# Rules for Multiplying and Dividing Integers

When multiplying and dividing integers, perform the operation as if both integers are positive and then change the sign of the answer as follows: If both integers have the same sign, the product is positive; if they have different signs, the product is negative. For example, 3(5)=15 and -3(-15)=15; 2(-6)=-12 and -2(6)=-12.

## Multiplying and Dividing Integers

When multiplying and dividing integers, perform the operation as if both integers were positive and then change the sign of the answer as follows.

If both the integers have the same sign, then their product is positive. If the two integers have different signs, then the product is negative.

Let’s look at some examples. On the left side, we have four different sets of numbers, and in each set the integers have the same sign.

Here we have a positive number times a positive number. Since they have the same sign, our result is positive. Again, we have a set of numbers with the same sign.

This time, they’re both negative. The result is still positive. -3 times -5 is positive 15. Whether both signs are positive or both signs are negative, the result is always positive.

The same is true with division. If both integers are positive, the result is positive. If both integers are negative, the result is positive.

As long as both your integers have the same sign when you’re multiplying or dividing, then your result is positive. In this set of numbers, each set has different signs.

Each number in the set has different signs. Here we have a positive 2 times a -6. When multiplying one positive number times one negative number, the result is always negative.

It’s the same even if we reverse which number has the negative on it. Now when we do -2 times positive 6, we’re still doing one negative number times one positive number, so the result will still be negative.

The same is true with division. If you’re dividing two integers and they have different signs, then your result is negative. It doesn’t matter if the numerator is negative or the denominator is negative. Here, we have -10 divided by 5. The negatives are reversed, but the result is still negative.

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Last updated: 12/03/2018