Question
Simplify and write the result in decimal form:
$\big(1\div\frac{2}{9}\big)+\big(1\div3\frac{1}{5}\big)+\big(1\div2\frac{2}{3}\big)$
$\big(1\div\frac{2}{9}\big)+\big(1\div3\frac{1}{5}\big)+\big(1\div2\frac{2}{3}\big)$
✓
Answer
Given, $\big(1\div\frac{2}{9}\big)+\big(1\div3\frac{1}{5}\big)+\big(1\div2\frac{2}{3}\big)$
$=\big(1+\frac{2}{9}\big)+\big(1+\frac{(5\times3)+1}{5}\big)+\big(1+\frac{(2\times9)+2}{3}\big)$
$=\big(1\times\frac{9}{2}\big)+\big(1\div\frac{16}{5}\big)+\big(1\div\frac{8}{3}\big)$
$=\big(1\times\frac{9}{2}\big)+\big(1\times\frac{5}{16}\big)+\big(1\times\frac{3}{8}\big)$
$=\frac{9}{2}+\frac{5}{16}+\frac{3}{8} [$taking $LCM]$
$=\frac{72+5+6}{16}=\frac{83}{16}$
$=5.1875$
$=\big(1+\frac{2}{9}\big)+\big(1+\frac{(5\times3)+1}{5}\big)+\big(1+\frac{(2\times9)+2}{3}\big)$
$=\big(1\times\frac{9}{2}\big)+\big(1\div\frac{16}{5}\big)+\big(1\div\frac{8}{3}\big)$
$=\big(1\times\frac{9}{2}\big)+\big(1\times\frac{5}{16}\big)+\big(1\times\frac{3}{8}\big)$
$=\frac{9}{2}+\frac{5}{16}+\frac{3}{8} [$taking $LCM]$
$=\frac{72+5+6}{16}=\frac{83}{16}$
$=5.1875$
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