Home > Pre-Algebra > Integers > Multiplying Integers

## Multiplying Integers

#### Introduction

Multiplying two positive integers is one of the earliest pieces of Math you learn in school. Knowing 2 x 2 = 4 is fundamental math knowledge. However, you should also know what to do when you are multiplying two negative numbers together (-2 x -2 = ?) or one positive and one negative (-2 x 2 = ?).

## Lesson

Multiplying numbers together depends on what signs the numbers have. Whether they are positive, negative, or mixed will dictate how you do it.

### Multiplying positives

When you multiply two numbers you are effectively adding one of the numbers together as many times as the other number denotes.

For example, when you calculate 3 x 4, you can add 3 together 4 times:

$3 * 4 = 3 + 3 + 3 + 3 = 12$

You can also add 4 together 3 times:

$3 * 4 = 4 + 4 + 4 = 12$

As you get better at Math, you often just learn math facts and can remember what 6 x 7 is (42) without having to add together the numbers.

### Multiplying negatives

When you multiply two negative numbers they effectively cancel each other out to make two positive numbers. For example:

-3 -7 is the same as 3 7, so the answer is 21.

If you have an odd number of negative numbers, the answer will be negative. If you have an even number of negative numbers, the answer will be positive.

So:

$-3 * -2 * -4 = -24$ (negative)

$-2 * -5 * -3 * -6 = 180$ (positive)

### Multiplying mixed equations

If you have an equation that has one positive and one negative value in it, then the answer will be negative.

$6 * -7 = -42$ (negative)

If you have an equation with multiple values in it, then the rule is that an odd number of negatives makes the answer negative, and an even number of negatives makes the answer positive.

So:

$-3 * 2 * 6 = -36$ (negative)

$-3 * 2 * 6 * -2 = 72$ (positive)

## Examples

$12 * -4$
Multiply numbers first and get 48
Because we have a positive times a negative, the resulting sign is negative
$12 * -4 = -48$
Kevin's favorite apples are on sale for \\$3 a bag. If he buys 6 bags, how much did she spend?
Multiply numbers first and get 18
Because we have a positive times a positive, the resulting sign is positive
$3 * 6 = 18$