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January 28th, 2016, 06:43 AM   #1
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Fraction problem

2/3 of a plot of land is garden. 1/5 of the garden is lawn. Find the fraction of the plot of land which is lawn.

I thought it would be 1/5 / 2/3 because it's one fifth out of 2/3. So, in my mind, it would have been 1/5 ÷ 2/3 = 1/5 × 3/2 = 3/10.
But the answer in the book is 2/15 so it has to be 1/5 × 3/2.
What am I missing here?
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January 28th, 2016, 06:59 AM   #2
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The word "of" in this context effectively means multiplication by the specified fraction. Such multiplication is equivalent to division by the reciprocal fraction, but you don't need to use that fact.

The garden is 2/3 of the plot.

The lawn is 1/5 of the garden, so it's 1/5 of 2/3 of the plot.

1/5 of 2/3 means 1/5 × 2/3, which is 2/15. You incorrectly wrote 1/5 × 3/2.
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January 28th, 2016, 09:33 AM   #3
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I see. Kinda got it all upside down. Thanks!
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February 1st, 2016, 06:07 PM   #4
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Think of a simple, practical example.
You cut an pie in half, and place that half of a plate.
You give your friend half of that half. What fraction of the whole pie does your friend get? Obviously, your friend gets a fourth of the pie.

So a half of a half is a fourth. That is:

1/2 × 1/2 = 1/4

Frequently we can replace "of" in mathematics by "times".

Another example:

half of 6 is 3

1/2 × 6 = 3

Last edited by skipjack; February 2nd, 2016 at 04:09 AM.
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