## Elementary Technical Mathematics

$\frac{155}{8}$ inch.
This question requires us to solve for length of the pipe left after the 3 given measurements are cut off it. We know that the pipe is 72 in. long, so, to solve, we must subtract the pieces cut off, and subtract the waste from each cut, to achieve our final answer. There is $\frac{1}{16}$ in. in waste every cut, so with 3 cuts, this value is multiplied by 3. $72 in - 16\frac{3}{4} in - 24\frac{7}{8} in - 12\frac{5}{16} in + (3 * \frac{1}{16} in)$ To subtract these values, we must convert these fractions into values with the same denominator (bottom number). Looking at the denominators, we have values 4, 8, and 16. We need to find the lowest common denominator (LCD) between these 3 numbers. Looking at 4, 8, and 16, the LCD would be 16. So, we must multiply the numerators and denominators by values that will give us a denominator of 16. We will have: $72 in - 16\frac{12}{16} in - 24\frac{14}{16} in - 12\frac{5}{16} in - (3 * \frac{1}{16} in)$ = $72 in - 16\frac{12}{16} in - 24\frac{14}{16} in - 12\frac{5}{16} in - \frac{3}{16} in$ Now, we can subtract our fractions: $\frac{12}{16}$ + $\frac{14}{16}$ + $\frac{5}{16}$ + $\frac{3}{16}$ 12 14 5 - 3 = -10 -> $-\frac{10}{16}$ = $-\frac{5}{8}$ Subtracting our whole numbers gives: 72 - 16 - 24 - 12 = 20 Adding the fraction to the whole number, using common denominators: $20 + (-\frac{5}{8})$ $\frac{160}{8} - \frac{5}{8}$ = $\frac{155}{8}$ $\textbf{Therefore, we know that remaining length of the pipe is$\frac{155}{8}$inch.}$