Absolute Value Answer Key
Answer Key & Guide Grade 7 • Mathematics
Opposites & Absolute Value
Date
11-5-26
Opposite (Additive Inverse)
Same distance from 0, opposite direction on the number line: \(a \leftrightarrow -a\).
Absolute Value \(|x|\)
Distance from 0 to the number. Because distance cannot be negative, \(|x| \ge 0\).
1
What is the opposite of -4?
Answer: 4
Explanation: Opposites are equidistant from 0 in opposite directions. Since \(-4\) is 4 units left of 0, its opposite is 4 units right of 0, which is \(4\) (or \(+4\)).
2
What is the opposite of 3?
Answer: -3
Explanation: The number \(3\) is 3 units to the right of 0. Reflecting across 0 gives \(-3\) (3 units left of 0). The opposite of any positive number is negative.
3
What is it called when you have the same number but opposite signs?
Answer: Opposites (Additive Inverses)
Explanation: Two numbers with the same numerical value but opposite signs (e.g., \(5\) and \(-5\)) are called opposites or additive inverses. Their sum is always zero (\(a + (-a) = 0\)).
4
What is the absolute value of -9? Why?
Answer: 9
Why: Absolute value measures distance from zero. Because distance is a physical measure and cannot be negative, \(-9\) is 9 units away from 0. Therefore, \(|-9| = \mathbf{9}\).
5
\(|6|\)
Answer: 6
Explanation: \(|6| = \mathbf{6}\). The number 6 is 6 units away from zero. For any positive number or zero, the absolute value is simply the number itself (\(|x| = x\) when \(x \ge 0\)).
6
What does absolute value mean?
Answer: Distance from Zero
Explanation: Absolute value represents the distance of a number from zero on a number line, regardless of direction. Because distance cannot be negative, absolute value is always non-negative (\(|x| \ge 0\)).
Opposites & Absolute Value • Solutions & Teacher Explanations Page 1 of 2
Opposites & Absolute Value • Questions 7 – 12
Teacher Reference
7
\(|-12|\)
Answer: 12
Explanation: \(-12\) is 12 units to the left of zero. Since absolute value measures only distance and disregards direction, \(|-12| = \mathbf{12}\).
8
What is the difference between an opposite and the absolute value?
Key Distinction
Answer:
- Opposite: Refers to direction and sign. The opposite can be positive or negative (e.g., opposite of \(5\) is \(-5\); opposite of \(-5\) is \(5\)).
- Absolute Value: Refers to distance from 0. It is never negative (e.g., \(|5| = 5\) and \(|-5| = 5\)).
9
What is the opposite of 8?
Answer: -8
Explanation: 8 is 8 units right of 0. Moving the same distance to the left yields \(-8\).
10
What is the opposite of -22?
Answer: 22
Explanation: Inverting the negative sign of \(-22\) yields \(22\) (or \(+22\)). The opposite of a negative integer is always positive.
11
What is the absolute value of 100? Why?
Answer: 100
Why: \(|100| = \mathbf{100}\). 100 is 100 units away from 0 on the number line. Because absolute value counts distance regardless of sign, it remains positive 100.
12
\(|-52|\)
Answer: 52
Explanation: \(-52\) is 52 units away from 0. Since distance cannot be negative, \(|-52| = \mathbf{52}\).
Side-by-Side Reference
| Value |
Opposite |
Absolute Value |
| \(7\) |
\(-7\) |
\( |
| \(-15\) |
\(15\) |
\( |
| \(0\) |
\(0\) |
\( |
Common Student Pitfalls
- Thinking \(|x|\) always changes sign: Emphasize \(|6| = 6\), never \(-6\).
- Confusing opposite with absolute value: Opposites change sign; absolute values are never negative.
- Zero edge cases: Opposite of \(0\) is \(0\), and \(|0| = 0\).
Opposites & Absolute Value • Solutions & Teacher Explanations Page 2 of 2
