Math

1  1/4 - 5/6 =   15/12 - 10/12 = 5/12 mile between the houses

∴  Joe's house is ( $1{1 \over 4}$-${5\over 6}$) mile far

    from Ralph's house

  i.e ($1{1 \over 4}$-${5\over 6}$) = ( ${4 + 1\over 4}$-${5\over 6}$)

                    = ( ${5\over 4}$-${5\over 6}$)

                    = ( ${5 * 3 - 5 * 2\over 12}$)

                    =  ${15 - 10\over 12}=$-${5\over 12}$
∴  Joe's house is $({5 \over 12})$ mile far from

    Ralph's house