Simplifying numerical expressions | Algebraic reasoning | Grade 5 (TX TEKS) | Khan Academy

All right, what we're going to do in this video is get a little bit of practice evaluating expressions that look a little bit complicated. So, why don't you pause the video and see how you would evaluate this expression on the left and this expression on the right before we do this together?

Okay, now let's do this together. So, when we think about order of operations, the first thing we want to do is think about doing any of the operations inside of grouping symbols like parentheses or brackets before we do anything else.

And you might say, "What's the difference between a parenthesis and a bracket?" Well, they're kind of the same. Sometimes people use brackets when you're really grouping a lot of stuff or if you just want to make it a little bit clear of what the left parenthesis matches to the right parenthesis, or the left bracket matches to the right one.

For example, in this expression here, it's a little bit cleaner writing it as a bracket than having double parentheses on this right-hand side. But let's tackle this.

So first, I like to go inside of these brackets and evaluate 14 minus 4. When you write four and then right next to three in parentheses, this is the same thing as 4 * 3. And actually, that would have been the same thing as if I wrote four next to a three in brackets. As I said, you should can think of parentheses and brackets in the same way.

So here, in order to subtract from 14, we have to do the multiplication first. Order of operations: you want to do the grouping things, then you want to do exponents, then you want to do multiplication from left to right, then you want to do addition and subtraction, or multiplication and division from left to right, and then you want to do addition and subtraction from left to right.

So the first thing I want to evaluate is that 4 * 3, which is going to be 12. And so now I can rewrite it as 7 times 14 minus—I’ll write that 12 in that same color—minus 12. And I'm going to close the brackets, and now I can evaluate this: 14 minus 12, which is of course equal to 2.

So this whole thing will simplify to 7 * 2, which is of course equal to 14, and we're done.

Let's move over to this one right over here. So the first thing my brain wants to do is say, "Let's go into this inner parentheses right over here." 9 + 2 is of course equal to 11, so this whole thing will simplify to 5 * 11 - 7 and then divided by 2.

Next, let's figure out what 11 - 7 is. That, of course, is equal to 4, and so this is now simplified to 5 * 4 / 2.

So now we're just going to do this multiplication and division left to right. So 5 * 4 is 20, so you get 20 divided by 2. 20 divided by 2 is of course equal to 10, and we are done again.