Question

A group of students recycled 7 2/3 pounds of glass and 9 3/4 pounds of paper. How many pounds of glass and paper did the students recycle alltogether?

Answer 1

Well, is namely just their sum, let's firstly convert the mixed fractions to "improper" and then add them,

$\bf \stackrel{mixed}{7\frac{2}{3}}\implies \cfrac{7\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{23}{3}} \\\\\\ \stackrel{mixed}{9\frac{3}{4}}\implies \cfrac{9\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{39}{4}}\\\\ -------------------------------\\\\ \cfrac{23}{3}+\cfrac{39}{4}\qquad \stackrel{LCD~of~12}{\implies }\qquad \cfrac{4(23)+3(39)}{12}\implies \cfrac{92+117}{12} \\\\\\ \cfrac{209}{12}\implies 17\frac{5}{12}$

Answer 2

9 9/12 + 7 8/12 = 16 17/12 which converts to your answer----> 17 5/12