Question

Simplify: $\left(\frac{3}{7}\right)+\left(\frac{-2}{21}\right)\times \left(\frac{-5}{6}\right)$

Answer 1

Simplify the given expression.

Step 1: Apply BODMAS rule to first find the product of the fractions.

$\begin{array}{rcl}\left(\frac{3}{7}\right)+\left(\frac{-2}{21}\right)\times \left(\frac{-5}{6}\right)& =& \left(\frac{3}{7}\right)+\left(\frac{-2}{21}\times \frac{-5}{6}\right)\\ & =& \left(\frac{3}{7}\right)+\left(\frac{2}{21}\times \frac{5}{6}\right)\left[\because \left(-\right)\times \left(-\right)=\left(+\right)\right]\\ & =& \left(\frac{3}{7}\right)+\left(\frac{1}{21}\times \frac{5}{3}\right)\\ & =& \left(\frac{3}{7}\right)+\left(\frac{1\times 5}{21\times 3}\right)\\ & =& \left(\frac{3}{7}\right)+\left(\frac{5}{63}\right)\end{array}$

Step 2: Convert the fractions into like fractions and add.

Like fractions.

Fractions with the same denominators are called like fractions.

The given fractions are $\frac{3}{7}$ and $\frac{5}{63}$.

The LCM of $7$ and $63$ is $63$. Therefore,

$\frac{3}{7}=\frac{3\times 9}{7\times 9}=\frac{27}{63}$

$\frac{5}{63}=\frac{5\times 1}{63\times 1}=\frac{5}{63}$

Substitute the obtained like fractions into the equation:

$\begin{array}{rcl}\left(\frac{3}{7}\right)+\left(\frac{-2}{21}\right)\times \left(\frac{-5}{6}\right)& =& \frac{27}{63}+\frac{5}{63}\\ & =& \frac{27+5}{63}\\ & =& \frac{32}{63}\end{array}$

Hence, $\left(\frac{3}{7}\right)+\left(\frac{-2}{21}\right)\times \left(\frac{-5}{6}\right)=\frac{32}{63}$.