SOLUTION: I was looking to find out if I am doing my homework correctly. The problem is there is a room that is 12'6" by 10'4" in length. I need to find out what the area is in square fee

Question 466520: I was looking to find out if I am doing my homework correctly. The problem is
there is a room that is 12'6" by 10'4" in length. I need to find out what the area is in square feet and then I need to express that as an improper fraction.
So far I have tried and got 129 for the area of the room. I am lost after that.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the room is 12 feet 6 inches by 10 feet 4 inches.
converting everything to feet, you get:
the room is 12.5 feet by 10.33333333 feet.
when you multiply 12.5 by 10.3333333, you get 19.16666666666 square feet.
that fractional part of .16666666666666 looks like the fraction 1/6.
i'll assume that's true for now and confirm it later.
assuming it's true, then the answer is 129 + 1/6 square feet.
converting that to an improper fraction means putting everything under a common denominator.
since 129 is equivalent to 6*129/6, then you get the answer being 774/6 + 1/6 square feet which comes out to be 775/6 square feet.
you could have also solved using improper fractions to start with.
we'll start again and solve it that way.
the room is 12 feet 6 inches by 10 feet 4 inches.
that's equivalent to 12 and 1/2 feet by 10 and 1/3 feet.
12 and 1/2 feet is equivalent to (12*2)/2 + 1/2 feet which is equivalent to 24/2 + 1/2 feet which is equivalent to 25/2 feet.
10 and 1/3 feet is equivalent to (30/3) + 1/3 feet which is equivalent to 31/3 feet.
the dimensions of your room are now:
25/2 feet by 31/3 feet.
the area is length times width which becomes:
25/2 * 31/3 which results in (25*31)/(2*3) square feet.
this is equivalent to 775/6 square feet.
i don't believe it can be reduced further than that since 775 is not divisible by 2 or 3 or 6, so that has to be your answer (if i am correct).
since i got the same answer 2 different ways, i'm reasonably confident it is.
to confirm that .1666666666..... is equivalent to 1/6, i simply use my calculator to divide 1 by 6 and get the decimal answer of 1.6666666667.
the difference is in rounding.
1.66666666667 is really 1.66666666666666666666666666666......... endlessly, so the answer is rounded to the last decimal place that the display on the calculator can show.

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