**Quote:**

genuinebot85 wrote:

John's front lawn is 1/3 the size of his back lawn. If John mows 1/2 of his front lawn and 2/3 of his back lawn, what fraction of his lawn is left unmowed?

1. 1/6

2. 1/3

3. 3/8

4 1/2

5.5/8

pannathat wrote:

why couldn't it be in this way?

let back = B

front = 1/3B

done for front = 1/2*1/3B = 1/6B

done for back = 2/3B

combining workdone for front and back = 1/6 + 4/6 = 5/6B

what left to be done = (front + back) - (work done for front and back) = (1/3B + B) - 5/6B = 4/3B - 5/6B = 1/2B

ans. D?

pannathat , it looks as if it should work. I had to stare at it for a minute. But the question asks for the

fraction left unmowed.

Thus your remaining amount, \(\frac{1}{2}B\), is the part. \(\frac{4}{3}B\) is the whole.

\(\frac{(\frac{1}{2})B}{(\frac{4}{3})B}\)= \(\frac{3}{8}\)

I think choosing numbers is easier on this question. Or, if algebra is preferred, maybe use whole numbers? Seems easier to see or remember the "fraction" part.

That is, maybe try front = F, back = 3F, whole = 4F

F(1/2 unmowed) = 1/2F left

3F(1/3 unmowed) = 1F left

Total left: \(\frac{3}{2}\)F

What remains as fraction of whole?

Whole = 4F

\(\frac{(\frac{3}{2})F}{4F}\)= \(\frac{3}{8}\)

Answer C

Hope it helps.

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