Introduction to Absolute Value – Practice Problems

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The absolute value of a number is its distance from zero. Another way of thinking of absolute value is it’s the magnitude of a number – without consideration of its sign.

So for a negative number, just drop the sign, and that’s the absolute value; for a positive number, the absolute value is the number. We can conclude the absolute value of a number is always a positive number. What about zero? The absolute value of zero is zero.

To help you understand absolute value, model problems using a vertical or horizontal number line. With help from the number line, the difference from zero and the absolute value of the difference between numbers will be quite obvious.

The symbol for absolute value is a vertical line on either side of the quantity, albeit number or variable. We can credit mathematician Karl Weierstrass with thinking up the symbol for absolute value.

How can we use this concept in the real world? There are many applications, but just to name a few: distance, weights and measures, and temperature. If your friend tells you there is a great record store just 4 blocks away, it might be helpful to understand that your friend is telling you the absolute value of the number of blocks, so you’ll know to ask which direction before you go off on a wild goose chase. I don’t know if you’ll ever find the record store, but I absolutely recommend that you watch this video.

Represent and solve equations with absolute value.


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Exercises in this Practice Problem
Describe absolute value.
Determine the absolute value of the numbers.
Determine the winner of the absolute value game.
Decide which terms have the same absolute value.
Decide which is further from sea level.
Find the absolute values.