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Absolute value is a fundamental concept in mathematics that refers to the distance of a number from zero on a number line. It is a measure of the magnitude of a number, regardless of its sign. In other words, the absolute value of a number is its distance from zero, regardless of whether it is positive or negative.

Definitions:

1. The absolute value of a number is denoted by two vertical bars on either side of the number, like so: |x|.
2. The absolute value of a number x is the distance from x to 0 on the number line.
3. If x is a positive number, then |x| = x.
4. If x is a negative number, then |x| = -x.
5. The absolute value of 0 is 0.

Examples:

1. The absolute value of 5 is 5, because 5 is 5 units away from 0 on the number line.
2. The absolute value of -3 is 3, because -3 is 3 units away from 0 on the number line.
3. The absolute value of 0 is 0, because 0 is 0 units away from 0 on the number line.
4. The absolute value of -7 is 7, because -7 is 7 units away from 0 on the number line.
5. The absolute value of 12 is 12, because 12 is 12 units away from 0 on the number line.

Quiz:

1. What is the absolute value of 5?
2. What is the absolute value of -3?
3. What is the absolute value of 0?
4. What is the absolute value of -7?
5. What is the absolute value of 12?
6. Is the absolute value of a positive number always positive?
7. Is the absolute value of a negative number always negative?
8. Is the absolute value of 0 always 0?
9. Can the absolute value of a number be negative?
10. Can the absolute value of a number be greater than the number itself?

Answers:

1. 5
2. 3
3. 0
4. 7
5. 12
6. No
7. No
8. Yes
9. No
10. No