`1/2+1/2+1/3+1/3`
`=(1/2+1/2)+(1/3+1/3)`
`=2/2+2/3`
`=1+2/3`
`=3/3+2/3`
`=5/3`
\(\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{3}=\dfrac{1}{2}\times2+\dfrac{1}{3}\times2=\left(\dfrac{1}{2}+\dfrac{1}{3}\right)\times2=\dfrac{5}{6}\times2=\dfrac{5}{3}\)