SOLUTION: A carpenter has a piece of lumber measuring 7 feet 6 3/4 inches long. how much must the carpenter saw off to be left with a piece 5 feet 11 5/6 inches long? Assume the saw cut has

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Question 444568: A carpenter has a piece of lumber measuring 7 feet 6 3/4 inches long. how much must the carpenter saw off to be left with a piece 5 feet 11 5/6 inches long? Assume the saw cut has no width.
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
First we need to get everything into the same units of measure.
7 ft 6 3/4 in = 7*12 + 6 3/4 = 90 3/4 inches
5 ft 11 5/6 = 5*12 + 11 5/6 = 71 5/6 inches
Hmmm...
The least common multiple of 4 and 6 is 12.
3/4 = ?/12
3/4 = 9/12
So, 90 3/4 inches = 90 9/12
5/6 = ?/12
5/6 = 10/12
So, 71 5/6 inches = 71 10/12
90 9/12 - ? = 71 10/12
Well, 9/12 has to be increased by 1 = 12/12 to be able to subtract 10/12.
89 21/12 - ? = 71 10/12
.
89 21/12
-71 10/12
18 11/12
or
1 ft 6 11/12 inches
.
Answer: Cut 1 foot 6 11/12 inches.
.
Does that make sense?
Always check your work.
In this case you can use a calculator and check using decimals.
3/4 = .75
90 3/4 inches = 90.75
.
5/6 = .8333333...
71 5/6 = 71.8333333...
.
90.75 - 71.8333333... = 18.91
18.91 = 1 ft 6 11/12 inches
.
Done.