Patterns with multiplying even and odd numbers

- [Instructor] We are told Liam multiplies two numbers and gets an even product. What could be true about the numbers Liam multiplied? It says Choose 2 answers. So pause this video and see if you can figure out which two of these could be true. All right, now let's do this together. And we have to think about what could be true. They don't have to be true. It just has to be possible. Okay, now is it possible that both numbers were even? Can you multiply two even numbers and get an even product? Well, sure. And I can imagine examples that get us there. If you multiply two times four, which is equal to eight, you have an even times an even that gets you an even. In fact, in general, when you multiply two evens together, you will get an even product. And so this is definitely, this definitely could be true. Both numbers were odd. You might remember that an odd times an odd is always going to be an odd, or you could look at a few examples and feel pretty confident that that's the case. If you multiply three times five, that's equal to 15. Odd times odd is equal to an odd number. If you multiply seven times nine, you get 63. Once again, odd times odd is equal to odd. So there's no way that you can multiply two odd numbers and get an even product. So we would rule this out. One number was even and one number was odd. Well, let's think about what happens when you multiply an even times an odd. If I multiply two times three, that's equal to six. So you have an even, I'll just put an e there, times an odd, is equal to an even. And so the two ways that you can get an even product is either if you're multiplying an even times an even or an even times an odd. Essentially, an even times either an even or an odd is going to give you an even product. Let's do another example. We're asked which of the following have an even product? It says, once again, Choose 2 answers. So pause this video again, and see if you can figure it out. Okay, 8 fives. So 8 fives is the same thing as eight times five, and this is a situation where we're multiplying an even, e for even, times an odd, which we've already talked about is going to give us an even result, an even product. You don't even have to know that eight times five is 40, which is an even number. We have an even times an odd, which is going to give us an even product. So this will definitely give us an even product. An odd number times an even number. Well, we've already talked about that. Any even, odd, or an even times an even is going to give you an even product. So we can fill that one in. And then five times three, you have an odd times an odd, which is going to give you an odd number. Even if you didn't know that this is going to be 15, you would know that an odd times an odd is always going to give you an odd product, not an even product. So we would pick these first two.