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

Absolutely! Let’s solve this worksheet step by step, explaining the reasoning behind each answer.

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## Section A: Using a number line

1) Put these integers in the correct position on the number line.

The numbers to place are:
> -2, 4, -7, 1, 3, -4, 8, -6, -1, 2, -3

How to do it:
- On a number line, numbers increase from left to right.
- Negative numbers go to the left of 0; positive numbers to the right.
- The farther left a negative number is, the smaller (more negative) it is.

So, ordering them from least to greatest:

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

On the number line, you would mark:
- -7 at the 7th tick to the left of 0
- -6 at the 6th tick to the left
- -4 at the 4th tick to the left
- -3 at the 3rd tick to the left
- -2 at the 2nd tick to the left
- -1 at the 1st tick to the left
- 1 at the 1st tick to the right
- 2 at the 2nd tick to the right
- 3 at the 3rd tick to the right
- 4 at the 4th tick to the right
- 8 at the 8th tick to the right

*(Note: Since we can’t draw here, imagine placing them in that order along the line.)*

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2) Use your number line to compare pairs using < and >

We’ll use the rule:
> On a number line, if A is to the left of B, then A < B
> If A is to the right of B, then A > B

Let’s go pair by pair:

#### First column:
- -2 □ 4 → -2 is left of 4 → -2 < 4
- -7 □ 1 → -7 is left of 1 → -7 < 1
- 3 □ -4 → 3 is right of -4 → 3 > -4

#### Second column:
- 8 □ -6 → 8 is right of -6 → 8 > -6
- -1 □ 2 → -1 is left of 2 → -1 < 2
- 4 □ -3 → 4 is right of -3 → 4 > -3

#### Third column:
- -8 □ -4 → -8 is left of -4 → -8 < -4
- -6 □ -7 → -6 is right of -7 → -6 > -7
- -3 □ -1 → -3 is left of -1 → -3 < -1

✔ Final Answers for Section A.2:

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

---

## Section B: Compare integers using < and >

Same logic: For negative numbers, the one with the *larger absolute value* is actually *smaller*.

Example: -10 vs -7 → -10 is more negative → -10 < -7

Let’s solve:

#### First column:
- -10 □ -7 → -10 is left of -7 → -10 < -7
- -10 □ 7 → negative < positive → -10 < 7
- -10 □ -17 → -10 is right of -17 → -10 > -17

#### Second column:
- -7 □ -17 → -7 is right of -17 → -7 > -17
- -170 □ 17 → negative < positive → -170 < 17
- 215 □ -649 → positive > negative → 215 > -649

#### Third column:
- -169 □ -254 → -169 is right of -254 → -169 > -254
- -583 □ -599 → -583 is right of -599 → -583 > -599
- -338 □ -180 → -338 is left of -180 → -338 < -180

✔ Final Answers for Section B:

```
-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!

For positive decimals: larger number = greater value
For negative decimals: the one closer to zero is greater.

Examples:
- 2.5 > 1.5 (obvious)
- -4.9 > -5.3 (because -4.9 is closer to zero)

Let’s solve:

#### First column:
- 2.5 □ 1.5 → 2.5 > 1.5 → 2.5 > 1.5
- -4.2 □ 3.6 → negative < positive → -4.2 < 3.6
- -3.5 □ -1.1 → -1.1 is closer to zero → -3.5 < -1.1

#### Second column:
- -4.9 □ -5.3 → -4.9 is closer to zero → -4.9 > -5.3
- -2.1 □ -2.4 → -2.1 is closer to zero → -2.1 > -2.4
- -8.9 □ -8.8 → -8.8 is closer to zero → -8.9 < -8.8

✔ Final 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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## ✔ All Answers Summarized:

Section A.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 Concept Recap:

- Number Line Rule: Left = smaller, Right = larger
- Negative Numbers: The “bigger” the number (like -100), the *smaller* its value.
- Decimals: Same as integers — compare digit by digit, or think of their position on the number line.

You’ve got this! 💪 Let me know if you want to visualize any part with a sketch or need extra practice.