Question

if you lose 3 1/2 pounds the first week of your diet and 2 2/3 pounds the second week, how many pounds do you still need to lose to reach your goal of losing 10 pounds?

Answer 1

let's firstly convert the mixed fractions to improper fractions, and then subtract.

`\bf \stackrel{mixed}{3(1)/(2)}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{2(2)/(3)}\implies \cfrac{2\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{8}{3}} \\\\[-0.35em] ~\dotfill`

`\bf \stackrel{\textit{goal}}{10}-\stackrel{\textit{first week}}{\cfrac{7}{2}}-\stackrel{\textit{second week}}{\cfrac{8}{3}}\implies \cfrac{10}{1}-\cfrac{7}{2}-\cfrac{8}{3}\implies \stackrel{\textit{using an LCD of 6}}{\cfrac{(6)10-(3)7-(2)8}{6}} \\\\\\ \cfrac{60-21-16}{6}\implies \cfrac{23}{6}\implies 3(5)/(6)`

Answer 2

3 5/6

Explanation:

3 1/2 plus 2 2/3 equals 6 1/6. 10 minus 6 1/6 equals 3 5/6. So they still need to lose 3 5/6 pounds to reach their go of losing 10 pounds.