Question

A man is building a gazebo and plans to use for the floor two boards that are 8 and three fourths feet ​, four boards that are 13 and five eighths feet ​, and two boards that are 6 one half feet. Find the total number of feet in all the boards.

Answer 1

Answer:

The total number of feet in all the boards is 90 and 5/6 feet

Step-by-step explanation:

First, it is necessary to transform the mixed number into a fraction. This can be made following the next rule:

$a\frac{b}{c} = \frac{(a*c) + b}{c}$

So, the number 8 and three fourth feet is equal to:

$8\frac{3}{4} = \frac{(8*4) + 3}{4} = \frac{35}{3}$

That means that we two boards that are 35/3 feet. So, multiplying 2 by 35/3 we get the total feets for the first type of board. That is:

$2*\frac{35}{3} = \frac{2*35}{3} =\frac{70}{3}$

At the same way, we can calculate the total number of feet for the second and third type of board as:

• Four boards that are 13 and five eighths feet:

$13\frac{5}{8} = \frac{(13*8) + 5}{8} = \frac{109}{8}$

$4*\frac{109}{8} = \frac{4*109}{8} =\frac{109}{2}$

• Two boards that are 6 one half feet:

$6\frac{1}{2} = \frac{(6*2) + 1}{2} = \frac{13}{2}$

$2*\frac{13}{2} = \frac{2*13}{2} =13$

Finally, to find the total number of feet in all the boards, we need to sum the total number of feet for every type as:

$\frac{70}{3} +\frac{109}{2} +\frac{13}{1} =\frac{545}{6}$

Converting this number to a mixed number we get:

$\frac{545}{6} =90\frac{5}{6}$

Because, when we divide 545 by 6, we get 90 as a quotient, 5 is the remainder and 6 is the divisor.