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As shown in the last lesson, Adding and Subtracting Negative Numbers, the next step is to multiply and divide them. Luckily, this is even easier!

Multiplication (Go to Division)

Let's take a look at a normal multiplication problem:

3 x 4 = 12

Why does it equal 12? You can look at it one of two ways:

1. The number 3 added to itself 4 times. (3 + 3 + 3 + 3 = 12)

2. The number 4 added to itself 4 times. (4 + 4 + 4 = 12)

What if you had a negative 3 in the above problem? It could be written as (-3 + -3 + -3 + -3). If you read our previous lesson, you know that this can be rewritten as: -3 - 3 - 3 - 3, which equals -12.

Important Rules for Multiplication (and Division) with Negative Numbers:

If there is an EVEN amount (or 0) of negative numbers in the problem, the answer will be a POSITIVE. A negative times a negative is a positive.

If there is a ODD amount of negative signs in the problem, the answer will be a NEGATIVE number. A positive times a negative is a negative number.

That's it. Nothing else changes. Simply multiply the numbers, count up the negative numbers, and depending on how many there are, you may need to add a negative sign in front of your answer. Yes, that's all there is to it!

Here are some examples to try. (Answers below)
1. 4 x 5
2. -4 x 6
3. -2 x -3 x 4
4. 3 x 5 x -1
5. 6 x -2 x -3

Answers:
1. 20.
2. -24.
3. 24.
4. -15.
5. 36.

Division

We'll try to keep this short:

Follow the exact same rules as for multiplication (above), but divide instead. The only thing to remember:

An even amount of negative signs and the answer will be positive; an odd amount and the answer is negative.

Try some:
1.   8 ÷ 4
2.   12 ÷ -3
3.   -4 ÷ -2
4.   -15 ÷ 5
5.   (16 ÷ 4) ÷ -2
(Hint: Do the calculation in the parenthesis first, and then finish with the last divide.)

Answers:
1.   2
2.   -4
3.   2
4.   -3
5.   -2

Nothing to it!

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