Free worksheets for comparing or ordering fractions - Free Printable

Sure! Let’s solve each problem step by step. The goal is to order the fractions from smallest to greatest.

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## 🔢 General Strategy:
- If denominators are the same → compare numerators.
- If numerators are the same → compare denominators (larger denominator = smaller fraction).
- If both differ → convert to decimals or find a common denominator to compare.

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# ✔ Problem 1a: `8/9`, `1/2`, `9/11`

Let’s convert to decimals for easy comparison:

- `8/9 ≈ 0.888...`
- `1/2 = 0.5`
- `9/11 ≈ 0.818...`

Order from smallest to greatest:
→ `1/2`, `9/11`, `8/9`

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# ✔ Problem 1b: `5/12`, `12/12`, `1/12`

All have same denominator → compare numerators:

- `1/12`, `5/12`, `12/12`

Order:
→ `1/12`, `5/12`, `12/12`

*(Note: `12/12 = 1`)*

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# ✔ Problem 2a: `1/2`, `4/9`, `4/4`

Convert to decimals:

- `1/2 = 0.5`
- `4/9 ≈ 0.444...`
- `4/4 = 1`

Order:
→ `4/9`, `1/2`, `4/4`

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# ✔ Problem 2b: `3/11`, `3/3`, `7/11`

- `3/3 = 1`
- `3/11 ≈ 0.272...`
- `7/11 ≈ 0.636...`

Order:
→ `3/11`, `7/11`, `3/3`

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# ✔ Problem 3a: `5/4`, `1/2`, `4/9`

Convert to decimals:

- `5/4 = 1.25`
- `1/2 = 0.5`
- `4/9 ≈ 0.444...`

Order:
→ `4/9`, `1/2`, `5/4`

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# ✔ Problem 3b: `5/6`, `11/6`, `4/6`

Same denominator → compare numerators:

- `4/6`, `5/6`, `11/6`

Order:
→ `4/6`, `5/6`, `11/6`

*(Note: `11/6 > 1`, since numerator > denominator)*

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# ✔ Problem 4a: `2/4`, `6/4`, `3/4`

Same denominator → compare numerators:

- `2/4`, `3/4`, `6/4`

Order:
→ `2/4`, `3/4`, `6/4`

*(Simplify if needed: `1/2`, `3/4`, `3/2` — but not required for ordering)*

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# ✔ Problem 4b: `2/5`, `7/7`, `10/9`

Convert to decimals:

- `2/5 = 0.4`
- `7/7 = 1`
- `10/9 ≈ 1.111...`

Order:
→ `2/5`, `7/7`, `10/9`

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# ✔ Problem 5a: `1/1`, `11/1`, `12/1`

All have denominator 1 → just compare numerators:

- `1`, `11`, `12`

Order:
→ `1/1`, `11/1`, `12/1`

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# ✔ Problem 5b: `1/10`, `1/3`, `1/2`

Same numerator → larger denominator = smaller fraction.

So: `1/10 < 1/3 < 1/2`

Check with decimals:

- `1/10 = 0.1`
- `1/3 ≈ 0.333...`
- `1/2 = 0.5`

Order:
→ `1/10`, `1/3`, `1/2`

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## 📝 Final Answers:

1a. `1/2, 9/11, 8/9`

1b. `1/12, 5/12, 12/12`

2a. `4/9, 1/2, 4/4`

2b. `3/11, 7/11, 3/3`

3a. `4/9, 1/2, 5/4`

3b. `4/6, 5/6, 11/6`

4a. `2/4, 3/4, 6/4`

4b. `2/5, 7/7, 10/9`

5a. `1/1, 11/1, 12/1`

5b. `1/10, 1/3, 1/2`

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✔ You can now fill in the worksheet with these answers!

Let me know if you’d like them simplified or written as mixed numbers where applicable.