Free worksheets for comparing or ordering fractions - Free Printable

Of course! I'll solve the "Ordering Fractions Worksheet" by ordering each set of fractions from smallest to greatest. I'll explain the method for each problem.

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General Strategy:

To order fractions, you can:
1. Find a common denominator and compare numerators.
2. Convert to decimals for easy comparison.
3. Use logic (e.g., if denominators are the same, compare numerators; if numerators are the same, compare denominators inversely).

I’ll use a mix of these depending on what’s easiest for each set.

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## Problem 1a: $\frac{8}{9}, \frac{1}{2}, \frac{9}{11}$

These have different denominators. Let's convert to decimals:

- $\frac{8}{9} ≈ 0.888...$
- $\frac{1}{2} = 0.5$
- $\frac{9}{11} ≈ 0.818...$

Now order decimals:
0.5 < 0.818... < 0.888...

✔ Answer: $\frac{1}{2}, \frac{9}{11}, \frac{8}{9}$

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## Problem 1b: $\frac{5}{12}, \frac{12}{12}, \frac{1}{12}$

All have the same denominator → compare numerators:

Numerators: 1, 5, 12

✔ Answer: $\frac{1}{12}, \frac{5}{12}, \frac{12}{12}$

*(Note: $\frac{12}{12} = 1$)*

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## Problem 2a: $\frac{1}{2}, \frac{4}{9}, \frac{4}{4}$

$\frac{4}{4} = 1$, so it’s the largest.

Compare $\frac{1}{2}$ and $\frac{4}{9}$:

- $\frac{1}{2} = 0.5$
- $\frac{4}{9} ≈ 0.444...$

So: $0.444... < 0.5 < 1$

✔ Answer: $\frac{4}{9}, \frac{1}{2}, \frac{4}{4}$

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## Problem 2b: $\frac{3}{11}, \frac{3}{3}, \frac{7}{11}$

$\frac{3}{3} = 1$ — largest.

Now compare $\frac{3}{11}$ and $\frac{7}{11}$ — same denominator → 3 < 7.

✔ Answer: $\frac{3}{11}, \frac{7}{11}, \frac{3}{3}$

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## Problem 3a: $\frac{5}{4}, \frac{1}{2}, \frac{4}{9}$

Convert to decimals:

- $\frac{5}{4} = 1.25$
- $\frac{1}{2} = 0.5$
- $\frac{4}{9} ≈ 0.444...$

Order: $0.444... < 0.5 < 1.25$

✔ Answer: $\frac{4}{9}, \frac{1}{2}, \frac{5}{4}$

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## Problem 3b: $\frac{5}{6}, \frac{11}{6}, \frac{4}{6}$

Same denominator → compare numerators: 4, 5, 11

✔ Answer: $\frac{4}{6}, \frac{5}{6}, \frac{11}{6}$

*(Note: $\frac{11}{6} > 1$, $\frac{4}{6} = \frac{2}{3}$)*

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## Problem 4a: $\frac{2}{4}, \frac{6}{4}, \frac{3}{4}$

Same denominator → numerators: 2, 3, 6

✔ Answer: $\frac{2}{4}, \frac{3}{4}, \frac{6}{4}$

*(Simplify if needed: $\frac{1}{2}, \frac{3}{4}, \frac{3}{2}$ — but not required for ordering)*

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## Problem 4b: $\frac{2}{5}, \frac{7}{7}, \frac{10}{9}$

First, simplify:

- $\frac{7}{7} = 1$
- $\frac{10}{9} ≈ 1.111...$ (greater than 1)
- $\frac{2}{5} = 0.4$

So: $0.4 < 1 < 1.111...$

✔ Answer: $\frac{2}{5}, \frac{7}{7}, \frac{10}{9}$

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## Problem 5a: $\frac{1}{1}, \frac{11}{1}, \frac{12}{1}$

All have denominator 1 → numerators: 1, 11, 12

✔ Answer: $\frac{1}{1}, \frac{11}{1}, \frac{12}{1}$

*(Which are just 1, 11, 12)*

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## Problem 5b: $\frac{1}{10}, \frac{1}{3}, \frac{1}{2}$

All have numerator 1 → larger denominator = smaller fraction.

Denominators: 10 > 3 > 2 → so fractions: $\frac{1}{10} < \frac{1}{3} < \frac{1}{2}$

Check with decimals:

- $\frac{1}{10} = 0.1$
- $\frac{1}{3} ≈ 0.333...$
- $\frac{1}{2} = 0.5$

✔ Answer: $\frac{1}{10}, \frac{1}{3}, \frac{1}{2}$

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## ✔ Final Answers Summary:

| Problem | Ordered Fractions (Smallest to Greatest) |
|---------|------------------------------------------|
| 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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Let me know if you’d like this formatted as a printable answer key or explained differently!