ShmoopTube

00:03

Here's a boring, unshmoopy question you'll find on an exam somewhere in life.

00:07

Which of the following is equivalent to 3/5 divided by 9/10 plus 1/3 squared?

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And here are the potential answers:...

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OK, so what's this question really asking?

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It's just a twisted arithmetic question testing whether you realize that exponents

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get calculated first...

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...then multiplication and division transactions get calculated...

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...and then last on the totem pole is addition and subtraction.

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So in this problem, the first thing we have to do is square 1/3...

00:39

...and 1/3 is the same as 1 squared over 3 squared.

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1 squared is 1 and 3 squared is 9 and there we go.

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Next, we have to deal with the division part of this problem...

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...and remember that dividing by a fraction is the same as MULTIPLYING by its inverse.

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So 3 fifths divided by 9 tenths is the same as 3 fifths TIMES 10 over 9...

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...and that gets us 30 over 45.

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Rewriting the problem, we have 30/45 plus 1 over 9.

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Hopefully by now a light goes off in your head that the people who write these things

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usually don't want a mess of an answer...

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...so fractions almost always come out even, and this problem is no exception --

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9 goes evenly into 45... 5 times.

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So even though 30 over 45 COULD reduce to 1 third -- don't reduce it that far.

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The big fat goal here is to get common denominators so that we can add the fractions.

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So let's multiply our second fraction by 5/5... and we get 35/45.

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NOW we can reduce... to get 7/9... which is answer C.

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Our sincere sympathy to all those pluses and minuses

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that have to bear the weight of everyone higher on the totem pole.

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It's just their... cross to bear.

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