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[Dino and Coop singing]

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Mathematicians have all sorts of tools at their disposal: numbers, operators, algebraic [Open toolbox]

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symbols, sandwiches…

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…hey, math makes them hungry. [A hand takes the sandwich away]

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Sandwiches aside, three very important tools that play similar roles are parentheses, braces,

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and brackets.

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Let's take a look at these different symbols.

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

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

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

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subtraction signs look bad…

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We still love you, subtraction sign!

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

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separate different groups of terms in an expression.

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

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get too rowdy…

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

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This separation is important because of the order of operations.

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

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addition and subtraction.

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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]

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

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

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

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6 times 2.

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

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…which gives us 12…

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…followed by the addition, which gives us 16.

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Simple enough.

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But what if we were to throw in some parentheses?

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

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…which gives us 10…

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

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

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…we see that those parentheses really changed our results.

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

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

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willy-nilly, like garbage.

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…Not that you should throw garbage around, anyway.

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

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

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

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

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

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out the original expression.

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

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

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off everything from 7.

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

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Phew.

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

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