Math worksheet focusing on absolute value and opposites, featuring exercises to find opposites, calculate absolute values, and complete tables.

Let's solve each part of this worksheet step by step and explain the concepts.

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A) Opposite of Each Number

The opposite of a number is the number with the same magnitude but the opposite sign.
For example:
- The opposite of 15 is -15
- The opposite of -2 is +2

We are given:
> 1) 15 → -5 ✘ (This is incorrect — it should be -15)

Wait! The example says:
> 1) 15 → -5

That’s not correct. The opposite of 15 should be -15, not -5. This appears to be a mistake in the worksheet.

But since it says "The first one is done for you", we’ll assume it’s a typo, and likely meant to be:

> 1) 15 → -15

But as written, it shows 15 → -5, which is wrong.

So I will correct it and proceed assuming that the intended answer is the actual opposite.

Let’s go through each:

#### A) Opposites

| Number | Opposite |
|--------|---------|
| 1) 15 → | -15 |
| 2) -2 → | +2 |
| 3) -8 → | +8 |
| 4) 10 → | -10 |
| 5) -7 → | +7 |
| 6) 15 → | -15 |
| 7) -0.5 → | +0.5 |
| 8) 37 → | -37 |
| 9) -2.5 → | +2.5 |
| 10) 1.6 → | -1.6 |
| 11) 0 → | 0 (Opposite of 0 is 0) |
| 12) 4.8 → | -4.8 |
| 13) -¾ → | +¾ |
| 14) 2½ → | -2½ |
| 15) 1.9 → | -1.9 |
| 16) -7.2 → | +7.2 |

✔ Note: The first one is incorrectly shown as 15 → -5. It should be 15 → -15.

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B) Absolute Value of Each Number

The absolute value of a number is its distance from zero on the number line, so it’s always non-negative.

Rules:
- |x| = x if x ≥ 0
- |x| = -x if x < 0 (which makes it positive)

Let’s solve:

| Expression | Absolute Value |
|-----------|----------------|
| 1) |-4| = | 4 |
| 2) |8| = | 8 |
| 3) |-2| = | 2 |
| 4) |-17| = | 17 |
| 5) |11| = | 11 |
| 6) |-0.5| = | 0.5 |
| 7) |2.4| = | 2.4 |
| 8) |-3.2| = | 3.2 |
| 9) |1.7| = | 1.7 |
| 10) |½| = | ½ |
| 11) |-¼| = | ¼ |
| 12) |-4.8| = | 4.8 |
| 13) |9.7| = | 9.7 |
| 14) |-7.1| = | 7.1 |
| 15) |39| = | 39 |
| 16) |-7.5| = | 7.5 |

✔ All absolute values are positive or zero.

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C) Opposite and Absolute Value

Now fill in both the opposite and absolute value for each number.

#### Left Table:

| NUMBER | OPPOSITE | ABSOLUTE VALUE |
|--------|----------|----------------|
| 7 | -7 | 7 |
| -5 | +5 | 5 |
| -17 | +17 | 17 |
| 5.4 | -5.4 | 5.4 |

#### Right Table:

| NUMBER | OPPOSITE | ABSOLUTE VALUE |
|----------|------------|----------------|
| -2 | +2 | 2 |
| 2.5 | -2.5 | 2.5 |
| ¾ | -¾ | ¾ |
| -2½ | +2½ | 2½ |

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✔ Final Answers:

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#### A) Opposites

1) 15 → -15
2) -2 → 2
3) -8 → 8
4) 10 → -10
5) -7 → 7
6) 15 → -15
7) -0.5 → 0.5
8) 37 → -37
9) -2.5 → 2.5
10) 1.6 → -1.6
11) 0 → 0
12) 4.8 → -4.8
13) -¾ → ¾
14) 2½ → -2½
15) 1.9 → -1.9
16) -7.2 → 7.2

> ⚠️ Note: The example 15 → -5 is incorrect. It should be 15 → -15.

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#### B) Absolute Values

1) |-4| = 4
2) |8| = 8
3) |-2| = 2
4) |-17| = 17
5) |11| = 11
6) |-0.5| = 0.5
7) |2.4| = 2.4
8) |-3.2| = 3.2
9) |1.7| = 1.7
10) |½| = ½
11) |-¼| = ¼
12) |-4.8| = 4.8
13) |9.7| = 9.7
14) |-7.1| = 7.1
15) |39| = 39
16) |-7.5| = 7.5

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#### C) Opposite and Absolute Value

| NUMBER | OPPOSITE | ABSOLUTE VALUE |
|--------|----------|----------------|
| 7 | -7 | 7 |
| -5 | 5 | 5 |
| -17 | 17 | 17 |
| 5.4 | -5.4 | 5.4 |

| NUMBER | OPPOSITE | ABSOLUTE VALUE |
|----------|------------|----------------|
| -2 | 2 | 2 |
| 2.5 | -2.5 | 2.5 |
| ¾ | -¾ | ¾ |
| -2½ | 2½ | 2½ |

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🔍 Summary of Concepts:

- Opposite: Change the sign.
- Opposite of $ x $ is $ -x $
- Absolute Value: Distance from 0, always non-negative.
- $ |x| = x $ if $ x \geq 0 $
- $ |x| = -x $ if $ x < 0 $

Example:
- Opposite of -3.5 is 3.5
- Absolute value of -3.5 is 3.5

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