Here's how you can picture absolute value: Think of a railroad track with a zero sitting in the middle of it. Every little notch to the left and right of the zero is another number. Negative numbers line up on the left; positive numbers run along the track to the right. So, the number –4.0 is 4 units away from zero. The number –45.3 is 45.3 units away from zero and the number 10 is 10 units away from zero. Therefore, the absolute value of any number is really a positive number (or zero). You identify an absolute value of a number by writing the number between two vertical bars: |number|. Here are some examples of how you depict an absolute value.
|12| = 12
|–12| = 12
|–98.6| = 98.6
|0| = 0
|–10498.5| = 10498.5
Even though you didn't ask, let me explain how you add and subtract positive and negative numbers and it might make it sink in more.
When you add numbers of the same sign, you add their absolute values and give the result the same sign. For example,
14 + 3.5 = 17.5
(–4) + (–2.2) = –(4 + 2.2) = –6.2
When you add numbers of opposite signs, you use their absolute signs and subtract the smaller number from the larger number and give the result the sign of the larger number. Piece of cake, right? Let me show you an example or two.
4 + (–3) = ?
The absolute value of 4 is 4 and –3 is 3. Subtract the smaller number from the larger and you get 4 – 3 = 1. The larger absolute value in the equation was 4 or a positive number so you give the result a positive result. Therefore, the result of 4 + –3 = 1.
Let's try another one for good measure.
10.5 + (–15.5) = ?
The absolute value of 10.5 is 10.5 and (–15.5) is 15.5. Subtract the smaller number from the larger and you get 15. 5 – 10. 5 = 5.0. The larger absolute value in the equation is 15.5 and is a negative number so the final result is a negative number. Therefore, the result of 10.5 + (–15.5) = –5.0.
Work out a few practice problems, and you're bound to absolutely value the fact you asked a great question!