Parentheses, braces and brackets. Oh, my.
|Elementary and Middle School||5th Grade|
Let's take a look at these different symbols.
Parentheses are the typical, curvy parentheses you know and love from writing. [Picture of a pair of parentheses]
Brackets look kinda similar, but they're a bit blockier, with rigid edges. [Picture of brackets]
And braces get super fancy, with little curls and points…geesh…way to make plain ol' [Picture of braces]
subtraction signs look bad…
We still love you, subtraction sign!
Anyway, though they might look different, these symbols all play a similar role: to [Coop pointing at a board]
separate different groups of terms in an expression.
They're kinda like the bouncers of the math world, though luckily mathematical terms don't [Bracket as a bouncer outside 'Math Lounge']
get too rowdy…
Except for this guy…that dude is so negative. [Negative sign looks annoyed]
This separation is important because of the order of operations.
You might remember it as PEMDAS: parentheses, exponents, multiplication and division, then
addition and subtraction.
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]
brackets, and braces are always the very first in line.
And unlike people waiting for the new iPhone, they don't have to sleep outside all night! [Man camping in a tent]
We can see the effect of parentheses in action if we look at a particular expression: 4 plus
6 times 2.
Following PEMDAS, we'd do the multiplication before the addition…
…which gives us 12…
…followed by the addition, which gives us 16.
But what if we were to throw in some parentheses?
Since parentheses are first in line, we do the addition first…
…which gives us 10…
…followed by the multiplication, which gives us 20. [Working written out]
And, since we know that 20 is definitely not equal to 16…
…we see that those parentheses really changed our results.
So they weren't just there to make one expression look a little bit prettier than the other. [Math expressions on a date]
It's also worth knowing that parentheses, brackets, and braces aren't just thrown around, [Math symbols being chucked onto the floor]
willy-nilly, like garbage.
…Not that you should throw garbage around, anyway.
There's a particular order to how we use them.
We start with parentheses, then add brackets, then braces.
We can see how this works if we take a look at our expression with parentheses.
Let's say we wanted to divide this whole thing by 3.
Since we've already got some parentheses in our expression, we use brackets to separate [An arrow points to the parentheses]
out the original expression.
And what if we wanted to multiply all of this by 7?
Well, we've already got parentheses and brackets, so it's braces' time to shine, separating
off everything from 7.
And unlike regular braces, you're unlikely to get any food stuck in this expression. [A hand picks out food stuck in someones braces]
We'd hate to get broccoli stuck in our math homework… [Girl eating a pizza]