Math 5: Writing Expressions with Parentheses, Braces & Brackets

Parentheses, braces and brackets. Oh, my.

5th GradeMath
Elementary and Middle School5th Grade
LanguageEnglish Language

Transcript

00:27

and brackets.

00:28

Let's take a look at these different symbols.

00:31

Parentheses are the typical, curvy parentheses you know and love from writing. [Picture of a pair of parentheses]

00:34

Brackets look kinda similar, but they're a bit blockier, with rigid edges. [Picture of brackets]

00:38

And braces get super fancy, with little curls and points…geesh…way to make plain ol' [Picture of braces]

00:42

subtraction signs look bad…

00:44

We still love you, subtraction sign!

00:46

Anyway, though they might look different, these symbols all play a similar role: to [Coop pointing at a board]

00:50

separate different groups of terms in an expression.

00:53

They're kinda like the bouncers of the math world, though luckily mathematical terms don't [Bracket as a bouncer outside 'Math Lounge']

00:56

get too rowdy…

00:57

Except for this guy…that dude is so negative. [Negative sign looks annoyed]

01:01

This separation is important because of the order of operations.

01:04

You might remember it as PEMDAS: parentheses, exponents, multiplication and division, then

01:09

addition and subtraction.

01:11

It means that when we're solving an expression, certain operations come first, and parentheses, [Braces and parentheses walk to the front of the queue]

01:15

brackets, and braces are always the very first in line.

01:18

And unlike people waiting for the new iPhone, they don't have to sleep outside all night! [Man camping in a tent]

01:22

We can see the effect of parentheses in action if we look at a particular expression: 4 plus

01:26

6 times 2.

01:27

Following PEMDAS, we'd do the multiplication before the addition…

01:30

…which gives us 12…

01:32

…followed by the addition, which gives us 16.

01:35

Simple enough.

01:36

But what if we were to throw in some parentheses?

01:38

Since parentheses are first in line, we do the addition first…

01:41

…which gives us 10…

01:42

…followed by the multiplication, which gives us 20. [Working written out]

01:45

And, since we know that 20 is definitely not equal to 16…

01:48

…we see that those parentheses really changed our results.

01:50

So they weren't just there to make one expression look a little bit prettier than the other. [Math expressions on a date]

01:55

It's also worth knowing that parentheses, brackets, and braces aren't just thrown around, [Math symbols being chucked onto the floor]

01:59

willy-nilly, like garbage.

02:00

…Not that you should throw garbage around, anyway.

02:03

There's a particular order to how we use them.

02:05

We start with parentheses, then add brackets, then braces.

02:08

We can see how this works if we take a look at our expression with parentheses.

02:12

Let's say we wanted to divide this whole thing by 3.

02:14

Since we've already got some parentheses in our expression, we use brackets to separate [An arrow points to the parentheses]

02:18

out the original expression.

02:20

And what if we wanted to multiply all of this by 7?

02:22

Well, we've already got parentheses and brackets, so it's braces' time to shine, separating

02:27

off everything from 7.

02:29

And unlike regular braces, you're unlikely to get any food stuck in this expression. [A hand picks out food stuck in someones braces]

02:33

Phew.

02:34

We'd hate to get broccoli stuck in our math homework… [Girl eating a pizza]