City hall to post office = 6 1/2 miles
City hall to library site = 1 1/4 miles
library site to post office = unknown. let it be x. 5 1/4 miles
1 1/4 miles + x = 6 1/2 miles
x = 6 1/2 miles - 1 1/4 miles
Find x.
1) convert the mixed fractions into fractions. 6 1/2 = 13/2 ; 1 1/4 = 5/4
x = 13/2 - 5/4
2) get the common denominator. 4 is twice as much as 2. multiply 13/2 by 2/2
13/2 * 2/2 = 26/4
3) Subtract the top numbers and put over the same denominator
x = 26/4 - 5/4 = (26-5) / 4 = 21 / 4
4) simplify the fraction
x = 21/4 = 5 1/4 miles from library site to post office.