Question

Kaitlin spent 2/3 of an hour on homework. Her sister Judy spent 1 1/2 times that amount. Explain why Judy’s homework time is between 2/3 of an hour and 1/2 of an hour?

Answer 1

`\bf \stackrel{mixed}{1(1)/(2)}\implies \cfrac{1\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{3}{2}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{Judy spent time}}{\stackrel{\textit{Kaitlin's time}}{\cfrac{2}{3}}\cdot \cfrac{3}{2}}\implies \cfrac{2}{2}\cdot \cfrac{3}{3}\implies 1~\hfill \boxed{\cfrac{1}{2}}\rule[0.35em]{3em}{0.25pt}\stackrel{\stackrel{Judy's}{\downarrow }}{1}\rule[0.35em]{5em}{0.25pt}\stackrel{1(2)/(3)}{\boxed{\cfrac{2}{3}}}`

so, Judy's time is really 1 hour exactly.

and on the number line, we could place that 1 in between the first half and the two thirds of the of the next number, as you see above.