Free worksheets for comparing or ordering fractions - Free Printable

Let's solve each problem on the Ordering Fractions Worksheet step by step. The goal is to order the fractions from smallest to greatest.

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1a. $\frac{8}{9}, \frac{1}{2}, \frac{9}{11}$

We compare these fractions. Since they have different denominators, we can either find a common denominator or convert them to decimals.

#### Convert to decimals:
- $\frac{8}{9} \approx 0.888...$
- $\frac{1}{2} = 0.5$
- $\frac{9}{11} \approx 0.818...$

Now order them:
- $0.5 < 0.818 < 0.888$

So:
$\boxed{\frac{1}{2},\ \frac{9}{11},\ \frac{8}{9}}$

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1b. $\frac{5}{12}, \frac{12}{12}, \frac{1}{12}$

All have same denominator (12), so compare numerators:
- $1 < 5 < 12$

So:
$\boxed{\frac{1}{12},\ \frac{5}{12},\ \frac{12}{12}}$

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2a. $\frac{1}{2}, \frac{4}{9}, \frac{4}{4}$

Note: $\frac{4}{4} = 1$

Convert others to decimals:
- $\frac{1}{2} = 0.5$
- $\frac{4}{9} \approx 0.444...$

So:
- $0.444 < 0.5 < 1$

Order:
$\boxed{\frac{4}{9},\ \frac{1}{2},\ \frac{4}{4}}$

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2b. $\frac{3}{11}, \frac{3}{3}, \frac{7}{11}$

Note: $\frac{3}{3} = 1$

Compare:
- $\frac{3}{11} \approx 0.2727$
- $\frac{7}{11} \approx 0.6363$
- $1 = 1$

So:
$\boxed{\frac{3}{11},\ \frac{7}{11},\ \frac{3}{3}}$

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3a. $\frac{5}{4}, \frac{1}{2}, \frac{4}{9}$

Convert to decimals:
- $\frac{5}{4} = 1.25$
- $\frac{1}{2} = 0.5$
- $\frac{4}{9} \approx 0.444...$

Order:
- $0.444 < 0.5 < 1.25$

So:
$\boxed{\frac{4}{9},\ \frac{1}{2},\ \frac{5}{4}}$

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3b. $\frac{5}{6}, \frac{11}{6}, \frac{4}{6}$

Same denominator (6), so compare numerators:
- $4 < 5 < 11$

So:
$\boxed{\frac{4}{6},\ \frac{5}{6},\ \frac{11}{6}}$

(You can simplify $\frac{4}{6} = \frac{2}{3}$, but not necessary unless asked.)

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4a. $\frac{2}{4}, \frac{6}{4}, \frac{3}{4}$

Same denominator (4):
- $2 < 3 < 6$

So:
$\boxed{\frac{2}{4},\ \frac{3}{4},\ \frac{6}{4}}$

(Simplify: $\frac{2}{4} = \frac{1}{2}, \frac{3}{4}, \frac{6}{4} = 1.5$)

But keep as given unless instructed.

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4b. $\frac{2}{5}, \frac{7}{7}, \frac{10}{9}$

Simplify:
- $\frac{7}{7} = 1$
- $\frac{10}{9} \approx 1.111$
- $\frac{2}{5} = 0.4$

So:
- $0.4 < 1 < 1.111$

Order:
$\boxed{\frac{2}{5},\ \frac{7}{7},\ \frac{10}{9}}$

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5a. $\frac{1}{1}, \frac{11}{1}, \frac{12}{1}$

These are just whole numbers:
- $1, 11, 12$

So:
$\boxed{\frac{1}{1},\ \frac{11}{1},\ \frac{12}{1}}$

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5b. $\frac{1}{10}, \frac{1}{3}, \frac{1}{2}$

Compare decimals:
- $\frac{1}{10} = 0.1$
- $\frac{1}{3} \approx 0.333$
- $\frac{1}{2} = 0.5$

So:
$\boxed{\frac{1}{10},\ \frac{1}{3},\ \frac{1}{2}}$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1a. | $\frac{1}{2},\ \frac{9}{11},\ \frac{8}{9}$ |
| 1b. | $\frac{1}{12},\ \frac{5}{12},\ \frac{12}{12}$ |
| 2a. | $\frac{4}{9},\ \frac{1}{2},\ \frac{4}{4}$ |
| 2b. | $\frac{3}{11},\ \frac{7}{11},\ \frac{3}{3}$ |
| 3a. | $\frac{4}{9},\ \frac{1}{2},\ \frac{5}{4}$ |
| 3b. | $\frac{4}{6},\ \frac{5}{6},\ \frac{11}{6}$ |
| 4a. | $\frac{2}{4},\ \frac{3}{4},\ \frac{6}{4}$ |
| 4b. | $\frac{2}{5},\ \frac{7}{7},\ \frac{10}{9}$ |
| 5a. | $\frac{1}{1},\ \frac{11}{1},\ \frac{12}{1}$ |
| 5b. | $\frac{1}{10},\ \frac{1}{3},\ \frac{1}{2}$ |

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🔍 Tips for Ordering Fractions:

- If denominators are the same → compare numerators.
- If numerators are the same → compare denominators (larger denominator = smaller fraction).
- Otherwise, convert to decimals or find a common denominator.

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