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Rodger wants to carpet a rectangular room with a length of 8 3/4 feet and a width of 9 1/3 feet. If he has 85 square feet of carpet, how many square feet of carpet will be left after he covers the room?

Soccerdude8  Aug 28, 2017

Best Answer 

 #1
avatar+1366 
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To solve this problem, we must figure out how much square feet the entire room is. We know the length and the width of the room. Since, this room is rectangular, we can use that information to figure out how much square feet this room covers. 

 

\(8\frac{3}{4}*9\frac{1}{3}\) First, convert both fractions to improper fractions so that we can multiply them. I will convert each one separately.
\(8\frac{3}{4}=\frac{4*8+3}{4}=\frac{35}{4}\)  
\(9\frac{1}{3}=\frac{3*9+1}{3}=\frac{28}{3}\) Now, let's multiply both together.
\(\frac{35}{4}*\frac{28}{3}\) 4 and 28 have a common factor of 4. Doing this simplification makes it easier computationally.
\(\frac{35}{1}*\frac{7}{3}\) Now, do the multiplication. One-digit multiplication is simpler than doing 2-digit.
\(\frac{245}{3}\)  
   

 

We aren't done yet, though! The question is asking how much carpet is remaining after covering the entire floor. This requires the subtraction operator.

 

\(85-\frac{245}{3}\) Make 85 a fraction in which it has a denominator of 3.
\(\frac{85}{1}*\frac{3}{3}=\frac{255}{3}\)  
\(\frac{255}{3}-\frac{245}{3}\) Now, we can subtract knowing that we have common denominators.
\(\frac{10}{3}ft^2\) And of course, do not forget to include units, if applicable. 
   

 

Therefore, after completely covering the \(\left(8\frac{3}{4}\right)^{'} * \left(9\frac{1}{3}\right)^{'}\)rectangular room in carpet, Rodger will have  \(\frac{10}{3}ft^2=3\frac{1}{3}ft^2=3.\overline{33}ft^2\) of carpet left. 

TheXSquaredFactor  Aug 28, 2017
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1+0 Answers

 #1
avatar+1366 
+1
Best Answer

To solve this problem, we must figure out how much square feet the entire room is. We know the length and the width of the room. Since, this room is rectangular, we can use that information to figure out how much square feet this room covers. 

 

\(8\frac{3}{4}*9\frac{1}{3}\) First, convert both fractions to improper fractions so that we can multiply them. I will convert each one separately.
\(8\frac{3}{4}=\frac{4*8+3}{4}=\frac{35}{4}\)  
\(9\frac{1}{3}=\frac{3*9+1}{3}=\frac{28}{3}\) Now, let's multiply both together.
\(\frac{35}{4}*\frac{28}{3}\) 4 and 28 have a common factor of 4. Doing this simplification makes it easier computationally.
\(\frac{35}{1}*\frac{7}{3}\) Now, do the multiplication. One-digit multiplication is simpler than doing 2-digit.
\(\frac{245}{3}\)  
   

 

We aren't done yet, though! The question is asking how much carpet is remaining after covering the entire floor. This requires the subtraction operator.

 

\(85-\frac{245}{3}\) Make 85 a fraction in which it has a denominator of 3.
\(\frac{85}{1}*\frac{3}{3}=\frac{255}{3}\)  
\(\frac{255}{3}-\frac{245}{3}\) Now, we can subtract knowing that we have common denominators.
\(\frac{10}{3}ft^2\) And of course, do not forget to include units, if applicable. 
   

 

Therefore, after completely covering the \(\left(8\frac{3}{4}\right)^{'} * \left(9\frac{1}{3}\right)^{'}\)rectangular room in carpet, Rodger will have  \(\frac{10}{3}ft^2=3\frac{1}{3}ft^2=3.\overline{33}ft^2\) of carpet left. 

TheXSquaredFactor  Aug 28, 2017

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