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Multiplying and Dividing Negative Numbers

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!

Find another math lesson at the Math Lesson and Tutorial Center!


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