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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