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### Course: 5th grade > Unit 13

Lesson 1: Writing expressions# Translating expressions with parentheses

Dive into the world of writing mathematical expressions from verbal statements. Understand the importance of parentheses in expressions, and how they can change the meaning of calculations.

## Want to join the conversation?

- Does "divide in half" actually mean "multiply by half" or "take a half of.."?(182 votes)
- yes, technically but, it is not really spliting it in half that would be for fractions(46 votes)

- Math is fun and boring in the same way(35 votes)
- how do you translate expressions with parenthesis the right way? Is there also an easier way?(9 votes)
- If they're are numbers in parenthesis you are suppose to do what it says first(3 votes)

- Starting at4:25we are told the importance of parentheses in the equation, that without them the standard way of interpreting 43-16+11 would be to first subtract 16 from 43 then to add the 11.

My question is, even without the parentheses wouldn't you follow PEMDAS. Adding the 16 and 11 before subtracting 43?

Any help would be appreciated.(5 votes)- That's true - parentheses go before everything else because they exist solely to group operations! And the Order of Operations is universally followed as it's how we read math expressions.

The thing is that addition and subtraction are really at the same level in the Order of Operations, because they are basically the same but inverse to each other. Operations at the same level are always done left-to-right. Preferably, acronyms such as`PEMDAS`

are taught as something like`PE(MD)(AS)`

to reflect this.

So addition and subtraction are done left-to-right, which is why`46-13+11`

is read as doing the`46-13=33`

then doing the`33+11=44`

.(4 votes)

- for the pink question he could of just done 43-16-11(4 votes)
- No, he can't it says on the pink line it says:"43 minus the sum of 16 and 11 "the sum is the total of 16 and 11 so you have to do that first if you do it as (43-16-11) you get 43-16-11 while the answer is 38.(5 votes)

- I was not working for me😕(3 votes)
- What is not working for you? Do you need help trying to figure PEMDAS?(5 votes)

- What are the order of operations(4 votes)
- The
**Order of Operations**tells us what order to do the math operations in any expression. Basically how we read it.

There are many acronyms that communicate this order, but they all tell the same story:

- Do everything inside parentheses first, along with exponents/roots.

- Do multiplications/divisions left-to-right.

- Do additions/subtractions left-to-right.

Hope it helped :)(3 votes)

- When he put the coma in the wrong spot I said in my deepest voice (Not very deep) "HE SAID IT WRONG" and then burst out in laughter and then he fixed his mistake. LOL(4 votes)
- would you please checke the4:39for the order of mathematecal exprethions. I thinke we should do the addtion first.(3 votes)
- Parentheses

Exponents

Multiplication

Division

Addition

Subtraction = PEMDAS which is the order of operations.(3 votes)

- you guys got this!(4 votes)

