Integer and absolute value practice worksheet for math education.

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Let me walk through the types of problems typically found on such a worksheet and provide solutions with explanations.

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🔹 Section 1: Finding Absolute Value

> *Find the absolute value of each integer.*

The absolute value of a number is its distance from zero on the number line, regardless of direction. So:

- $ |a| = a $ if $ a \geq 0 $
- $ |a| = -a $ if $ a < 0 $

#### Example:
- $ |-5| = 5 $
- $ |7| = 7 $

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🔹 Section 2: Opposites of Integers

> *Write the opposite of each integer.*

The opposite of an integer is the number with the same magnitude but the opposite sign.

#### Examples:
- Opposite of $ 12 $ is $ -12 $
- Opposite of $ -79 $ is $ 79 $

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🔹 Section 3: Absolute Value of Each Integer

This section asks for the absolute value again — same as Section 1.

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🔹 Section 4: Problem Solving

> 20. Name a pair of integers with the same absolute value.

Answer:
Any two integers that are opposites have the same absolute value.

For example:
- $ 8 $ and $ -8 $ → both have absolute value $ 8 $
- $ -15 $ and $ 15 $ → both have absolute value $ 15 $

So, one valid answer is:
👉 $ 5 $ and $ -5 $

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✔ Let’s Solve the Problems Based on Typical Worksheet Format

Assuming the worksheet has these problems:

#### Finding Absolute Value
1. $ |-12| = 12 $
2. $ |45| = 45 $
3. $ |-7| = 7 $
4. $ |0| = 0 $
5. $ |-100| = 100 $

#### Opposites
6. Opposite of $ 12 $ is $ -12 $
7. Opposite of $ -3 $ is $ 3 $
8. Opposite of $ -18 $ is $ 18 $
9. Opposite of $ 79 $ is $ -79 $

#### Absolute Value Again
10. $ |-72| = 72 $
11. $ |80| = 80 $
12. $ |-247| = 247 $
13. $ |-47| = 47 $
14. $ |-35| = 35 $
15. $ |-110| = 110 $
16. $ |-76| = 76 $
17. $ |-214| = 214 $

#### Problem Solving
20. A pair of integers with the same absolute value:
👉 $ 10 $ and $ -10 $ (or any other pair like $ 23 $ and $ -23 $)

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📌 Key Concepts Recap:

- Absolute value: Distance from zero → always non-negative.
- Opposite: Same number, different sign.
- Two numbers have the same absolute value if they are opposites.

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If you can describe or list the exact numbers in your worksheet (e.g., "find the absolute value of -15, 20, etc."), I can give you the precise answers.

But based on standard homework formats, the above should cover all parts.

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