Question

a machine - part is diagrammed in the figure below with its dimensions given in inches. if the centers of the circles lie on the same line parallel to the bottom of the part, what is the distance, in inches, between the centers of the 2 holes in the machine - part? a. 5 1/16 b. 5 1/12 c. 5 d. 4 13/16 e. 4 1/2

Explanation:

Step1: Convert mixed - numbers to improper fractions

$11\frac{3}{4}=\frac{11\times4 + 3}{4}=\frac{44+3}{4}=\frac{47}{4}$, $2\frac{1}{16}=\frac{2\times16 + 1}{16}=\frac{32 + 1}{16}=\frac{33}{16}$, $4\frac{1}{4}=\frac{4\times4+1}{4}=\frac{16 + 1}{4}=\frac{17}{4}$

Step2: Calculate the distance between the centers

The distance $d$ between the centers of the two holes is $11\frac{3}{4}-2\frac{1}{16}-4\frac{1}{4}$.
First, rewrite the expression with improper fractions: $\frac{47}{4}-\frac{33}{16}-\frac{17}{4}$.
Combine the fractions with the same denominator: $\frac{47}{4}-\frac{17}{4}-\frac{33}{16}=\frac{47 - 17}{4}-\frac{33}{16}=\frac{30}{4}-\frac{33}{16}$.
Make a common denominator of 16: $\frac{30\times4}{4\times4}-\frac{33}{16}=\frac{120}{16}-\frac{33}{16}=\frac{120 - 33}{16}=\frac{87}{16}=5\frac{7}{16}$

Answer:

A. $5\frac{7}{16}$