Algebra Review - Positive and Negative Numbers

1. What They Are

Positive numbers are the numbers you normally see every day such as 5, 17, 23, 30.
Negative numbers always have a negative sign in front: -1, -3, -4, -10.

2. Usage On The Number Line

A number line looks like this: Numbers become large when you move right. For example, -3 is less than -.5, and 2 is greater than -3.
The additive inverse of a number is basically its opposite. For example, the additive inverse of 2 is -2, of .5 is -.5, of -3 is 3. Zero is its own additive inverse.

Integers are whole numbers such as 1, 2, 3. They do not have decimals, such as 1.5.

Graphing On The Number Line

The following shows how to graph on the number line.

When graphing points, you just use dots: Here we graphed the points 0, .5, and 2.

When graphing a range of numbers, including the end numbers, use solid dots and a line: Here we graphed numbers from .5 to 2.

When graphing numbers that do not include the endpoints, use open dots and a line: Here we graphed the numbers between .5 and 2.

3. Adding Positive and Negative Numbers

You should already know how to do this. Here are some quick examples:

-5 + (-6) = -11
5 + 6 = 11
0 + (-6) = -6
0 + 6 = 6

-5 + 5 = 0
-5 + 8 = 3
-5 + 3 = -2

8 + 5 + (-12) + 10 + (-5) = 12 - 12 + 10 - 5 = 5

4. Subtracting Positive and Negative Numbers

When you subtract negatives, and you see two negatives next to each other, such as 5 - (-5), it turns into a positive: 5 + 5. When you see a negative and a positive, such as 5 + (-5) or 5 - (5), it becomes negative: 5 - 5.

Here are some examples:

6 - (-5) = 6 + 5 = 11

5. Multiplying and Dividing Positive and Negative Numbers

1. Multiplying 2 positive numbers is positive.
2. Multiplying 2 negative numbers is positive.
3. Multiplying a positive and negative number is negative.
4. Dividing 2 positive numbers is positive.
5. Dividing 2 negative numbers is positive.
6. Dividing a positive and negative number is negative.

6. Inequalities

Inequalities use the > , < , ≤ , and ≥ symbols. They work like equations with the = symbol. You must add to both sides, subtract, etc. However, when you multiply or divide by a negative number, the symbol is flipped around.

x + 8 > 5
x > -3

y - 3 < 6
y < 9

-2y < 6
y > -3

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