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[Dino and Coop singing]

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We all know that fractions are parts of wholes, like slices of a cake. [Woman looks excited by cheesecake]

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But is it possible to divide these fractions up even further?

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Absolutely.

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Although we don't recommend handing out one tenth of a slice of cake at a birthday party.

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Unless you like seeing kids cry, you monster.

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Let's think about this in terms of an example.

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Carly has five pieces of a pizza left, from a pizza that was originally cut into eight

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equal slices.

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She wants to divide these five slices between herself, her brother, and her sister. [Carly looks confused]

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So how much of the original pizza should each sibling get?

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If Carly happened to have an extra set of twin siblings, that'd be pretty easy: everyone

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would get one slice each. [Extra siblings appear]

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However, we can't just make up twins to make our calculations easier––trust us, we've

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tried it before––so we'll have to do some math.

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Let's think in terms of fractions.

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We have five slices of a pizza that was originally cut into eight slices, so we've got five eighths

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of the original pizza.

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And, since there's a total of three siblings, we want to divide this fraction by three.

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Uh-oh.

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We've never seen a division sign near a fraction before.

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Does that mean Carly and her siblings should abandon the pizza and flee from the house, just

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in case they make a mathematical mistake?

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Well, they could, or they could just learn about reciprocals. [Carly and her sibling looks scared and run out the house]

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…Uh…we're sure they'll be back…soon…ish…

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Anyway, a number's reciprocal is the number flipped upside down.

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With a fraction, that means the original numerator becomes the denominator…

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…and the original denominator becomes the numerator.

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If you're getting dizzy, then you're doing something wrong…the reciprocal's the one

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who actually has to flip upside down.

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You can stay right where you are. [Woman falls out of office chair]

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When we divide fractions, we're really multiplying by a reciprocal.

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We take the second number in our expression, flip it upside down, and then multiply everything

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together.

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Let's see how this works with our particular example.

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We're dividing a fraction by three, so since three's the second number, we need to find

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it's reciprocal.

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Remember, all whole numbers are really just the whole number over one…

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…so the reciprocal of three is one third.

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Now all we've gotta do is some familiar fraction multiplication… [Dino points to a blackboard]

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…and we find our answer: five twenty-fourths.

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Now the only difficult part is cutting those slices up into even skinnier slices.

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We hope Carly's got some precise measuring equipment…

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Actually, we hope Carly comes back…has anyone seen her? [Carly's mum looks worried]

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Or her siblings…?

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