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Odd Numbers

Wednesday, October 17, 2018Wednesday, October 17, 2018 admin

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The easiest way I think about odd, it's not a multiple of two, it's not even. So another way, it is not So now that we know what an odd or an even number is, let's think about what happens when we operate on odd or even numbers. So let's think, in particular, actually let me move over to the side right over here. Let me move over Fell off the screen. Let's think about what happens if I take an even number, an even number, plus another even number.

Is this number, the sum, is it going to be even or odd? Well you could take some examples. If I say two plus six, that is going to be equal to eight. Well eight is an even number. If I say 14 plus four, well that equals Once again, eight in the ones place. This is an even number. If I say Zero in the ones place, this also is an even number.

So it looks like all the examples that I've done so far, when I add an even to an even, I get an even number. And I encourage you to keep trying this out. I encourage you to keep trying, pick some even number, then another even number, add them together and you'll see that you keep getting even numbers. And it makes sense.

Because if you had one number that's a multiple of two, and you add it to another number that's a multiple of two, it makes sense that the sum is going to be a multiple of two. Now what happens if you add an odd and an odd? What happens if you add an odd number plus another odd number? What is one plus three?

Well that's equal to four. You actually get an even number. You add two odd numbers, you get an even number. Well maybe that was just that special case. What if I add 15 plus seven? These are both odd numbers, when I add them together I get I get another even number. If I take, let me say 19 plus 3.

Patterns in arithmetic

Actually that gets us 22 again. We have an even number. What about, what about, let's see Once again, get an even number. So the pattern that seems to be forming here is that if I have an even plus an even I get an even, but also if I have an odd plus an odd, then I also get an even number. And once again, I encourage you to try out as many numbers as you can to see if this pattern holds. And you will see that it is true.

An odd plus an odd number is an even. Now let's think about one last combination. What about an even, what about an even plus an odd? An even plus an odd. So let's say I have two plus one. Two plus one, well what is that going to be? Well that's going to be equal to three. That's going to be an odd number. Well what about, what about four plus three?

Four plus three, well that's equal to seven. That's equal to an odd number. And so it looks like if I have an even plus an odd, and I've only tried out two cases here, but I encourage you to try out many, many, many more to make sure that you feel good about this, but an even and an odd is always going to give you an odd. Four doughnuts, you could split that evenly with two people.

They could each get two doughnuts. And then we could keep going. All of the multiples of two, these are even numbers. An easy way to spot an even number is that it's ones place is going to be even.

odd number

So, for example, the number 32 is an even number because in the ones place you have a two. The number 5,,, 5,,, well that's an even number, because the ones place is even. Now there's one number that's an interesting one, why some people sometimes say, "Well is this one really even? And the number zero is even because it is a multiple of two. How is it a multiple of two?

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Well, zero times two is equal to zero. So zero is a multiple of two, and so zero, for sure, is an even number. And then that actually makes our looking at the ones place idea hold up. Because a number like And a zero is an even number. So if, in the ones place, you have an even number, you are looking, the whole thing is going to be an even number. So what are odd numbers?

Well one way to think about them is they're the numbers that aren't even. So not multiples of two. So what are some examples of odd numbers? Well one, three, five, seven, nine, and of course you can go on, and on, and on. And just like we could look at the ones place to spot an even number, you can also look at the ones place to spot an odd number. The number 59, well I have a nine over here in the ones place. Nine is odd, so this is going to be an odd number.

The number 1, has a one in the ones place. That is an odd number. So this whole thing is going to be odd. And so what's another way of Well, it'd be hard to split 1, doughnuts. You can't split it evenly between two people without breaking up a doughnut. If you wanted to leave the doughnuts whole, one person would have to get one extra doughnut than the other person. You can't split it evenly. The easiest way I think about odd, it's not a multiple of two, it's not even.

Even and Odd Numbers

So another way, it is not So now that we know what an odd or an even number is, let's think about what happens when we operate on odd or even numbers. So let's think, in particular, actually let me move over to the side right over here. Let me move over Fell off the screen. Let's think about what happens if I take an even number, an even number, plus another even number.

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Intro to even and odd numbers (video) | Khan Academy