yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

What order to do operations in


2m read
·Nov 11, 2024

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.

More Articles

View All
Introduction to irregular verbs | The parts of speech | Grammar | Khan Academy
Hello, Garans. Today I want to start talking about irregular verbs. That is to say, verbs that are a little weird. You know, we have this idea of a regular verb that we can conjugate in all tenses, and it’s just going to behave in a way that we expect. L…
Directional derivatives and slope
Hello everyone! So what I want to talk about here is how to interpret the directional derivative in terms of graphs. I have here the graph of a function, a multivariable function: it’s ( F(x, y) = x^2 \cdot y ). In the last couple of videos, I talked abo…
Worked example: separable equation with an implicit solution | Khan Academy
We’re given a differential equation right over here: cosine of y + 2, this whole thing times the derivative of y with respect to x is equal to 2x. We’re given that for a particular solution, when x is equal to 1, y of 1 is equal to zero. We’re asked, what…
15 Money Secrets They Don't Teach You In School
The school system is designed to keep people poor and mediocre. It was never designed so you could become rich and live a life full of prosperity. It was designed to raise employees that are obedient and never dream big. And if you want to change that pro…
Immerse Yourself in the Rugged Beauty of Ireland's West Coast | National Geographic
I don’t think anybody can live and be here for very long periods of time without falling completely in love with the place in the sea and the hills and everything it has to offer. The cosine Harrods, there’s no defense against the Atlantic Ocean. You have…
Representing solutions using particulate models | AP Chemistry | Khan Academy
The goal of this video is to help us visualize what’s going on with the solution at a microscopic level, really at a molecular level, and also to get practice drawing these types of visualizations because you might be asked to do so depending on the type …