Question

example 4: a carpenter is installing new wood flooring. he bought boards that are 10ft long, \\(\frac{3}{4}\\) inches thick, and \\(\frac{11}{24}\\) ft., wide. determine the number of boards the carpenter will need for a 10ft by \\(16\frac{1}{2}\\) ft. room.

Explanation:

Step1: Calculate the area of the room

The room is a rectangle, and the area of a rectangle is given by \( A = length \times width \). The length of the room is \( 16\frac{1}{2}\) ft and the width is \( 10\) ft. First, convert \( 16\frac{1}{2}\) to an improper fraction: \( 16\frac{1}{2}=\frac{33}{2}\). Then the area of the room \( A_{room}=\frac{33}{2}\times10 = 33\times5=165\) square feet.

Step2: Calculate the area of one board

The board is also a rectangle. The length of the board is \( 10\) ft and the width is \( \frac{11}{24}\) ft. The area of a rectangle is \( A = length \times width \), so the area of one board \( A_{board}=10\times\frac{11}{24}=\frac{110}{24}=\frac{55}{12}\) square feet.

Step3: Calculate the number of boards needed

To find the number of boards, we divide the area of the room by the area of one board. So the number of boards \( n=\frac{A_{room}}{A_{board}}=\frac{165}{\frac{55}{12}}\). When dividing by a fraction, we multiply by its reciprocal, so \( n = 165\times\frac{12}{55}\). Simplify \( 165\div55 = 3\), so \( n=3\times12 = 36\).

Answer:

36