Negative times negative

Hello, and welcome to Myriora Maths! Negative three times negative two is positive six. Why? A negative times a negative makes a positive! It sounds like magic, but there's a pattern that shows why. Let's find it.

First, a positive times a negative. Three times negative two means three lots of negative two. That's like three debts of two pounds each: you owe six pounds. So three times negative two is negative six.

Here's the same thing as a pattern. Three times two is six. Three times one is three. Three times zero is zero. Each time, the answer goes down by three. So next comes negative three, and then negative six!

Now let's start with negative three. Negative three times two is negative six. Times one is negative three. Times zero is zero. This time, each answer goes up by three! So negative three times negative one is three, and negative three times negative two is six.

So here are the rules. A positive times a positive is positive. A positive times a negative, either way round, is negative. And a negative times a negative is positive!

Let's try one together. What is negative four times negative three? Say it out loud!

First, four times three is twelve. And a negative times a negative is positive, so the answer is twelve!

Here's a question that catches lots of people. What is negative two times negative five? Some people say negative ten, because both numbers are negative. But two negatives multiplied make a positive: ten!

Your turn! What is negative five times four? Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! Five times four is twenty. And a negative times a positive is negative. So the answer is negative twenty!

Quick review. A positive times a negative is negative, like three debts of two pounds. The patterns show why, as the answers carry on past zero. Two negatives multiplied make a positive. And work out the number first, then the sign. See you next time!