Question

Simplify and write the result in decimal form:

${\displaystyle (1÷\frac{2}{9})+(1÷3\frac{1}{5})+ (1÷2\frac{2}{3})}$

Answer 1

Given, ${\displaystyle (1÷\frac{2}{9})+(1÷3\frac{1}{5})+ (1÷2\frac{2}{3})}$

= ${\displaystyle (1÷\frac{2}{9})+(1÷\frac{(5\times 3)+1}{5})+(1÷\frac{(2\times 3)+2}{3})}$

= ${\displaystyle (1\times \frac{9}{2})+(1÷\frac{16}{5})+(1÷\frac{8}{3})}$

= ${\displaystyle (1\times \frac{9}{2})+(1\times \frac{5}{16})+(1\times \frac{3}{8})}$

= ${\displaystyle \frac{9}{2}+\frac{5}{16}+\frac{3}{8}}$

= ${\displaystyle \frac{72+5+6}{16}}$  .....[Taking LCM]

= ${\displaystyle \frac{83}{16}}$

= 5.1875