Number Lines:

We have seen that numbers on a number line can have "opposite" values, such as +3 and -3.
These numbers are the same distance from zero, but on opposite sides of zero. Sopph2.gif
Notice that the sum of these two opposite numbers is zero!
Such numbers are called "additive inverses" of each other.
-3 + 3 = 0
You can also arrive at an opposite number by multiplying by -1.
3 • (-1) = -3                   -3 • (-1) = 3

The opposite of the opposite of a number is the number itself.
-(-3) = 3

The value of 0 is its own opposite.

beware When working with absolute value, you must evaluate the absolute value before finding its opposite. For example: | -5 | = 5 whose opposite is -5.
So the opposite of | -5 | is -5. And the opposite of | 5 | is also -5.

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bullet Number Line Graphing:

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Observations:
• As you move from left to right on a number line, the number values get larger.
      7 > 4             4 > 0             0 > -4             -4 > -9

• Positive numbers are always larger than negative numbers.

• Zero is less than a positive number, but greater than a negative number.

Hint: When determining which of two negative numbers is larger (or smaller), picture them on the number line. The number to the right will be larger. The number to the left will be smaller.

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bullet Number Line Adding and Subtracting:
The number line can be used to add and subtract signed numbers. For adding and subtracting positive numbers, the movement on the number line is as would be expected. Adding go right. Subtracting go left.

numberlineAS

This form of addition and subtraction is easy to see with adding going to the right and subtraction going to the left. But, then we have the adding and subtracting of negative numbers and our easy process becomes a bit harder.
If you are adding a negative number, you will need to move in a negative direction, as the negative indicates the opposite of adding that value.

numberlineADD


Also, if you are subtracting a negative number, you will need to move in a positive directions, as the negative indicates the opposite of subtracting that value.

numberlineSUBT

 


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