{12} \)
3. \( \frac{1}{3}, \frac{6}{13}, \frac{3}{5}, \frac{9}{14} \)
4. \( \frac{2}{5}, \frac{6}{7}, \frac{13}{15}, \frac{11}{12} \)
5. \( \frac{2}{5}, \frac{5}{9}, \frac{9}{16}, \frac{15}{17} \)
6. \( \frac{5}{16}, \frac{7}{19}, \frac{13}{18}, \frac{8}{9} \)

\[
\boxed{
\begin{array}{l}
1. \frac{1}{2}, \frac{2}{3}, \frac{7}{9}, \frac{5}{6} \\
2. \frac{3}{17}, \frac{6}{11}, \frac{4}{7}, \frac{7}{12} \\
3. \frac{1}{3}, \frac{6}{13}, \frac{3}{5}, \frac{9}{14} \\
4. \frac{2}{5}, \frac{6}{7}, \frac{13}{15}, \frac{11}{12} \\
5. \frac{2}{5}, \frac{5}{9}, \frac{9}{16}, \frac{15}{17} \\
6. \frac{5}{16}, \frac{7}{19}, \frac{13}{18}, \frac{8}{9}
\end{array}
}
\]