## Video transcript

- [Voiceover] What I
hope to do in this video, is give ourselves some practice interpreting statements and writing them as
mathematical expressions, possibly using parentheses. So let's get started. And for any of these statements, if you get so inspired, and I encourage you to get so inspired, pause the video and see
if you can write them as mathematical expressions. So this first one says 700 minus 19, divided in half. So we could say, another way to think about divided in half is divided by two, so we could write this as 709 minus 19, and we're going to do that first, so that's why I put the
parentheses around it, divided by two, or divided in half. That's one way that we could write this. Now the next one, and once again, pause
it if you get inspired, and I encourage you to. Three times the sum of 56 and seven. So it's gonna be three times the sum of 56 and seven. So the sum of 56 and seven, we want to take that first, so it's going to be 56 plus the seven, that's the sum of 56 and seven, and then we want to do three times that. We want to do three times this sum. So we could write it like that. Another way we could write it, when you're dealing with parentheses, and you're going to see this more and more as you get into more
and more fancy algebra, I guess you could say, but what I'm about to
show you isn't so fancy, is, you don't have to write
the multiplication sign here. You could just write three,
and then open parentheses, 56 plus seven, and this, too, is three times the sum of 56 and seven. And you want to be very careful, because you might be
tempted to maybe do it without the parentheses, so you might be tempted
to do something like this, three times 56 plus seven, but this one isn't, obviously, three times the sum of 56 and seven. In fact, the standard
way to interpret this is that you would do the
multiplication first. You would do three times 56, and then add seven, which is going to give
you a different value, and you could try it out, than if you were to add
the 56 and the seven first. So, to make sure that you do
the 56 and the seven first, you want to put this
parentheses around it. So let's keep going. The sum of three times 56 and seven. So we're gonna take the sum of two things. The first thing that we're
gonna take the sum of is three times 56. So, three times 56, and seven. Let me do that in a different color. And seven. So this right over here is the sum of three times 56, and seven. Now it's always good to
write the parentheses. It makes it a little bit cleaner, a little bit more obvious. Look, I'm gonna take the three times 56, I'm gonna do that first, and then I'm gonna add seven, but based on what I just told you, the standard way, if
someone were to just write three times 56 plus seven, this actually can still be interpreted as the sum of three times 56, and seven, because as I just said, the standard, the convention, so to speak, is to do your multiplication first. Order of operations,
which you may or may not, if you're not familiar, you
will be familiar with it soon, is to do the multiplication first, and then add the seven,
or then do the addition. But just to make it clear, it doesn't hurt to put
the parentheses there. Three times 56, plus seven. Now we have 43 minus the sum of 16 and 11. So, 43 minus, so we're gonna have 43 minus, minus the sum of 16 and 11. So, minus the sum of 16 and 11. So, from 43, we're gonna take the sum of 16 and 11, and so, once again, the
parentheses make it clear that we're going to take
the sum of 16 and 11, and we're gonna take that from 43. The parentheses are very,
very, very important here, because if we just did 43 minus 16 plus 11, the standard way of
interpreting this would be 43 minus 16, and then adding 11, which would give you
a different value than 43 minus the sum of 16 and 11. So once again, the parentheses are very, very, very important here to make it clear that you're
gonna add the 16 and 11 first, and then subtract that sum from 43. This is fun, let's keep going. 10 times the quotient of 104 and eight. So, we're gonna do 10 times something. 10 times the quotient of 104 and eight, and so the quotient of 104 and
8 we could write like this, 104 divided by eight, or, based on what we told
you a little earlier, you could write this as 10 times the quotient of 104 and eight, or 104 divided by eight. Now let's just do this last one. Four times as large as the expression 175 minus 58. So I'm gonna do four times
as large as something, so I'm gonna multiply
something times four. It's four times as large as the expression 175 minus 58. And once again, I could write it as four times as large as the expression, let me do that in that purple color, as the expression 175 minus 58. Either way, and once again, if you
were to do it like this, if you didn't write the parentheses, then, it wouldn't be the same thing, 'cause if the parentheses weren't here, then you would want to do
the four times 175 first, and then subtract the 58, which isn't what this
statement is telling us. And this last one, I think, brings up an interesting
thing for us to think about, because if someone were to
walk up to you on the street, and they were to show you-- Whoops, what's going on with my computer? And they were to show you two different expressions. Well, the first expression said two-- Let's write it this way, actually, I'm not gonna
even speak 'em out. I'm just gonna write it down. I'm just gonna write
some crazy number here. Some crazy numbers here. So that's one expression that someone were to write, and let's say another one is this one, and I'm intentionally-- What, I put the commas in the wrong place. Let me make sure I get this right. Alright, that's 183,576. This is 37,399. So that's one expression, and then another expression is this. And I'm intentionally not reading it out. Well, I'll read it out a little bit, 37,399. And someone said, "Quick! "Which expression is larger?" And you might be tempted, or you might not be tempted, but you might be tempted, "Oh, let me calculate this thing. "Gee, I'm gonna have to
write this thing down, "or use a calculator or something, "or whatever else to add "183,576 "plus 37,399, "and then I'm gonna have
to multiply that by two, "and figure out what
that number is equal to, "and then I would have to take "183,576 plus 37,399 "and figure out what that is, "multiply that by seven, "and figure out what that's going to be. "That's hard! "That's gonna take--" Not hard, it's just
gonna take you some time, you might make some careless mistakes. But the big realization to say, "Well, which one is larger? "Well I don't have to even
calculate these things!" 'Cause this is two times this
craziness right over here, this thing that's gonna
be 200 something thousand, and this is seven times that thing that is going to be 200
and something thousand. So seven times that thing is going to be larger
than two times that thing, and so, one way to-- Before you dive deep, and
start computing things, it's always good to take
a step back and say, "Hey, look, can I look at how
the expressions are formed, "the structure of these expressions?" And say, "Look, this is
two times this thing, "and this is seven times this thing." Well, the seven is going to be, this one right over here is going to be a larger expression. Anyway, hopefully you enjoyed that as much as I did.