Question

A candle maker has 4 1/2 pounds of clear wax. He wants to cut the wax into pieces that are 2/3 pound each. How many 2/3 pound pieces can he divide the wax into. How much wax does he have leftover

Answer 1

10 1/8 is your answer

Answer 2

$\bf \cfrac{4\frac{1}{2}}{\quad \frac{2}{3}\quad }\implies \cfrac{\frac{4\cdot 2+1}{2}}{\quad \frac{2}{3}\quad }\implies \cfrac{\frac{9}{2}}{\quad \frac{2}{3}\quad }\implies \cfrac{9}{2}\cdot \cfrac{3}{2}\implies \cfrac{27}{4}\implies 6\frac{3}{4} \\\\\\ \textit{so, 6 whole pieces, and }\frac{3}{4}\textit{ of another one}$

now, what's the leftover?  well, 3/4 of the last one, namely 3/4 of 2/3, what is 3/4 of 2/3 anyway?  well, is just their product,

$\bf \cfrac{\underline{3}}{4}\cdot \cfrac{2}{\underline{3}}\implies \cfrac{2}{4}\implies \stackrel{lbs}{\cfrac{1}{2}}$