Printable math worksheet featuring exercises on ordering unlike fractions in both increasing and decreasing sequences.

Let's solve the problem step by step.

We are asked to order unlike fractions — that is, fractions with different denominators — either in increasing or decreasing order. To do this, we need to compare them by converting them into equivalent fractions with a common denominator or by converting them to decimals.

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🔷 General Strategy:

1. Find a common denominator (LCM of denominators) or
2. Convert each fraction to a decimal for easier comparison.

We’ll use decimal conversion here because it’s faster and less error-prone for most cases.

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## ✔ Part A: Write each set in increasing order

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1) $\frac{1}{8}, \frac{9}{13}, \frac{3}{11}, \frac{2}{5}$

Convert to decimals:

- $\frac{1}{8} = 0.125$
- $\frac{9}{13} \approx 0.6923$
- $\frac{3}{11} \approx 0.2727$
- $\frac{2}{5} = 0.4$

Now order:
$0.125 < 0.2727 < 0.4 < 0.6923$

So increasing order:
$$
\boxed{\frac{1}{8},\ \frac{3}{11},\ \frac{2}{5},\ \frac{9}{13}}
$$

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2) $\frac{5}{4}, \frac{7}{3}, \frac{12}{7}, \frac{10}{3}$

Convert to decimals:

- $\frac{5}{4} = 1.25$
- $\frac{7}{3} \approx 2.333$
- $\frac{12}{7} \approx 1.714$
- $\frac{10}{3} \approx 3.333$

Order: $1.25 < 1.714 < 2.333 < 3.333$

So increasing order:
$$
\boxed{\frac{5}{4},\ \frac{12}{7},\ \frac{7}{3},\ \frac{10}{3}}
$$

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3) $\frac{8}{10}, \frac{7}{6}, \frac{3}{9}, \frac{9}{2}$

Simplify and convert:

- $\frac{8}{10} = 0.8$
- $\frac{7}{6} \approx 1.1667$
- $\frac{3}{9} = \frac{1}{3} \approx 0.333$
- $\frac{9}{2} = 4.5$

Order: $0.333 < 0.8 < 1.1667 < 4.5$

So increasing order:
$$
\boxed{\frac{3}{9},\ \frac{8}{10},\ \frac{7}{6},\ \frac{9}{2}}
$$

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4) $\frac{12}{13}, \frac{8}{9}, \frac{3}{4}, \frac{3}{5}$

Convert:

- $\frac{12}{13} \approx 0.923$
- $\frac{8}{9} \approx 0.888$
- $\frac{3}{4} = 0.75$
- $\frac{3}{5} = 0.6$

Order: $0.6 < 0.75 < 0.888 < 0.923$

So increasing order:
$$
\boxed{\frac{3}{5},\ \frac{3}{4},\ \frac{8}{9},\ \frac{12}{13}}
$$

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5) $\frac{3}{13}, \frac{11}{12}, \frac{5}{7}, \frac{2}{11}$

Convert:

- $\frac{3}{13} \approx 0.2308$
- $\frac{11}{12} \approx 0.9167$
- $\frac{5}{7} \approx 0.7143$
- $\frac{2}{11} \approx 0.1818$

Order: $0.1818 < 0.2308 < 0.7143 < 0.9167$

So increasing order:
$$
\boxed{\frac{2}{11},\ \frac{3}{13},\ \frac{5}{7},\ \frac{11}{12}}
$$

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6) $\frac{8}{5}, \frac{10}{4}, \frac{9}{7}, \frac{11}{2}$

Convert:

- $\frac{8}{5} = 1.6$
- $\frac{10}{4} = 2.5$
- $\frac{9}{7} \approx 1.2857$
- $\frac{11}{2} = 5.5$

Order: $1.2857 < 1.6 < 2.5 < 5.5$

So increasing order:
$$
\boxed{\frac{9}{7},\ \frac{8}{5},\ \frac{10}{4},\ \frac{11}{2}}
$$

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## ✔ Part B: Write each set in decreasing order

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1) $\frac{1}{3}, \frac{9}{10}, \frac{5}{11}, \frac{4}{6}$

Convert:

- $\frac{1}{3} \approx 0.333$
- $\frac{9}{10} = 0.9$
- $\frac{5}{11} \approx 0.4545$
- $\frac{4}{6} = \frac{2}{3} \approx 0.6667$

