The lengths of the bolts are given,
[tex] \frac{3}{8} [/tex] inch, [tex] \frac{1}{2} [/tex] inch, [tex] \frac{5}{8} [/tex] inch, [tex] \frac{7}{8} [/tex] inch, [tex] 1\frac{1}{4} [/tex] inch.
First we have to convert the mised fraction [tex] 1 \frac{1}{4} [/tex] to improper fraction.
[tex] 1\frac{1}{4} =\frac{(1)(4)+1}{4} [/tex]
= [tex] \frac{4+1}{4} =\frac{5}{4} [/tex]
Now we have to make the all the denominators equal of the given fraction to find the longest and shortest bolt.
We can make the common denominator 8, as the multiple of all the denominators is 8.
[tex] \frac{1}{2} =\frac{(1)(4)}{(2)(4)} =\frac{4}{8} [/tex] inch
[tex] \frac{5}{4} =\frac{(5)(2)}{(4)(2)} =\frac{10}{8} [/tex] inch
So in the given lengths, [tex] \frac{3}{8} [/tex] inch is shortest and [tex] 1\frac{1}{4} [/tex] or [tex] \frac{10}{8} [/tex] inch is longest.
The difference between them is,
[tex] \frac{10}{8} -\frac{3}{8} [/tex]
As the denominator is same, we can subtract the numerator. We will get,
[tex] \frac{(10-3)}{8} [/tex] = [tex] \frac{7}{8} [/tex]
So we have got the required answer.
The difference between longest and shortest lengths is [tex] \frac{7}{8} [/tex].
