Questions: in the figure below, find the following. (a) the length of the tool in inches (Enter your answer as a simplified mixed number.) (b) the length of diameter A in inches (Simplify your answer completely.)

Solution Steps

The lengths given in the figure are:

• \(5 \frac{7}{8}\) inches
• \(1 \frac{3}{8}\) inches
• \(2 \frac{1}{4}\) inches

Convert each mixed number to an improper fraction:

• \(5 \frac{7}{8} = \frac{47}{8}\)
• \(1 \frac{3}{8} = \frac{11}{8}\)
• \(2 \frac{1}{4} = \frac{9}{4} = \frac{18}{8}\) (since \(2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4}\))

Add the fractions: \[ \frac{47}{8} + \frac{11}{8} + \frac{18}{8} = \frac{47 + 11 + 18}{8} = \frac{76}{8} \]

Simplify \(\frac{76}{8}\): \[ \frac{76}{8} = 9 \frac{1}{2} \]

Final Answer