Comparing Rational Numbers Worksheet | Fun and Engaging 6th Grade ... - Free Printable

Let's solve this step-by-step, explaining each section of the worksheet.

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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

We need to place them on a number line centered at 0.

Step-by-step placement (from left to right):

- The most negative number is -7, then -6, -4, -3, -2, -1, then 0, followed by 1, 2, 3, 4, and finally 8.

So, from left to right on the number line:
```
-7 -6 -4 -3 -2 -1 0 1 2 3 4 8
```

You would mark each of these numbers at their correct positions on the number line.

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#### 2) Compare pairs using < and > symbols

Use the number line: Numbers to the right are greater than numbers to the left.

Let’s compare each pair:

| Pair | Comparison | Reason |
|------|------------|--------|
| -2 ___ 4 | -2 < 4 | -2 is to the left of 4 |
| 8 ___ -6 | 8 > -6 | 8 is to the right of -6 |
| -8 ___ -4 | -8 < -4 | -8 is to the left of -4 |
| -7 ___ 1 | -7 < 1 | -7 is to the left of 1 |
| -1 ___ 2 | -1 < 2 | -1 is to the left of 2 |
| -6 ___ -7 | -6 > -7 | -6 is to the right of -7 |
| 3 ___ -4 | 3 > -4 | 3 is to the right of -4 |
| 4 ___ -3 | 4 > -3 | 4 is to the right of -3 |
| -3 ___ -1 | -3 < -1 | -3 is to the left of -1 |

✔ Answers:
- -2 < 4
- 8 > -6
- -8 < -4
- -7 < 1
- -1 < 2
- -6 > -7
- 3 > -4
- 4 > -3
- -3 < -1

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Section B: Compare integers using < and >

Rules:
- Positive numbers > negative numbers
- For negatives: the one with smaller absolute value is greater (closer to zero)

Let’s go through each:

| Pair | Comparison | Explanation |
|------|------------|-----------|
| -10 ___ -7 | -10 < -7 | -10 is further left than -7 |
| -7 ___ -17 | -7 > -17 | -7 is closer to 0 than -17 |
| -169 ___ -254 | -169 > -254 | -169 is closer to 0 |
| -10 ___ 7 | -10 < 7 | Negative < positive |
| -170 ___ 17 | -170 < 17 | Negative < positive |
| -583 ___ -599 | -583 > -599 | -583 is closer to 0 |
| -10 ___ -17 | -10 > -17 | -10 is closer to 0 |
| 215 ___ -649 | 215 > -649 | Positive > negative |
| -338 ___ -180 | -338 < -180 | -338 is further left |

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

---

Section C: Compare decimals using < and >

Same rules apply. Remember:
- Compare digit by digit from left to right.
- For negatives: the one with smaller absolute value is greater.

Let’s do each:

| Pair | Comparison | Explanation |
|------|------------|-----------|
| 2.5 ___ 1.5 | 2.5 > 1.5 | 2.5 is larger |
| -4.9 ___ -5.3 | -4.9 > -5.3 | -4.9 is closer to 0 |
| -4.2 ___ 3.6 | -4.2 < 3.6 | Negative < positive |
| -2.1 ___ -2.4 | -2.1 > -2.4 | -2.1 is closer to 0 |
| -3.5 ___ -1.1 | -3.5 < -1.1 | -3.5 is further left |
| -8.9 ___ -8.8 | -8.9 < -8.8 | -8.9 is further left |

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

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✔ Final Answer Summary

#### Section A – Part 2
- -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

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🔍 Key Concepts Recap:

- On a number line: Right = Greater, Left = Smaller
- All positive numbers > negative numbers
- Among negative numbers: the one closer to zero is greater
- For decimals, compare digits from left to right; for negatives, same rule applies

This helps build a strong foundation in understanding rational numbers and their ordering!

Let me know if you'd like a visual number line or printable version!