Arranging fractions in ascending order worksheet for math practice.

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 in ascending order of 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 in ascending order based on 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 in ascending order based on 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 in ascending order based on 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 in ascending order based on 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 in ascending order based on 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. \( \frac{5}{16}, \frac{7}{19}, \frac{13}{18}, \frac{8}{9} \)

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