The carpenter needs \(2\frac{7}{12}\) feet of wooden plank to fix the stairs.
Further Explanation
Given:
Total wooden of plank is \(10\frac{1}{2}\) feet
He then cut \(4\frac{1}{4}\) feet for the slat of a deck
\(3\frac{2}{3}\) feet for repairing a Bannister
and the rest for fixing the stairs
Question:
How many feet of wood does the carpenter use to fix the stair?
The rest to fix the stairs = Total wooden of plank - wooden of plank use for the slat of a deck - wooden of plank use for repairing a Bannister.
\(\boxed {= 10\frac{1}{2} - 4\frac{1}{4} - 3\frac{2}{3} }\)
the denominator is different, so we need to find a common denominator for 2, 4 and 3 which is 12, so :
\(\boxed {= 10\frac{6}{12} - 4\frac{3}{12} -3 \frac{8}{12} }\)
we can write the above equation as follow
\(\boxed {=10+\frac{6}{12} - ((4 + \frac{3}{12}) - (3 +\frac{8}{12})) }\)
we can break up 10 into two smaller numbers
\(\boxed {=9 +\frac{12}{12} + \frac{6}{12} - ((4 +\frac{3}{12}) - (3 +\frac{8}{12})) }\\\boxed {=9-4-3 +\frac{12}{12}+\frac{6}{12} -\frac{3}{12} -\frac{8}{12} }\\\boxed {= 2+\frac{7}{12} }\\\boxed {=2\frac{7}{12} }\)
So, the wooden plank use for fixing the stairs is \(2\frac{7}{12}\) feet.
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Keyword: mixed fraction, subtraction, improper fraction, part to whole relationship, grouping, mixed fraction additional
