Plotting Rational Numbers on a Number Line - Math worksheet for students to practice placing fractions and mixed numbers on number lines.

Let's solve each problem step by step. We are asked to plot rational numbers on a number line. Each number is a fraction or mixed number, and we need to determine its position on the given number line.

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1. $-\frac{3}{5}$

- This is a negative fraction between -1 and 0.
- Since $\frac{3}{5} = 0.6$, then $-\frac{3}{5} = -0.6$.
- On the number line from -1 to 1, divide the segment from 0 to -1 into 5 equal parts (each part = 0.2).
- $-\frac{3}{5}$ is 3 parts to the left of 0 → at -0.6.

✔ Plot at -0.6 (3/5 of the way from 0 to -1).

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2. $3\frac{1}{4}$

- This is a mixed number: $3 + \frac{1}{4} = 3.25$
- The number line goes from 1 to 5.
- Between 3 and 4, divide into 4 equal parts (each = 0.25).
- $3\frac{1}{4}$ is one-quarter past 3 → at 3.25

✔ Plot at 3.25 (1/4 of the way from 3 to 4).

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3. $\frac{11}{6}$

- Convert to mixed number: $\frac{11}{6} = 1\frac{5}{6} \approx 1.833...$
- So it’s between 1 and 2.
- Number line from -1 to 3.
- Divide space between 1 and 2 into 6 parts (each ≈ 0.1667).
- $\frac{5}{6}$ of the way from 1 to 2 → $1 + \frac{5}{6} = 1.833$

✔ Plot at approximately 1.83, just before 2.

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4. $-2\frac{2}{7}$

- Mixed number: $-2 - \frac{2}{7} = -2.2857...$
- Number line from -3 to 0.
- Between -3 and -2, divide into 7 equal parts (each ≈ 0.1429).
- From -3, move up 2/7 of the way toward -2 → $-3 + \frac{2}{7} = -2\frac{2}{7}$
- Alternatively: $-2\frac{2}{7}$ is 2/7 of the way from -3 to -2

✔ Plot at -2.2857, closer to -2 than to -3.

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5. $\frac{3}{8}$

- This is positive and less than 1: $0.375$
- Number line from -2 to 1.
- Between 0 and 1, divide into 8 equal parts (each = 0.125).
- $\frac{3}{8} = 3 \times 0.125 = 0.375$

✔ Plot at 0.375, which is 3/8 of the way from 0 to 1.

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6. $\frac{21}{9}$

- Simplify: $\frac{21}{9} = \frac{7}{3} = 2\frac{1}{3} \approx 2.333...$
- Number line from 0 to 3.
- Between 2 and 3, divide into 3 equal parts (each = 1/3 ≈ 0.333).
- $2\frac{1}{3}$ is one-third of the way from 2 to 3.

✔ Plot at 2.333, one-third beyond 2.

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7. $6\frac{1}{3}$

- $6 + \frac{1}{3} = 6.333...$
- Number line from 3 to 8.
- Between 6 and 7, divide into 3 parts (each = 1/3 ≈ 0.333).
- $6\frac{1}{3}$ is one-third of the way from 6 to 7.

✔ Plot at 6.333, just after 6.

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8. $-4\frac{4}{5}$

- $-4 - \frac{4}{5} = -4.8$
- Number line from -6 to -2.
- Between -5 and -4: wait — let’s check:
- $-4.8$ is between -5 and -4.
- But the number line shows: -6, -5, -4, -3, -2
- So $-4.8$ is 0.8 units to the left of -4, or 0.2 units to the right of -5
- Distance from -5 to -4 is 1 unit.
- $-4.8$ is 0.8 units from -5 → so 8/10 = 4/5 of the way from -5 to -4

✔ Plot at -4.8, which is 4/5 of the way from -5 to -4.

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✔ Summary of Plots:

| Problem | Number | Decimal | Position on Number Line |
|--------|----------------|-------------|--------------------------|
| 1 | $-\frac{3}{5}$ | -0.6 | Between -1 and 0, 3/5 from 0 to -1 |
| 2 | $3\frac{1}{4}$ | 3.25 | 1/4 from 3 to 4 |
| 3 | $\frac{11}{6}$ | ~1.83 | 5/6 from 1 to 2 |
| 4 | $-2\frac{2}{7}$| ~-2.2857 | 2/7 from -3 to -2 |
| 5 | $\frac{3}{8}$ | 0.375 | 3/8 from 0 to 1 |
| 6 | $\frac{21}{9}$ | ~2.333 | 1/3 from 2 to 3 |
| 7 | $6\frac{1}{3}$ | ~6.333 | 1/3 from 6 to 7 |
| 8 | $-4\frac{4}{5}$| -4.8 | 4/5 from -5 to -4 |

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📌 How to Plot:

For each:
1. Identify whole number part.
2. Determine fractional part.
3. Divide the interval between two integers into appropriate parts (based on denominator).
4. Count the required number of divisions.

> You can now use this guide to mark each point accurately on the number lines provided in the worksheet.

Let me know if you'd like a visual representation or help drawing them!