Question

Simplify : $1\frac{4}{9}-\frac{7}{9}of\frac{6}{7}+(2\frac{4}{9}-1\frac{1}{3})\times 2$

Answer 1

Step 1 : Converting all the mixed fractions to improper fractions

$=\frac{13}{9}-\frac{7}{9}of\frac{6}{7}+(\frac{22}{9}-\frac{4}{3})\times 2$

Step 2 : Solving the brackets by taking the LCM and then subtracting them, LCM is $9$

$$\begin{gathered} =\frac{13}{9}-\frac{7}{9}of\frac{6}{7}+\left(\frac{22-(4\times 3)}{9}\right)\times 2 \\ =\frac{13}{9}-\frac{7}{9}of\frac{6}{7}+\left(\frac{10}{9}\right)\times 2 \end{gathered}$$

Step 3 : Now solving the $of$ operator we get $\frac{2}{3}$, so, the equation becomes

$=\frac{13}{9}-\frac{2}{3}+\frac{10}{9}\times 2$

Step 4 : Now multiplying $\frac{10}{9}and2$ we get $\frac{20}{9}$

$=\frac{13}{9}-\frac{2}{3}+\frac{20}{9}$

Step 5 : Now again solving the equation by taking the LCM which comes out to be $9$

$$\begin{gathered} =\frac{13-(2\times 3)+20}{9} \\ =\frac{13-6+20}{9} \\ =\frac{27}{9} \end{gathered}$$

$=3$

Hence the result is $3$