Practice worksheet for plotting rational numbers on number lines.

Sure! Let’s solve the worksheet “Rational Numbers on Number Lines” step by step.

---

## 📌 Part 1: Plot each number on the number line

There are 8 number lines, each with a rational number to plot. We’ll go one by one.

---

1. Plot 5/8

- This is a positive fraction between 0 and 1.
- Divide the segment from 0 to 1 into 8 equal parts.
- Count 5 parts to the right of 0 → that’s 5/8.
- ✔ Place a dot at the 5th tick mark after 0.

---

2. Plot 0.8

- 0.8 = 8/10 = 4/5
- Between 0 and 1, divide into 10 parts (tenths).
- The 8th tick mark after 0 → 0.8
- ✔ Place a dot at 0.8 — same as 4/5 or 8/10.

> Note: 5/8 = 0.625, so it’s to the left of 0.8.

---

3. Plot 7/5

- 7/5 = 1.4 → greater than 1.
- On the number line from 0 to 2, find 1.4.
- Divide 1 to 2 into 5 parts → each part = 0.2
- 1 + 0.4 = 1.4 → 2nd tick after 1.
- ✔ Place a dot at 1.4.

---

4. Plot –0.5

- Halfway between –1 and 0.
- ✔ Place a dot midway between –1 and 0.

---

5. Plot –1/2

- Same as –0.5!
- ✔ Same point as above.

> So both –0.5 and –1/2 go in the same place.

---

6. Plot –2/5

- –2/5 = –0.4
- Between 0 and –1, divide into 5 parts → each = –0.2
- 2nd tick to the left of 0 → –0.4
- ✔ Place dot at –0.4

---

7. Plot –0.75

- –0.75 = –3/4
- Between –1 and 0, divide into 4 parts → each = –0.25
- 3rd tick from 0 toward –1 → –0.75
- ✔ Place dot at –0.75

---

8. Plot 2 1/2

- That’s 2.5 → halfway between 2 and 3.
- ✔ Place dot midway between 2 and 3.

---

9. Plot –1.4

- –1.4 is between –1 and –2.
- From –1, go 0.4 left → so 4/10 = 2/5 left of –1.
- Or: –1.4 = –14/10 = –7/5
- ✔ Place dot 0.4 units left of –1 (or 4 ticks if divided into tenths).

---

10. Plot –1 3/4

- –1 3/4 = –1.75
- Between –1 and –2, divide into 4 parts → each = –0.25
- 3rd tick from –1 toward –2 → –1.75
- ✔ Place dot at –1.75

---

## 📌 Part 2: Plot all of the numbers on the number line below

You’re given 6 numbers:

> A. –0.2
> B. 1 1/10 → 1.1
> C. –1/2 → –0.5
> D. –0.9
> E. 1.6
> F. –2/5 → –0.4

We need to plot these on the final number line (from –3 to 3, with marks every 0.2 or 0.5? Let’s assume it's marked in 0.2 increments based on spacing.)

---

Let’s convert all to decimals for easy plotting:

- A. –0.2
- B. 1.1
- C. –0.5
- D. –0.9
- E. 1.6
- F. –0.4

Now, locate each:

✔ A. –0.2 → 1 tick left of 0 (if each tick = 0.2)

✔ B. 1.1 → halfway between 1.0 and 1.2 → if ticks are every 0.2, then halfway between 1.0 and 1.2 → you might need to estimate or mark slightly past 1.0

✔ C. –0.5 → halfway between –0.4 and –0.6 → or exactly 2.5 ticks left of 0 (if each tick = 0.2)

✔ D. –0.9 → very close to –1, just 0.1 right of –1 → if ticks are every 0.2, this is halfway between –0.8 and –1.0

✔ E. 1.6 → 3 ticks right of 1.0 (since 1.0 → 1.2 → 1.4 → 1.6)

✔ F. –0.4 → 2 ticks left of 0

---

## 🎯 Final Tips for Students:

- Always convert fractions to decimals if unsure.
- Use benchmarks: 0, 0.5, 1, –0.5, etc.
- Negative numbers go left of zero; positive go right.
- Fractions like 1/2, 1/4, 3/4 are easy to plot using halves or quarters.
- Mixed numbers >1 go beyond 1.

---

## ✔ Summary of Answers (for plotting):

| Number | Decimal | Where to Plot |
|---------------|---------|----------------------------------------|
| 5/8 | 0.625 | Between 0 and 1, closer to 0.6 |
| 0.8 | 0.8 | 8/10 mark after 0 |
| 7/5 | 1.4 | Between 1 and 2, 4/10 past 1 |
| –0.5 | –0.5 | Midway between –1 and 0 |
| –1/2 | –0.5 | Same as above |
| –2/5 | –0.4 | 2/5 left of 0 |
| –0.75 | –0.75 | 3/4 left of 0 |
| 2 1/2 | 2.5 | Midway between 2 and 3 |
| –1.4 | –1.4 | 0.4 left of –1 |
| –1 3/4 | –1.75 | 3/4 left of –1 |

---

For the final number line (Part 2):

Plot these points:

- –0.9 → near –1
- –0.5 → middle of –1 and 0
- –0.4 → slightly right of –0.5
- –0.2 → closer to 0
- 1.1 → just past 1
- 1.6 → 3 ticks past 1 (if tick = 0.2)

---

✔ You’ve now successfully plotted all rational numbers on their respective number lines!

Let me know if you want a visual sketch or printable answer key! 😊