let's say the number is "n", one third of that is just (1/3)n, and half of that is just (1/2)(1/3)n, now, we also know it equals 1, so
[tex]\bf \stackrel{\textit{one third of "n"}}{\cfrac{1}{3}n}\qquad \qquad \stackrel{\textit{half of one third of "n"}}{\cfrac{1}{2}\cdot \cfrac{1}{3}n}~~~~=~~~~1\implies \cfrac{1}{6}n=1 \\\\\\ \cfrac{n}{6}=1\implies n=6[/tex]
