Worksheet for ordering fractions on a number line, designed for partner activity.

Let's solve each of the Ordering Fractions problems step by step. The goal is to place each fraction on a number line from 0 to 1, in order from smallest to largest, and then write them in the correct order.

We'll analyze each set, compare the fractions, and determine their positions on the number line.

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Problem 1:

Fractions: $ \frac{3}{4}, \frac{2}{4}, \frac{1}{4} $

- All have the same denominator (4), so we can compare numerators:
- $ \frac{1}{4} < \frac{2}{4} < \frac{3}{4} $
- So, order: $ \frac{1}{4}, \frac{2}{4}, \frac{3}{4} $

✔ On the number line:
```
0 ------------------------|------------------------- 1
1/4 2/4 (1/2) 3/4
```

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Problem 2:

Fractions: $ \frac{4}{8}, \frac{4}{10}, \frac{4}{5} $

All have numerator 4, but different denominators. Let's convert to decimals or find common denominators.

- $ \frac{4}{8} = 0.5 $
- $ \frac{4}{10} = 0.4 $
- $ \frac{4}{5} = 0.8 $

So:
- $ 0.4 < 0.5 < 0.8 $
- Therefore: $ \frac{4}{10} < \frac{4}{8} < \frac{4}{5} $

✔ Order: $ \frac{4}{10}, \frac{4}{8}, \frac{4}{5} $

On number line:
```
0 ------------------|-----------|------------------- 1
4/10 4/8 4/5
```

---

Problem 3:

Fractions: $ \frac{3}{6}, \frac{1}{4}, \frac{2}{3} $

Convert to decimals or common denominator.

- $ \frac{3}{6} = \frac{1}{2} = 0.5 $
- $ \frac{1}{4} = 0.25 $
- $ \frac{2}{3} \approx 0.666... $

So:
- $ 0.25 < 0.5 < 0.666 $
- Therefore: $ \frac{1}{4} < \frac{3}{6} < \frac{2}{3} $

✔ Order: $ \frac{1}{4}, \frac{3}{6}, \frac{2}{3} $

Number line:
```
0 --------|------------|-------------|-------------- 1
1/4 3/6 (1/2) 2/3
```

---

Problem 4:

Fractions: $ \frac{1}{10}, \frac{1}{2}, \frac{1}{5} $

Convert to decimals:
- $ \frac{1}{10} = 0.1 $
- $ \frac{1}{5} = 0.2 $
- $ \frac{1}{2} = 0.5 $

So:
- $ 0.1 < 0.2 < 0.5 $
- Therefore: $ \frac{1}{10} < \frac{1}{5} < \frac{1}{2} $

✔ Order: $ \frac{1}{10}, \frac{1}{5}, \frac{1}{2} $

Number line:
```
0 ----|------|------------|--------------- 1
1/10 1/5 1/2
```

---

Problem 5:

Fractions: $ \frac{5}{7}, \frac{1}{3}, \frac{5}{10} $

Convert to decimals:
- $ \frac{5}{7} \approx 0.714 $
- $ \frac{1}{3} \approx 0.333 $
- $ \frac{5}{10} = 0.5 $

So:
- $ 0.333 < 0.5 < 0.714 $
- Therefore: $ \frac{1}{3} < \frac{5}{10} < \frac{5}{7} $

✔ Order: $ \frac{1}{3}, \frac{5}{10}, \frac{5}{7} $

Number line:
```
0 -------|------------|-------------|------------- 1
1/3 5/10 (1/2) 5/7
```

---

Problem 6:

Fractions: $ \frac{2}{10}, \frac{3}{4}, \frac{2}{8} $

Simplify and convert:
- $ \frac{2}{10} = 0.2 $
- $ \frac{2}{8} = \frac{1}{4} = 0.25 $
- $ \frac{3}{4} = 0.75 $

So:
- $ 0.2 < 0.25 < 0.75 $
- Therefore: $ \frac{2}{10} < \frac{2}{8} < \frac{3}{4} $

✔ Order: $ \frac{2}{10}, \frac{2}{8}, \frac{3}{4} $

Number line:
```
0 ----|-------|---------------------|------------- 1
2/10 2/8 (1/4) 3/4
```

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✔ Final Answers:

| Problem | Ordered Fractions |
|--------|-------------------|
| 1 | $ \frac{1}{4}, \frac{2}{4}, \frac{3}{4} $ |
| 2 | $ \frac{4}{10}, \frac{4}{8}, \frac{4}{5} $ |
| 3 | $ \frac{1}{4}, \frac{3}{6}, \frac{2}{3} $ |
| 4 | $ \frac{1}{10}, \frac{1}{5}, \frac{1}{2} $ |
| 5 | $ \frac{1}{3}, \frac{5}{10}, \frac{5}{7} $ |
| 6 | $ \frac{2}{10}, \frac{2}{8}, \frac{3}{4} $ |

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📝 Tips for Number Lines:

- Use benchmarks: $ \frac{1}{4} = 0.25 $, $ \frac{1}{2} = 0.5 $, $ \frac{3}{4} = 0.75 $
- Convert to decimals or find common denominators when comparing.
- Always simplify fractions first if possible.

Let me know if you'd like this as a printable answer key!