Question

Divide the sum of 3/8  and 5/12 by reciprocal of -15/8 × 16/27

Answer 1

$\frac{3}{8}+\frac{5}{12}\\\\Find\ LCD(8;\ 12)\\The\ multiples\ of\ 8:\ 8;\ 16;\ \fbox{24};\ 32;...\\The\ multiples\ of\ 12:\ 12;\ \fbox{24};\ 36;...\\\\LCD(8;\ 12)=24\\\\\frac{3}{8}=\frac{3\times3}{8\times3}=\frac{9}{24};\ \frac{5}{12}=\frac{5\times2}{12\times2}=\frac{10}{24}\\\\\frac{3}{8}+frac{5}{12}=\frac{9}{24}+\frac{10}{24}=\frac{19}{24}$

$-\frac{15}{8}\times\frac{16}{27}=-\frac{5}{1}\times\frac{2}{9}=-\frac{10}{9}\\\\The\ reciprocal\ of\ -\frac{10}{9}\ equal\ -\frac{9}{10}\\------------------------------\\\\\frac{19}{24}:(-\frac{9}{10})=\frac{19}{24}\times(-\frac{10}{9})=-\frac{19}{12}\times\frac{5}{9}=\boxed{-\frac{95}{108}}$

Answer 2

3/8+ 5/12=(9+10)/24 =19/24

division by reciprocal is the same as multiplication

19/24 x -15/8 x 16/27 = -19/24 x 10/9 = -95/108