Question

Simplify $\frac{3}{10}\times \frac{8}{9}÷\frac{20}{27}+\frac{4}{9}$

Answer 1

Given,

$\frac{3}{10}\times \frac{8}{9}÷\frac{20}{27}+\frac{4}{9}$

Step:$1$

We have to use the BODMAS rule,

BODMAS rule,

B$\to$Brackets $\left[\left\{\left(\right)\right\}\right]$

O$\to$Of

D$\to$Division

M$\to$Multiplication

A$\to$Addition

S$\to$Subtraction

Replace the sign of $÷$ by $\times$ taking the reciprocal of the term next to $÷$sign and divide by the common factor.

$\frac{3}{10}\times \frac{8}{9}÷\frac{20}{27}+\frac{4}{9}$$=$$\frac{3}{10}\times \frac{8}{9}\times \frac{27}{20}+\frac{4}{9}$

$$\begin{gathered} =\frac{3}{10}\times \frac{8}{20}\times \frac{27}{9}+\frac{4}{9} \\ =\frac{3}{10}\times \frac{2}{5}\times \frac{3}{1}+\frac{4}{9}\left(\therefore \frac{8}{20}=\frac{2}{5},\frac{27}{9}=\frac{3}{1}\right) \\ =\frac{3}{10}\times \frac{2\times 3}{5\times 1}+\frac{4}{9} \\ =\frac{3}{10}\times \frac{6}{5}+\frac{4}{9} \\ =\frac{3\times 6}{10\times 5}+\frac{4}{9} \\ =\frac{18}{50}+\frac{4}{9} \end{gathered}$$

Step:$2$

Find LCM of the denominators $\left(50,9\right)$

$$\begin{gathered} 50=2\times 5\times 5 \\ 3=3\times 3 \end{gathered}$$

Choose each factor with the highest exponent.

LCM$\left(50,9\right)$$=$$2\times 3\times 3\times 5\times 5$

LCM$\left(50,9\right)$$=$$450$

Step:$3$

Make all the denominators equal to $450$.

$$\begin{gathered} \frac{18}{50}+\frac{4}{9}=\frac{18\times 9}{50\times 9}+\frac{4\times 50}{9\times 50} \\ =\frac{162}{450}+\frac{200}{450} \\ =\frac{162+200}{450} \\ =\frac{362}{450} \end{gathered}$$

$=\frac{181}{225}$

Therefore, $\frac{3}{10}\times \frac{8}{9}÷\frac{20}{27}+\frac{4}{9}$$=\frac{181}{225}$