Math worksheet for practicing rational numbers on a number line, including graphing, additive inverses, and absolute values.

Let's solve each part of this worksheet step by step and explain the reasoning.

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Section 1: Graph each rational number on the number line.

We are given six numbers to plot:

1. $ \frac{4}{5} = 0.8 $
2. $ -\frac{3}{10} = -0.3 $
3. $ 2.75 $
4. $ -3\frac{2}{3} = -3.666... $
5. $ \frac{7}{8} = 0.875 $
6. $ -0.25 $

Explanation:
To graph these, we need to locate them on the number line from -4 to 4.

- $ \frac{4}{5} = 0.8 $ → Between 0 and 1, closer to 1.
- $ -\frac{3}{10} = -0.3 $ → Between -1 and 0, closer to 0.
- $ 2.75 $ → Between 2 and 3, three-quarters of the way.
- $ -3\frac{2}{3} \approx -3.67 $ → Between -4 and -3, closer to -4.
- $ \frac{7}{8} = 0.875 $ → Slightly less than 1, very close to 1.
- $ -0.25 $ → Between -1 and 0, halfway between 0 and -0.5.

> These should be plotted accordingly on the number line provided.

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Section 2: Write the rational number that corresponds to the point on the number line.

Given a number line with labeled points A, B, C, D, E, F.

From the image:
- The number line goes from -6 to 6.
- Each tick mark represents 0.5 units (since it’s divided into halves).

Let’s identify each point:

#### 7. C → Already given: $ -4\frac{1}{2} = -4.5 $

#### 8. F
- F is between -2 and -1, at the first tick after -1 → so it's $ -1.5 $
- Answer: $ -1.5 $ or $ -\frac{3}{2} $

#### 9. A
- A is just to the right of 0 → at the first tick after 0 → $ 0.5 $
- Answer: $ 0.5 $ or $ \frac{1}{2} $

#### 10. E
- E is at the last tick before 6 → between 5 and 6, halfway → $ 5.5 $
- Answer: $ 5.5 $ or $ 5\frac{1}{2} $

#### 11. B
- B is at -2 → exactly on the tick
- Answer: $ -2 $

#### 12. D
- D is between 1 and 2, at the first tick after 1 → $ 1.5 $
- Answer: $ 1.5 $ or $ \frac{3}{2} $

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Section 3: Write the additive inverse and absolute value of each rational number.

Recall:
- Additive inverse: the opposite number (same distance from 0, opposite side).
- Absolute value: distance from 0, always positive.

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#### 13. 9.14
- Additive inverse: $ -9.14 $
- Absolute value: $ |9.14| = 9.14 $
→ Answer: $ -9.14; 9.14 $ ✔

#### 14. -6.11
- Additive inverse: $ 6.11 $
- Absolute value: $ |-6.11| = 6.11 $
→ Answer: $ 6.11; 6.11 $

#### 15. -18.75
- Additive inverse: $ 18.75 $
- Absolute value: $ |-18.75| = 18.75 $
→ Answer: $ 18.75; 18.75 $

#### 16. $ -\frac{5}{3} $
- Additive inverse: $ \frac{5}{3} $
- Absolute value: $ \left|-\frac{5}{3}\right| = \frac{5}{3} $
→ Answer: $ \frac{5}{3}; \frac{5}{3} $

#### 17. $ -\frac{11}{12} $
- Additive inverse: $ \frac{11}{12} $
- Absolute value: $ \left|-\frac{11}{12}\right| = \frac{11}{12} $
→ Answer: $ \frac{11}{12}; \frac{11}{12} $

#### 18. -3.01
- Additive inverse: $ 3.01 $
- Absolute value: $ |-3.01| = 3.01 $
→ Answer: $ 3.01; 3.01 $

#### 19. 4.76
- Additive inverse: $ -4.76 $
- Absolute value: $ |4.76| = 4.76 $
→ Answer: $ -4.76; 4.76 $

#### 20. -0.225
- Additive inverse: $ 0.225 $
- Absolute value: $ |-0.225| = 0.225 $
→ Answer: $ 0.225; 0.225 $

#### 21. -0.914
- Additive inverse: $ 0.914 $
- Absolute value: $ |-0.914| = 0.914 $
→ Answer: $ 0.914; 0.914 $

#### 22. $ -18\frac{2}{7} = -\frac{128}{7} $
- Additive inverse: $ 18\frac{2}{7} $
- Absolute value: $ \left|-18\frac{2}{7}\right| = 18\frac{2}{7} $
→ Answer: $ 18\frac{2}{7}; 18\frac{2}{7} $

