Comparing Negative Numbers worksheet with number line and comparison exercises.

Problem: Comparing Negative Numbers

The task involves comparing negative numbers using a number line and the symbols `<` (less than) and `>` (greater than). Let's solve each section step by step.

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Section A: Using a Number Line

#### 1) Put these integers in the correct position on the number line.
The integers given are:
-2, 4, -7, 1, 3, -4, 8, -6, -1, 2, -3

Steps:
- The number line is already provided with 0 marked in the center.
- Positive numbers go to the right of 0.
- Negative numbers go to the left of 0.
- Each tick mark represents one unit.

Placement:
- Positive numbers: 1, 2, 3, 4, 8
- Place 1 one unit to the right of 0.
- Place 2 two units to the right of 0.
- Place 3 three units to the right of 0.
- Place 4 four units to the right of 0.
- Place 8 eight units to the right of 0.
- Negative numbers: -1, -2, -3, -4, -6, -7
- Place -1 one unit to the left of 0.
- Place -2 two units to the left of 0.
- Place -3 three units to the left of 0.
- Place -4 four units to the left of 0.
- Place -6 six units to the left of 0.
- Place -7 seven units to the left of 0.

Number Line:
```
-7 -6 -4 -3 -2 -1 0 1 2 3 4 8
|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
```

#### 2) Now use your number line to help compare the following pairs of numbers using the < and > symbols.

Comparisons:
1. -2 ? 4
- -2 is to the left of 4 on the number line.
- Therefore, \(-2 < 4\).

2. -7 ? 1
- -7 is to the left of 1 on the number line.
- Therefore, \(-7 < 1\).

3. 3 ? -4
- 3 is to the right of -4 on the number line.
- Therefore, \(3 > -4\).

4. 8 ? -6
- 8 is to the right of -6 on the number line.
- Therefore, \(8 > -6\).

5. -1 ? 2
- -1 is to the left of 2 on the number line.
- Therefore, \(-1 < 2\).

6. -8 ? -4
- -8 is to the left of -4 on the number line.
- Therefore, \(-8 < -4\).

7. -6 ? -7
- -6 is to the right of -7 on the number line.
- Therefore, \(-6 > -7\).

8. -3 ? -1
- -3 is to the left of -1 on the number line.
- Therefore, \(-3 < -1\).

Answers for Section A:
1. \(-2 < 4\)
2. \(-7 < 1\)
3. \(3 > -4\)
4. \(8 > -6\)
5. \(-1 < 2\)
6. \(-8 < -4\)
7. \(-6 > -7\)
8. \(-3 < -1\)

---

Section B: Use the < and > symbols to compare the following pairs of integers.

#### Comparisons:
1. -10 ? -7
- -10 is to the left of -7 on the number line.
- Therefore, \(-10 < -7\).

2. -10 ? 7
- -10 is to the left of 7 on the number line.
- Therefore, \(-10 < 7\).

3. -10 ? -17
- -10 is to the right of -17 on the number line.
- Therefore, \(-10 > -17\).

4. -7 ? -17
- -7 is to the right of -17 on the number line.
- Therefore, \(-7 > -17\).

5. -170 ? 17
- -170 is to the left of 17 on the number line.
- Therefore, \(-170 < 17\).

6. -169 ? -254
- -169 is to the right of -254 on the number line.
- Therefore, \(-169 > -254\).

7. -583 ? -599
- -583 is to the right of -599 on the number line.
- Therefore, \(-583 > -599\).

8. 215 ? -649
- 215 is to the right of -649 on the number line.
- Therefore, \(215 > -649\).

9. -338 ? -180
- -338 is to the left of -180 on the number line.
- Therefore, \(-338 < -180\).

Answers for Section B:
1. \(-10 < -7\)
2. \(-10 < 7\)
3. \(-10 > -17\)
4. \(-7 > -17\)
5. \(-170 < 17\)
6. \(-169 > -254\)
7. \(-583 > -599\)
8. \(215 > -649\)
9. \(-338 < -180\)

---

Section C: Use the < and > symbols to compare the following pairs of decimals.

#### Comparisons:
1. 2.5 ? 1.5
- 2.5 is greater than 1.5.
- Therefore, \(2.5 > 1.5\).

2. -4.2 ? 3.6
- -4.2 is less than 3.6.
- Therefore, \(-4.2 < 3.6\).

3. -3.5 ? -1.1
- -3.5 is to the left of -1.1 on the number line.
- Therefore, \(-3.5 < -1.1\).

4. -4.9 ? -5.3
- -4.9 is to the right of -5.3 on the number line.
- Therefore, \(-4.9 > -5.3\).

5. -2.1 ? -2.4
- -2.1 is to the right of -2.4 on the number line.
- Therefore, \(-2.1 > -2.4\).

6. -8.9 ? -8.8
- -8.9 is to the left of -8.8 on the number line.
- Therefore, \(-8.9 < -8.8\).

Answers for Section C:
1. \(2.5 > 1.5\)
2. \(-4.2 < 3.6\)
3. \(-3.5 < -1.1\)
4. \(-4.9 > -5.3\)
5. \(-2.1 > -2.4\)
6. \(-8.9 < -8.8\)

---

Final Answer:

\[
\boxed{
\begin{array}{l}
\text{Section A:} \\
1. -2 < 4 \\
2. -7 < 1 \\
3. 3 > -4 \\
4. 8 > -6 \\
5. -1 < 2 \\
6. -8 < -4 \\
7. -6 > -7 \\
8. -3 < -1 \\
\\
\text{Section B:} \\
1. -10 < -7 \\
2. -10 < 7 \\
3. -10 > -17 \\
4. -7 > -17 \\
5. -170 < 17 \\
6. -169 > -254 \\
7. -583 > -599 \\
8. 215 > -649 \\
9. -338 < -180 \\
\\
\text{Section C:} \\
1. 2.5 > 1.5 \\
2. -4.2 < 3.6 \\
3. -3.5 < -1.1 \\
4. -4.9 > -5.3 \\
5. -2.1 > -2.4 \\
6. -8.9 < -8.8 \\
\end{array}
}
\]