Question

A section of a boardwalk is made using 15 boards. Each board is 9 1/4 inches wide. The total width of the section is 144 inches. The spacing between each board is equal. What is the width of the spacing between each board? Write your answer in simplest form.

Answer 1

The space between each board is 15.56 144/9.25=15.56

Answer 2

Answer:

The width of the spacing between  each board is $\frac{21}{56}$ inches.

Step-by-step explanation:

Given: Each board $9\frac{1}{4} inches$.

Let's convert the mixed number $9\frac{1}{4} inches$ to improper fraction.

$9\frac{1}{4} = \frac{37}{4}$

Total width of 15 boards = $15 . \frac{37}{4} = 138 \frac{3}{4}$ inches

Now we have to find the total space between the boards.

The total space = 144 - $138 \frac{3}{4}$

The total space = $5 \frac{1}{4}$

There 14 equal spaces between each board.

To find the width of spacing between each board, we need to divide $5 \frac{1}{4}$ by 14.

The width of spacing between each board = $\frac{5\frac{1}{4} }{14}$

Now we can convert the mixed number to improper and multiply with the reciprocal of 14.

The reciprocal of 14 is $\frac{1}{14}$

= $\frac{21}{4} . \frac{1}{14} = \frac{21}{56}$

Therefore, the width of the spacing between  each board is $\frac{21}{56}$ inches.