Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.3 The Rational Numbers - Exercise Set 5.3: 133

Answer

The remaining piece of the board is 1 foot 4$\frac{7}{16}$ inches long. This could also be written as 16$\frac{7}{16}$ inches long.

Work Step by Step

The longer board is 2 feet long. Using the fact that 12 inches = 1 foot, we know that the longer board is 24 inches long (24 inches = 2 feet). A 7$\frac{1}{2}$ board is removed using a $\frac{1}{16}$ inch wide saw blade. This means that 7$\frac{1}{2}$ inches + $\frac{1}{16}$ inches are removed from the larger board. We need common denominators to add. The common denominator for fractions with denominators of 2 and 16 is 16. So, we have 7$\frac{8}{16}$ + $\frac{1}{16}$ = 7$\frac{9}{16}$. Now, we subtract the number we just calculated from the 24 inches (the length of the longer board. 24 - 7$\frac{9}{16}$ We could convert both numbers to improper fractions, however, a quicker (and simpler) way to subtract, would be to convert 24 to a mixed numeral. (24 = 23 + 1 = 23 + $\frac{16}{16}$= 23$\frac{16}{16}$) Now subtract: 23$\frac{16}{16}$ - 7$\frac{9}{16}$ = 16$\frac{7}{16}$ Note: Since the fractional part of the smaller number was less than the fractional part of the larger number, we did not have to "borrow" from the 23 to complete the subtraction. 16$\frac{7}{16}$ inches of the board is left. We can convert this back to feet and inches by using the fact that 12 inches = 1 foot. Using this conversion factor, 16 inches = 1 foot 4 inches. We still have the fractional part of the answer, so the final answer is 1 foot 4$\frac{7}{16}$ inches.
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