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Rational and Irrational Numbers, a la Shmoop.

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Welcome, listeners.

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It's time for our weekly radio show: Rational Smashional… [The number 5 talking into a microphone]

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… where we let people know if their numbers... and their problems... are rational or irrational.

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Caller one, you're on the air...

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<> For my movie award party, I have six gelatin molds in the shape [The number six speaking into a mobile phone]

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of Ben Affleck's face.

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But I have eight guests.

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Can I divide them evenly?

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Is this rational?

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Thanks for the question caller 1.

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Although each guest won't get a whole head of Affleck, they can get a fraction of one. [6 Affleck gelatin heads on a blackboard]

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Since you’ve got six molds, you’d divide that number by the number of guests – eight.

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Six divided by eight is the same as the fraction six-eighths.

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So each guest would get six-eighths of Affleck… which can be reduced to three-fourths.

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This may not be a whole number, but it is a rational number: a number that can be written [The number 3 listening to the answer on the phone]

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as the quotient of two integers.

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Next caller, you're on the air.

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I really want bangs like the First Lady. [The number 6 in a rocking chair]

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I would have to grow my hair an additional three inches.

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Is that rational?

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Yes, three is a whole number, and an integer.

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It is totally rational. [5 holding up the answer]

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Okay, but my hairstylist wants to charge me “square root of two” [Number 6 having her hair done]

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dollars for the haircut.

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I don't even know if it’s a deal or not.

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Is that rational?

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We're glad you asked caller 2.

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There is no rational number that, when multiplied by itself, gives us an answer of 2.

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There is no real-world equivalent for square root of two.

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So no…

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That number is irrational… which means it might be time for you to find a new hairstylist.

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Tune in next time when we talk about how leading a life of pi would be irrational… [Thought bubble of the Life of Pi appears]

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…but dividing three pies among four people would be perfectly rational. [4 people behind a table with 3 pies on it]

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