Question

the mounting bracket shown was purchased at a hardware store. find the diameter of the hole, which is the distance across it.
the diameter of the hole is
(simplify your answer. type a whole number, fraction, or mixed number.)

Explanation:

Step1: Understand the total length and the two segments

The total length of the bracket is $\frac{35}{24}$ inches, and we have two segments: $\frac{7}{12}$ inches and $\frac{5}{8}$ inches. To find the diameter of the hole (the middle segment), we subtract the sum of the two known segments from the total length. First, find a common denominator for $\frac{7}{12}$ and $\frac{5}{8}$. The least common denominator of 12 and 8 is 24.

Step2: Convert fractions to have denominator 24

Convert $\frac{7}{12}$ to $\frac{14}{24}$ (since $7\times2 = 14$ and $12\times2 = 24$) and $\frac{5}{8}$ to $\frac{15}{24}$ (since $5\times3 = 15$ and $8\times3 = 24$).

Step3: Sum the two known segments

Sum of the two segments: $\frac{14}{24}+\frac{15}{24}=\frac{29}{24}$.

Step4: Subtract the sum from the total length

Subtract this sum from the total length $\frac{35}{24}$: $\frac{35}{24}-\frac{29}{24}=\frac{35 - 29}{24}=\frac{6}{24}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$