#### 23. $ \frac{9}{10} = 0.9 $
- Additive inverse: $ -\frac{9}{10} $
- Absolute value: $ \left|\frac{9}{10}\right| = \frac{9}{10} $
→ Answer: $ -\frac{9}{10}; \frac{9}{10} $

#### 24. -7.23
- Additive inverse: $ 7.23 $
- Absolute value: $ |-7.23| = 7.23 $
→ Answer: $ 7.23; 7.23 $

#### 25. 9.008
- Additive inverse: $ -9.008 $
- Absolute value: $ |9.008| = 9.008 $
→ Answer: $ -9.008; 9.008 $

#### 26. -11.1
- Additive inverse: $ 11.1 $
- Absolute value: $ |-11.1| = 11.1 $
→ Answer: $ 11.1; 11.1 $

#### 27. -3.54
- Additive inverse: $ 3.54 $
- Absolute value: $ |-3.54| = 3.54 $
→ Answer: $ 3.54; 3.54 $

#### 28. $ -\frac{29}{30} $
- Additive inverse: $ \frac{29}{30} $
- Absolute value: $ \left|-\frac{29}{30}\right| = \frac{29}{30} $
→ Answer: $ \frac{29}{30}; \frac{29}{30} $

#### 29. $ -\frac{4}{9} $
- Additive inverse: $ \frac{4}{9} $
- Absolute value: $ \left|-\frac{4}{9}\right| = \frac{4}{9} $
→ Answer: $ \frac{4}{9}; \frac{4}{9} $

#### 30. $ -42.\overline{1} $ (repeating decimal)
- This is $ -42.1111... $
- Additive inverse: $ 42.\overline{1} $
- Absolute value: $ |-42.\overline{1}| = 42.\overline{1} $
→ Answer: $ 42.\overline{1}; 42.\overline{1} $

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✔ Final Answers Summary:

#### Section 2: Points on Number Line
7. C: $ -4\frac{1}{2} $
8. F: $ -1.5 $ or $ -\frac{3}{2} $
9. A: $ 0.5 $ or $ \frac{1}{2} $
10. E: $ 5.5 $ or $ 5\frac{1}{2} $
11. B: $ -2 $
12. D: $ 1.5 $ or $ \frac{3}{2} $

#### Section 3: Additive Inverse and Absolute Value

| # | Number | Additive Inverse | Absolute Value |
|---|--------|------------------|----------------|
| 13 | 9.14 | -9.14 | 9.14 |
| 14 | -6.11 | 6.11 | 6.11 |
| 15 | -18.75 | 18.75 | 18.75 |
| 16 | $-\frac{5}{3}$ | $\frac{5}{3}$ | $\frac{5}{3}$ |
| 17 | $-\frac{11}{12}$ | $\frac{11}{12}$ | $\frac{11}{12}$ |
| 18 | -3.01 | 3.01 | 3.01 |
| 19 | 4.76 | -4.76 | 4.76 |
| 20 | -0.225 | 0.225 | 0.225 |
| 21 | -0.914 | 0.914 | 0.914 |
| 22 | $-18\frac{2}{7}$ | $18\frac{2}{7}$ | $18\frac{2}{7}$ |
| 23 | $\frac{9}{10}$ | $-\frac{9}{10}$ | $\frac{9}{10}$ |
| 24 | -7.23 | 7.23 | 7.23 |
| 25 | 9.008 | -9.008 | 9.008 |
| 26 | -11.1 | 11.1 | 11.1 |
| 27 | -3.54 | 3.54 | 3.54 |
| 28 | $-\frac{29}{30}$ | $\frac{29}{30}$ | $\frac{29}{30}$ |
| 29 | $-\frac{4}{9}$ | $\frac{4}{9}$ | $\frac{4}{9}$ |
| 30 | $-42.\overline{1}$ | $42.\overline{1}$ | $42.\overline{1}$ |

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Let me know if you'd like a visual explanation for plotting or understanding repeating decimals!