Absolute Value
Concept
The following numbers are integers:
... ... ..., -3, -2, -1, 0, 1, 2, 3, ... ... ...
The absolute value of an integer is its distance from the origin on the number line. It is denoted by a pair of vertical bars surrounding the number. For example:
|3| = 3.
|-3| = 3.
|0| = 0.
|2+3| = 5.
|2-3| = 1.
Instructions
Drag the blue circle to change the number, shown in red.
The absolute value of that number is shown in black.
Questions
Are absolute values always positive?
Can absolute values be negative? Be zero?
When is a number equal to its absolute value?
When are a number and its absolute value opposites?
Which numbers have absolute value 5? -5? 0?
Answers
Are absolute values always positive?
No: Absolute value of 0 is 0. |0| = 0.
Can absolute values be negative? Be zero?
Absolute values cannot be negative.
They can be zero: |0| = 0.
When is a number equal to its absolute value?
If a number is positive or zero. In other words, if this number is nonnegative.
When are a number and its absolute value opposites?
If a number is negative or zero. In other words, if this number is nonpositive.
Remember that zero is its own opposite.
Which numbers have absolute value 5? -5? 0?
5 and -5 have absolute value 5.
|5| = |-5| = 5.
No number has absolute value -5, because absolute values are nonnegative.
0 has absolute value 0.
|0| = 0.
Pre-Skills
6.EE.3
Related Concepts
Rational numbers
Irrational numbers
Positive and Negative Numbers, Zero
Square and square root
Inspirations and Applications
[Source] https://www.geogebra.org/material/simple/id/p65jeA5w
[by] VTMike
Absolute value is a function that "take away the sign" of a number. It is useful in times where you need to find the nonnegative difference of two numbers. For example, to find the difference between two points a and b on the number line, all you need is |a - b|.
Common Core
7.NS.1
7.NS.2
7.NS.3