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What are Negative Numbers and Absolute Values?

Negative numbers are simply numbers that have a value less than 0. That is, their position on the number line is to the left of zero. This is expressed visually on the graphic below.

As you can see, everything to the left of 0 is in the red, which is a negative number. Everything to the right, in blue, is a positive number.

The further to the left you go, the higher the absolute value becomes. The absolute value, used most simply, is the value of the number without the negative sign. Meaning the absolute value of -4 is 4. However,the further left you go down the number line, the lower value of the number. This means that -4 is "bigger" than -5 (bigger meaning it has a greater value.) However, the absolute value of -4 is "smaller" than -5 (smaller meaning a lesser value.)

Practice:
Which number has a greater value? Which number has a greater absolute value?
1. -10 and -1
2. -5 and -2.5
3. 1/2 and -2.
4. 3 and -3.
5. 0 and -2

As you probably already know, once you get the hang of these, they are really quite simple! But just what is an "absolute value?" Let's say that on Friday, you had $5. The absolute value of the amount of money you had is 5. It just so happens that, since you had the money, the 5 was a positive value. On Saturday, you saw something you wanted at a store and it cost $15. Luckily, you have a very nice friend that loaned you $10. So now, you have -10 dollars. But your total amount that you have (or in this case, don't have), is 10.

Answers to the above practice:

1. Greater Value: -1, Greater Absolute Value: -10.
2. Greater Value: -2.5, Greater Absolute Value: -5.
3. Greater Value: 1/2, Greater Absolute Value: -2
4. Greater Value: 3, Greater Absolute Value: They are equal!
5. Greater Value: 0, Greater Absolute Value: -2.

We've got the basics down, get ready to learn to Add and Subtract Negative Numbers!

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