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.
