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:

- Negative numbers go to the left of 0.
- Positive numbers go to the right of 0.
- The farther left a number is, the smaller it is.
- The farther right, the larger it is.

So from left to right (smallest to largest):

- -7, -6, -4, -3, -2, -1, 1, 2, 3, 4, 8

Number line positions (from left to right):

```
-7 -6 -4 -3 -2 -1 0 1 2 3 4 8
```

You would mark each of these integers on the corresponding tick marks.

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

Use the number line concept:
- Numbers to the right are greater than those to the left.

Now compare each pair:

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

✔ Answers for Section A, Part 2:

```
-2 < 4 8 > -6 -8 < -4
-7 < 1 -1 < 2 -6 > -7
3 > -4 4 > -3 -3 < -1
```

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Section B: Comparing Integers

Compare using < or >.

Rule:
- For negative numbers: the one with the larger absolute value is smaller.
- Positive numbers are always greater than negative ones.
- Zero is greater than negative numbers.

Let’s go through each:

| Pair | Reasoning | Answer |
|------|---------|--------|
| -10 ___ -7 | |-10| = 10 > |-7| = 7 → -10 is smaller → -10 < -7 |
| -7 ___ -17 | |-7| = 7 < |-17| = 17 → -7 is larger → -7 > -17 |
| -169 ___ -254 | |-169| = 169 < 254 → -169 is larger → -169 > -254 |
| -10 ___ 7 | Negative vs positive → -10 < 7 |
| -170 ___ 17 | Negative vs positive → -170 < 17 |
| -583 ___ -599 | |-583| = 583 < 599 → -583 is larger → -583 > -599 |
| -10 ___ -17 | |-10| = 10 < 17 → -10 is larger → -10 > -17 |
| 215 ___ -649 | Positive vs negative → 215 > -649 |
| -338 ___ -180 | |-338| = 338 > 180 → -338 is smaller → -338 < -180 |

✔ Answers for Section B:

```
-10 < -7 -7 > -17 -169 > -254
-10 < 7 -170 < 17 -583 > -599
-10 > -17 215 > -649 -338 < -180
```

---

Section C: Comparing Decimals

Same rules apply. Compare digit by digit, especially for negatives.

| Pair | Reasoning | Answer |
|------|---------|--------|
| 2.5 ___ 1.5 | 2.5 > 1.5 → 2.5 > 1.5 |
| -4.9 ___ -5.3 | Compare absolute values: 4.9 < 5.3 → so -4.9 is greater → -4.9 > -5.3 |
| -4.2 ___ 3.6 | Negative vs positive → -4.2 < 3.6 |
| -2.1 ___ -2.4 | |-2.1| = 2.1 < 2.4 → so -2.1 is greater → -2.1 > -2.4 |
| -3.5 ___ -1.1 | |-3.5| = 3.5 > 1.1 → so -3.5 is smaller → -3.5 < -1.1 |
| -8.9 ___ -8.8 | |-8.9| = 8.9 > 8.8 → so -8.9 is smaller → -8.9 < -8.8 |

✔ Answers for 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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✔ Final Answers Summary

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#### 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
```

---

🔍 Key Concepts Recap:

- On a number line: Right = greater, Left = smaller
- For negative numbers: the one with the larger absolute value is smaller
- Positive numbers > Negative numbers
- When comparing decimals, look at digits from left to right; for negatives, reverse logic based on magnitude

Let me know if you'd like a visual number line drawn out!