What order to do operations in

If I were to ask you what is five minus three plus two, what would you say that is? Pause this video and try to figure that out.

All right, well, if you wanted to tackle this, you would really just read it from left to right, or you would compute it from left to right. You'd first figure out what 5 minus 3 is, and 5 minus 3 is equal to 2. And so you'd say, okay, that's going to be 2 plus 2, which of course we know is equal to 4.

Now, what if I were to involve a little bit of multiplication or division? If I were to go up to you and I were to say, what is five plus three times two? Pause this video and try to figure that out.

Well, you might be tempted to do it in a similar way. You might be tempted to say, okay, I'll just go from left to right. I'll first compute what 5 plus 3 is, and that of course would be equal to 8. And then I would multiply 8 times 2 to get 16.

But it turns out that this would not be the right way to approach this. For very good reasons that we'll study in perhaps future videos, we don't always go left to right, especially when we're dealing with different types of operations. The standard way that this is approached is that multiplication and division will be done before addition and subtraction.

So the way that you would actually compute this is that you would compute the 3 times 2 first. So you would say that this is the same thing as 5 plus 6. 5 plus 6, which is going to be equal to 11, not 16. So this is going to be equal to 11.

So with that out of the way, let's do a few more examples. Let's say someone were to approach you and say, what is 9 minus 6 divided by 3? Pause this video and see if you can figure that out.

Well, as I just said, we would do multiplication or division before we do subtraction. So we'll actually do the six divided by three first, and six divided by three is two. So this simplifies to nine minus two, which is equal to seven.

And I really wanna emphasize it's important that you get this idea that multiplication and division should be done before the addition or subtraction unless you're given some other types of directions. Because if you just went left to right here, you would have said 9 minus 6 is 3, and then you would have divided that by three, which would have given you one, which is clearly a different number than seven.

Let's do one more example just for kicks. Let's say that someone were to ask you, what is two times three minus one? Pause the video and try to figure that one out.

Well, in this one, doing our multiplication first is also the same as going left to right first. So if we do 2 times 3 first, 2 times 3 is 6, so that's 6. And then we would want to calculate 6 minus 1, which is of course equal to 5.

So, big picture, if you just have a bunch of things that are being added, subtracted, multiplied, and divided, and there's no parentheses in it, you would always prioritize the multiplication or the division over the addition or the subtraction.