The oak board had originally 4 5/8 in. wide, and the joiner wants to remove 7/64 in. from the width. This basically wants us to subtract 7/64 in. from 4 5/8 in.
To do this operation, we just need to put those two fractions with the same denominator and then subtract the numerators.
[tex]4\frac{5}{8}=4+\frac{5}{8}=\frac{4\times8}{8}+\frac{5}{8}=\frac{32}{8}+\frac{5}{8}=\frac{37}{8}[/tex]If we multiply the width, both the numerator and denominator by 8, we're going to get the same denominator as the number we want to subtract.
[tex]\frac{37}{8}\times\frac{8}{8}=\frac{296}{64}[/tex]Doing the subtraction:
[tex]\frac{296}{64}-\frac{7}{64}=\frac{289}{64}=4+\frac{33}{64}=4\frac{33}{64}[/tex]The width after joining once is 4 33/64 in.
