Question

Using appropriate properties find:$\frac{2}{5}\times \left(\frac{-3}{7}\right)-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}$

Answer 1

Solving $\frac{2}{5}\times \left(\frac{-3}{7}\right)-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}$

By commutativity

Commutative property – As per the commutative property or commutative law, when two numbers are added or multiplied together, then change in their positions does not change the result.

$\Rightarrow \frac{2}{5}\times \left(\frac{-3}{7}\right)+\frac{1}{14}\times \frac{2}{5}-\frac{1}{6}\times \frac{3}{2}$

By distributivity

Distributive Property – The distributive property of multiplication lets you simplify expressions wherein you multiply a number by a sum or difference. According to this property, the product of a sum or difference of a number is equal to the sum or difference of the products.

$$\begin{gathered} \Rightarrow \frac{2}{5}(\frac{-3}{7}+\frac{1}{14})-\frac{1}{6}\times \frac{3}{2} \\ \Rightarrow \frac{2}{5}\left[\frac{(-6+1)}{14}\right]-\frac{1}{4} \end{gathered}$$

$\Rightarrow \frac{2}{5}[\frac{(–5)}{14}]-\frac{1}{4}$

$$\begin{gathered} \Rightarrow \frac{-10}{70}-\frac{1}{4} \\ \Rightarrow \frac{-1}{7}-\frac{1}{4} \\ \Rightarrow \frac{(-4-7)}{28} \\ \Rightarrow \frac{-11}{28} \end{gathered}$$

Hence, $\frac{2}{5}\times \left(\frac{-3}{7}\right)-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}=\frac{-11}{28}$.