Question: Mr. Cortez owns a 10 1/2-acre of tract land, and he plans to subdivide this tract into 1/4-acre lots. He must first set aside 1/6 of the TOTAL land for roads. Which of the following expressions shows how many lots this tract will yield?

(A). $\quad 10 \frac 1 2 \div \frac 1 4 - \frac 1 6$

(B). $\quad (10\frac1 2 - \frac 1 6) \div \frac 1 4$

(C). $\quad 10 \frac1 2 + \frac 1 6 \times \frac 1 4$

(D). $\quad 10 \frac1 2 \times \frac1 4 - \frac 1 6$

(E). Not enough information is given.

Book says answer is (B), which seems wrong because if the question is saying 1/6 of the total 10 1/2-acre land I don't think you should subtract.

So, is my book wrong in telling me the answer is (B)? If so how would the real expression look like? I'm thinking it would look something more like:

10 1/2 x 5/6 divided by 1/4 (5/6 being the amount of land you have left after using 1/6 of it).

So that's it, help would be much appreciated since there is only 1 other similar question like this in the whole book and I don't know if I'm doing it right or this book is just wrong. This wouldn't be the first time the book is wrong either.

Book is McGraw Hill's GED, page 774 question #8.

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    $\begingroup$ Your book is entirely wrong (and you are right). Your tag partial-fractions is wrong however. $\endgroup$ – Marc van Leeuwen Mar 29 '14 at 14:16
  • $\begingroup$ Thanks for clarifying, I was stuck on that one for a while. Sorry about tag, I'm new here, I'll try to get it fixed $\endgroup$ – Mark Mar 29 '14 at 14:21
  • $\begingroup$ Also, your book's notation is contrary to convention as I know it - $10\frac{1}{2}$ is not $10+\frac{1}{2}$, it's $10\times \frac{1}{2}$. You do sometimes see fractions written the way the book is writing them, but not usually in formulae... $\endgroup$ – Jack M Mar 29 '14 at 14:49

You're correct (I will write $10\frac12$ as $10.5$ for clarity).

You need $\dfrac16$ of $10.5 \text{ acres}$ for the roads. So you're left with $10.5-(10.5)\cdot\dfrac16=(10.5)\cdot\dfrac56$ acres of land.

To obtain the number of $\dfrac14\text{ acres}$ contained in $(10.5)\cdot\dfrac56\text{ acres}$, divide the latter by the former to obtain, $\dfrac{(10.5)\cdot\dfrac56\text{ acres}}{\dfrac14\text{ acres}}=10.5\cdot\dfrac{20}{6}=\dfrac{21}2\cdot\dfrac{20}{6}=35$.


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