Absolute Value

Grade 6 · mathematics · 100 practice problems · read aloud

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Understanding Absolute Value

The absolute value of a number is simply its distance from zero on a number line. Distance is always positive (or zero), so absolute value is never negative! 🎯 We use two vertical bars to show it, like this: | -5 |.

It's useful because it helps us find magnitude or size without worrying about direction (positive or negative). Think of it like a car's odometer—it only tells you how far you've gone, not if you drove forward or backward.

How to Find Absolute Value: A Step-by-Step Guide

  1. Identify the number inside the absolute value bars.
  2. Ask yourself: "What is this number's distance from zero?"
  3. If the number is positive or zero, the absolute value is the same number.
  4. If the number is negative, just remove the negative sign. The absolute value is the positive version.

Worked Examples

Example 1: | 8 |

The number 8 is 8 units away from zero on the number line.

Answer: | 8 | = 8

Example 2: | -3 |

The number -3 is also 3 units away from zero on the number line.

Answer: | -3 | = 3

Example 3: | 0 |

Zero is already at zero, so its distance is zero.

Answer: | 0 | = 0

Common Mistakes to Avoid

❌ Mistake: Thinking absolute value can be negative.

✅ Fix: Remember, it's a distance! Distance is always positive or zero.

❌ Mistake: Just copying the number and ignoring the sign.

✅ Fix: Always check if the number inside is positive or negative first.

Tips & Tricks

Memory Aid: Think of the absolute value symbol as a "magic eraser" that wipes away any negative sign. ✨

Shortcut: The absolute value is the number without its negative sign (if it has one).

Strategy: Always draw a quick number line in your mind. How many steps to zero?

How to Practice

  • Create flashcards with numbers like 7, -12, 0, -1, and 45. Practice finding their absolute values.
  • Ask a friend or parent to quiz you with random numbers.
  • Solve real-world problems: "If the temperature is -5°C, what is the absolute value of the temperature?"

Practice problems

6 of the 100, worked through step by step — try them before opening the answer.

1 |−15 + 7| = ?

Hint: First, perform the operation inside the absolute value symbols. Then, take the non-negative value of the result.

Show the answer

Answer: 8

  1. First, look inside the absolute value symbols: |−15 + 7|
  2. Perform the addition inside the absolute value. We are adding a negative number and a positive number: −15 + 7. Think of this as starting at −15 on a number line and moving 7 steps to the right. −15 + 7 = −8.
  3. Now the expression becomes |−8|. The absolute value of a number is its distance from zero, which is always a positive number (or zero). The distance from −8 to 0 is 8.
  4. Therefore, |−8| = 8. Final Answer: 8

2 |−15| + |7| = ?

Hint: Absolute value represents distance from zero, so both numbers become positive before adding.

Show the answer

Answer: 22

  1. Understand the absolute value operation. The absolute value of a number is its distance from zero, so it is always non-negative. For example, |−15| means the absolute value of −15, and |7| means the absolute value of 7.
  2. Calculate |−15|. Since −15 is 15 units away from 0, |−15| = 15.
  3. Calculate |7|. Since 7 is already positive, |7| = 7.
  4. Add the results. 15 + 7 = 22.
  5. Final answer. |−15| + |7| = 22.

3 |−1250 + 750| = ?

Hint: First calculate the expression inside the absolute value symbols, then take the non-negative value of that result.

Show the answer

Answer: 500

  1. Perform the addition inside the absolute value. −1250 + 750 = −500
  2. Apply the absolute value. The absolute value of a number is its distance from zero, so it is always non-negative. |−500| = 500 Final Answer: 500

First, we have the expression: |−1250 + 750|

4 |−8| + |5| − |−3| = ?

Hint: Remember that absolute value makes any number inside positive. Consider finding each absolute value separately before combining them.

Show the answer

Answer: 10

  1. Calculate |−8| = 8
  2. Calculate |5| = 5
  3. Calculate |−3| = 3
  4. Substitute back into the expression: 8 + 5 − 3
  5. Add first: 8 + 5 = 13
  6. Subtract: 13 − 3 = 10

The answer is 10.

5 |−8| × |5| − |−3| = ?

Hint: Remember that absolute value makes numbers positive. Consider the order of operations.

Show the answer

Answer: 37

  1. Calculate |−8| = 8
  2. Calculate |5| = 5
  3. Calculate |−3| = 3
  4. Multiply the first two absolute values: 8 × 5 = 40
  5. Subtract the third absolute value: 40 − 3 = 37

The answer is 37.

6 |−216 + 96| ÷ |−6| = ?

Hint: First, simplify the expression inside the first absolute value bars. Then find the absolute value of each part before dividing.

Show the answer

Answer: 20

  1. Simplify inside the first absolute value: −216 + 96 = −120
  2. Find the absolute value: |−120| = 120
  3. Find the absolute value of the second part: |−6| = 6
  4. Divide: 120 ÷ 6 = 20

The answer is 20.

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