Question

Evaluate the expression shown at the right. Write your answer in the simplest form.

$\frac{-{\displaystyle \frac{1}{2}}+{\displaystyle \frac{2}{3}}}{{\displaystyle \frac{3}{5}}\left({\displaystyle \frac{3}{4}}-{\displaystyle \frac{11}{8}}\right)}$

Answer 1

Step 1: $=\frac{-{\displaystyle \frac{1}{2}}+{\displaystyle \frac{2}{3}}}{{\displaystyle \frac{3}{5}}\left({\displaystyle \frac{3}{4}}-{\displaystyle \frac{11}{8}}\right)}$

Step 2: $=\frac{{\displaystyle \frac{-1\times 3+2\times 2}{6}}}{{\displaystyle \frac{3}{5}}\left({\displaystyle \frac{3\times 2-11\times 1}{8}}\right)}$.

(First solving the numerator and denominator part respectively)

Step 3: $=\frac{{\displaystyle \frac{-3+4}{6}}}{{\displaystyle \frac{3}{5}}\left({\displaystyle \frac{6-11}{8}}\right)}$

Step 4: $=\frac{{\displaystyle \frac{+1}{6}}}{{\displaystyle \frac{3}{5}}\left({\displaystyle \frac{-5}{8}}\right)}$

Step 5: $=\frac{{\displaystyle \frac{+1}{6}}}{{\displaystyle \frac{3}{5}}\left({\displaystyle \frac{-5}{8}}\right)}$

Step 6: $=\frac{{\displaystyle \frac{+1}{6}}}{{\displaystyle \frac{-3}{8}}}or\frac{+1}{6}÷\frac{-3}{8}or\frac{+1}{6}\times \frac{8}{-3}$

$=\frac{4}{-9}$

Hence The final answer is $\frac{4}{-9}$