**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