Math worksheet for comparing rational numbers, featuring exercises on number lines, integer comparisons, and decimal comparisons.

Let’s solve this step by step.

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Section A, Question 1: Put integers on the number line

We are given these integers:
-2, 4, -7, 1, 3, -4, 8, -6, -1, 2, -3

The number line has 0 in the middle. We need to place each number at its correct position.

Think of it like this:
- Negative numbers go to the left of 0.
- Positive numbers go to the right of 0.
- The farther left a negative number is, the smaller it is (e.g., -7 is less than -1).
- The farther right a positive number is, the bigger it is (e.g., 8 is more than 2).

So let’s order them from smallest to largest:

Start with negatives:
-7, -6, -4, -3, -2, -1
Then positives:
1, 2, 3, 4, 8

Now we can imagine placing them on the number line accordingly — but since we’re not drawing here, we’ll use this ordering for comparisons next.

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Section A, Question 2: Compare using < or >

Remember:
- If the first number is to the left of the second on the number line → use <
- If the first number is to the right → use >

Let’s do each pair:

1. -2 ___ 4 → -2 is left of 4 → -2 < 4

2. 8 ___ -6 → 8 is right of -6 → 8 > -6

3. -8 ___ -4 → -8 is left of -4 → -8 < -4

4. -7 ___ 1 → -7 is left of 1 → -7 < 1

5. -1 ___ 2 → -1 is left of 2 → -1 < 2

6. -6 ___ -7 → -6 is right of -7 → -6 > -7

7. 3 ___ -4 → 3 is right of -4 → 3 > -4

8. 4 ___ -3 → 4 is right of -3 → 4 > -3

9. -3 ___ -1 → -3 is left of -1 → -3 < -1

✔ All done for Section A.

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Section B: Compare pairs of integers (no number line needed now)

Same rule: Left = smaller (<), Right = larger (>)

1. -10 ___ -7 → -10 is left of -7 → -10 < -7

2. -7 ___ -17 → -7 is right of -17 → -7 > -17

3. -169 ___ -254 → -169 is right of -254 → -169 > -254

4. -10 ___ 7 → -10 is left of 7 → -10 < 7

5. -170 ___ 17 → -170 is left of 17 → -170 < 17

6. -583 ___ -599 → -583 is right of -599 → -583 > -599

7. -10 ___ -17 → -10 is right of -17 → -10 > -17

8. 215 ___ -649 → 215 is right of -649 → 215 > -649

9. -338 ___ -180 → -338 is left of -180 → -338 < -180

✔ Done with Section B.

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Section C: Compare decimals

Same idea! Just look at their positions on the number line.

Tip: For negative decimals, remember — the one closer to zero is BIGGER.

Example: -2.1 is greater than -2.4 because -2.1 is closer to 0.

Let’s go:

1. 2.5 ___ 1.5 → 2.5 is right of 1.5 → 2.5 > 1.5

2. -4.9 ___ -5.3 → -4.9 is right of -5.3 → -4.9 > -5.3

3. -4.2 ___ 3.6 → -4.2 is left of 3.6 → -4.2 < 3.6

4. -2.1 ___ -2.4 → -2.1 is right of -2.4 → -2.1 > -2.4

5. -3.5 ___ -1.1 → -3.5 is left of -1.1 → -3.5 < -1.1

6. -8.9 ___ -8.8 → -8.9 is left of -8.8 → -8.9 < -8.8

✔ All done!

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Final Answer:

Section A, Q2:
-2 < 4
8 > -6
-8 < -4
-7 < 1
-1 < 2
-6 > -7
3 > -4
4 > -3
-3 < -1

Section B:
-10 < -7
-7 > -17
-169 > -254
-10 < 7
-170 < 17
-583 > -599
-10 > -17
215 > -649
-338 < -180

Section C:
2.5 > 1.5
-4.9 > -5.3
-4.2 < 3.6
-2.1 > -2.4
-3.5 < -1.1
-8.9 < -8.8