Question

Simplify:

${\displaystyle 2\frac{1}{3}÷(5\frac{1}{2}+3\frac{3}{4})}$

Answer 1

${\displaystyle 2\frac{1}{3}÷(5\frac{1}{2}+3\frac{3}{4})=\frac{7}{3}÷(\frac{11}{2}+\frac{15}{4})}$

= ${\displaystyle \frac{7}{3}÷\left(\frac{2\times 11+1\times 15}{4}\right)}$

= ${\displaystyle \frac{7}{3}÷\left(\frac{22+15}{4}\right)=\frac{7}{3}÷\left(\frac{37}{4}\right)}$

= ${\displaystyle \frac{7}{3}\times \frac{4}{37}=\frac{28}{111}}$