SOLUTION: Ran across this: "The weight of a fraction of a square foot of any material can be quickly computed by the breakdown method; The weight of 1 sq. ft. of steel, 0.22 in. thick

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Ran across this: "The weight of a fraction of a square foot of any material can be quickly computed by the breakdown method; The weight of 1 sq. ft. of steel, 0.22 in. thick      Log On

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Question 1210257: Ran across this:
"The weight of a fraction of a square foot of any material can be quickly computed by the breakdown method;
The weight of 1 sq. ft. of steel, 0.22 in. thick, is 8.976 lbs., how much will 81 sq. in. of this thickness weigh ?
72 sq. in. (1/2 of 8.976 lbs.) = 4.488 lbs.
9 sq. in. (1/8 of 4.888 lbs.) = .561 lbs.
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81 sq. in. = 5.049 lbs. "

My question:

Why was 1/2 and 1/8 used ?



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


One square foot
= 1 foot by 1 foot
= 12 inches by 12 inches
= 12*12 = 144 square inches

The "breakdown method": (NOT a standard mathematical term -- but a valid method you are apparently learning....)

81 square inches = 72 square inches plus 9 square inches

72 square inches = 1/2 of 144 square inches, so 72 square inches weighs 1/2 as much as 144 square inches -- 1/2 of 8.976 pounds = 4.488 pounds

9 square inches = 1/8 of 72 square inches, so 9 square inches weighs 1/8 as much as 72 square inches -- 1/8 of 4.488 pounds = 0.561 pounds

Weight of 81 square inches of the material
= weight of 72 square inches plus weight of 9 square inches
= 4.488 + 0.561 pounds = 5.049 pounds

A summary without so many words to help see where the "1/2" and "1/8" came from:

81 = 72+9 = red%281%2F2%29 of 144 plus red%281%2F8%29 of 72