Question

4 and 1/2 - 3 and 5/6

Answer 1

`4(1)/(2)-3(5)/(6)\\\\\text{Find the common denominator.}\\\\6=2\cdot3.\ \text{Therefore the common denominator is 6}.\\\\(1)/(2)=(1\cdot3)/(2\cdot3)=(3)/(6)\\\\\Downarrow\\\\4(1)/(2)-3(5)/(6)=4(3)/(6)-3(5)/(6)=(*)\\\\Method\ \#1:\\\\(*)=(4-3)+\left((3)/(6)-(5)/(6)\right)=1+\left(-(2)/(6)\right)=(6)/(6)-(2)/(6)=(4)/(6)=(4:2)/(6:2)=\boxed{(2)/(3)}\\\\Method\ \#2\\\\(*)=3(6+3)/(6)-3(5)/(6)=3(9)/(6)-3(5)/(6)=(4)/(6)=\boxed{(2)/(3)}`