Order descending: $0.9 > 0.6667 > 0.4545 > 0.333$

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

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2) $\frac{5}{2}, \frac{13}{4}, \frac{11}{8}, \frac{15}{9}$

Convert:

- $\frac{5}{2} = 2.5$
- $\frac{13}{4} = 3.25$
- $\frac{11}{8} = 1.375$
- $\frac{15}{9} = \frac{5}{3} \approx 1.6667$

Order: $3.25 > 2.5 > 1.6667 > 1.375$

So decreasing order:
$$
\boxed{\frac{13}{4},\ \frac{5}{2},\ \frac{15}{9},\ \frac{11}{8}}
$$

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3) $\frac{8}{3}, \frac{12}{11}, \frac{13}{10}, \frac{15}{2}$

Convert:

- $\frac{8}{3} \approx 2.6667$
- $\frac{12}{11} \approx 1.0909$
- $\frac{13}{10} = 1.3$
- $\frac{15}{2} = 7.5$

Order: $7.5 > 2.6667 > 1.3 > 1.0909$

So decreasing order:
$$
\boxed{\frac{15}{2},\ \frac{8}{3},\ \frac{13}{10},\ \frac{12}{11}}
$$

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4) $\frac{4}{7}, \frac{6}{11}, \frac{4}{15}, \frac{9}{14}$

Convert:

- $\frac{4}{7} \approx 0.5714$
- $\frac{6}{11} \approx 0.5455$
- $\frac{4}{15} \approx 0.2667$
- $\frac{9}{14} \approx 0.6429$

Order: $0.6429 > 0.5714 > 0.5455 > 0.2667$

So decreasing order:
$$
\boxed{\frac{9}{14},\ \frac{4}{7},\ \frac{6}{11},\ \frac{4}{15}}
$$

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5) $\frac{3}{5}, \frac{5}{8}, \frac{13}{15}, \frac{7}{11}$

Convert:

- $\frac{3}{5} = 0.6$
- $\frac{5}{8} = 0.625$
- $\frac{13}{15} \approx 0.8667$
- $\frac{7}{11} \approx 0.6364$

Order: $0.8667 > 0.6364 > 0.625 > 0.6$

So decreasing order:
$$
\boxed{\frac{13}{15},\ \frac{7}{11},\ \frac{5}{8},\ \frac{3}{5}}
$$

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

Convert:

- $\frac{9}{8} = 1.125$
- $\frac{5}{3} \approx 1.6667$
- $\frac{1}{4} = 0.25$
- $\frac{7}{5} = 1.4$

Order: $1.6667 > 1.4 > 1.125 > 0.25$

So decreasing order:
$$
\boxed{\frac{5}{3},\ \frac{7}{5},\ \frac{9}{8},\ \frac{1}{4}}
$$

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## ✔ Final Answers:

A) Increasing Order

1) $\frac{1}{8},\ \frac{3}{11},\ \frac{2}{5},\ \frac{9}{13}$
2) $\frac{5}{4},\ \frac{12}{7},\ \frac{7}{3},\ \frac{10}{3}$
3) $\frac{3}{9},\ \frac{8}{10},\ \frac{7}{6},\ \frac{9}{2}$
4) $\frac{3}{5},\ \frac{3}{4},\ \frac{8}{9},\ \frac{12}{13}$
5) $\frac{2}{11},\ \frac{3}{13},\ \frac{5}{7},\ \frac{11}{12}$
6) $\frac{9}{7},\ \frac{8}{5},\ \frac{10}{4},\ \frac{11}{2}$

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B) Decreasing Order

1) $\frac{9}{10},\ \frac{4}{6},\ \frac{5}{11},\ \frac{1}{3}$
2) $\frac{13}{4},\ \frac{5}{2},\ \frac{15}{9},\ \frac{11}{8}$
3) $\frac{15}{2},\ \frac{8}{3},\ \frac{13}{10},\ \frac{12}{11}$
4) $\frac{9}{14},\ \frac{4}{7},\ \frac{6}{11},\ \frac{4}{15}$
5) $\frac{13}{15},\ \frac{7}{11},\ \frac{5}{8},\ \frac{3}{5}$
6) $\frac{5}{3},\ \frac{7}{5},\ \frac{9}{8},\ \frac{1}{4}$

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✔ Note: Always double-check decimal approximations for accuracy. For exact comparisons, you can use LCM method, but decimals are efficient here.

Let me know if you'd like the solutions using LCM method instead!