Math worksheet for comparing negative numbers using number lines, integers, and decimals.

Problem Overview:

The task involves comparing negative numbers using a number line and the symbols `<` (less than) and `>` (greater than). The worksheet is divided into three sections:

1. Section A: Placing integers on a number line and comparing pairs of integers.
2. Section B: Comparing pairs of integers without a number line.
3. Section C: Comparing pairs of decimals.

Solution:

#### Section A: Using a Number Line

##### Step 1: Place the integers on the number line
The integers to place are: `-2, 4, -7, 1, 3, -8, -6, -1, 2, -3`.

- Number Line: The number line provided ranges from approximately `-10` to `+5`.
- Placement:
- `-2`: Between `0` and `-4`.
- `4`: To the right of `0`, between `2` and `6`.
- `-7`: To the left of `0`, between `-8` and `-6`.
- `1`: Between `0` and `2`.
- `3`: Between `2` and `4`.
- `-8`: To the left of `0`, between `-10` and `-6`.
- `-6`: To the left of `0`, between `-8` and `-4`.
- `-1`: Between `0` and `2`.
- `2`: Between `0` and `4`.
- `-3`: Between `0` and `-6`.

##### Step 2: Compare pairs of integers using `<` and `>`
We use the number line to determine which number is greater or smaller.

1. `-2` ___ `4`
- `-2` is to the left of `4` on the number line.
- Therefore, `-2 < 4`.

2. `8` ___ `-6`
- `8` is to the right of `-6` on the number line.
- Therefore, `8 > -6`.

3. `-8` ___ `-4`
- `-8` is to the left of `-4` on the number line.
- Therefore, `-8 < -4`.

4. `-7` ___ `1`
- `-7` is to the left of `1` on the number line.
- Therefore, `-7 < 1`.

5. `-1` ___ `2`
- `-1` is to the left of `2` on the number line.
- Therefore, `-1 < 2`.

6. `-6` ___ `7`
- `-6` is to the left of `7` on the number line.
- Therefore, `-6 < 7`.

7. `3` ___ `-4`
- `3` is to the right of `-4` on the number line.
- Therefore, `3 > -4`.

8. `4` ___ `-3`
- `4` is to the right of `-3` on the number line.
- Therefore, `4 > -3`.

9. `-3` ___ `-1`
- `-3` is to the left of `-1` on the number line.
- Therefore, `-3 < -1`.

#### Section B: Comparing Pairs of Integers

We compare the pairs of integers directly based on their positions relative to zero and each other.

1. `-10` ___ `-7`
- `-10` is to the left of `-7` on the number line.
- Therefore, `-10 < -7`.

2. `-7` ___ `-17`
- `-7` is to the right of `-17` on the number line.
- Therefore, `-7 > -17`.

3. `-169` ___ `-254`
- `-169` is to the right of `-254` on the number line.
- Therefore, `-169 > -254`.

4. `-10` ___ `7`
- `-10` is to the left of `7` on the number line.
- Therefore, `-10 < 7`.

5. `-170` ___ `17`
- `-170` is to the left of `17` on the number line.
- Therefore, `-170 < 17`.

6. `-583` ___ `-599`
- `-583` is to the right of `-599` on the number line.
- Therefore, `-583 > -599`.

7. `-10` ___ `-17`
- `-10` is to the right of `-17` on the number line.
- Therefore, `-10 > -17`.

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`.

#### Section C: Comparing Pairs of Decimals

We compare the pairs of decimals directly based on their numerical values.

1. `2.5` ___ `1.5`
- `2.5` is greater than `1.5`.
- Therefore, `2.5 > 1.5`.

2. `-4.9` ___ `-5.3`
- `-4.9` is to the right of `-5.3` on the number line.
- Therefore, `-4.9 > -5.3`.

3. `-4.2` ___ `3.6`
- `-4.2` is to the left of `3.6` on the number line.
- Therefore, `-4.2 < 3.6`.

4. `-2.1` ___ `-2.4`
- `-2.1` is to the right of `-2.4` on the number line.
- Therefore, `-2.1 > -2.4`.

5. `-3.5` ___ `-1.1`
- `-3.5` is to the left of `-1.1` on the number line.
- Therefore, `-3.5 < -1.1`.

6. `-8.9` ___ `-8.8`
- `-8.9` is to the left of `-8.8` on the number line.
- Therefore, `-8.9 < -8.8`.

Final Answers:

#### Section A
1. `-2 < 4`
2. `8 > -6`
3. `-8 < -4`
4. `-7 < 1`
5. `-1 < 2`
6. `-6 < 7`
7. `3 > -4`
8. `4 > -3`
9. `-3 < -1`

#### Section B
1. `-10 < -7`
2. `-7 > -17`
3. `-169 > -254`
4. `-10 < 7`
5. `-170 < 17`
6. `-583 > -599`
7. `-10 > -17`
8. `215 > -649`
9. `-338 < -180`

#### Section C
1. `2.5 > 1.5`
2. `-4.9 > -5.3`
3. `-4.2 < 3.6`
4. `-2.1 > -2.4`
5. `-3.5 < -1.1`
6. `-8.9 < -8.8`

Boxed Final Answer:

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