Aims Grade 8 Mathematics Sample Test And Think-Throughs With Answers Page 14
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36December 2009
How many square feet are there in 288 square inches?
3
Scale
1 foot = 12 inches
2
A
24
B
93
C
144
D
This problem is asking me to convert, or change, square inches into square feet. And, just in case
I do not know that 12 inches is the same as 1 foot, it is given to me in the key.
The first thing that I think of when I see that I have to convert one unit into another is to make a
proportion. I will set up a proportion in order to know how much of one unit is equal to another
unit.
Since I know that 1 foot equals 12 inches, that will be my first proportion,1 foot : 12 inches.
But I need to know square feet. I will square the proportion to go from feet and inches to square
feet and square inches. The exponent applies to the numbers as well as the units.
2
feet
1
=
1
square feet
inches
12
= 144
square inches
Now I can complete my proportion. I will make a second proportion for what I need to find. The
problem tells me I have 288 square inches, but I do not know how many square feet. Since the
number of square feet is my unknown, I will call it x.
I need to set up the proportion the same way as my
square feet
1
x
first proportion, with the square feet in the numerator
=
and the square inches in the denominator.
square inches
144
288
The next step looks like I should
square feet
1
x
=
cross-multiply.
square inches
144
288
288 • 1 = 144x
Then, since I need to get x by itself, I
288 = 144 x
divide each side by 144.
144
144
Now I see that x is 2. That means there
2 = x
are 2 square feet in 288 square inches,
which is answer choice A.
Arizona Department of Education
14
Grade 8
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