Simplifying numerical expressions

0:00- [Instructor] All right, what we're gonna 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.

0:15Okay, now let's do this together. So when we think about order of operations, the first thing we wanna 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 parentheses and a bracket?"

0:35Well, they're kind of the same. Sometimes people use brackets when you're really grouping a lot of stuff, or if you just wanna make it a little bit clearer of what the left parentheses matches to the right parentheses or the left bracket matches to the right one.

0:49For 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'd like to go inside of these brackets and evaluate 14 minus four, and when you write four and then right next to it, three in parentheses, this is the same thing as four times three.

1:10And actually that would've been the same thing as if I wrote four next to a three in brackets. As I said, you 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.

1:24You wanna do the grouping things, then you wanna do exponents, then you wanna do multiplication from left to right. Then you wanna do addition, subtraction, or multiplication and division from left to right. And then you want to do addition and subtraction from left to right.

1:34So the first thing I wanna evaluate is that four times three, which is going to be 12. And so now I can rewrite it as seven. This is really seven 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 two.

1:57So this whole thing will simplify to seven times two, 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, nine plus two is of course equal to 11.

2:19So this whole thing will simplify to five times 11 minus seven, and then divided by two. Next, let's figure out what 11 minus seven is. That of course, is equal to four. And so this is now simplified to five times four divided by two. So now we're just gonna do this multiplication and division left to right.

2:48So five times four is 20, so you get 20 divided by two. 20 divided by two is of course equal to 10 and we are done again.