Question

Using appropriate properties find:$-\frac{2}{3}\times \frac{3}{5}+\frac{5}{2}–\frac{3}{5}\times \frac{1}{6}$

Answer 1

To find : $-\frac{2}{3}\times \frac{3}{5}+\frac{5}{2}–\frac{3}{5}\times \frac{1}{6}$

By commutativity

$\Rightarrow \frac{-2}{3}\times \frac{3}{5}–\frac{3}{5}\times \frac{1}{6}+\frac{5}{2}$

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.

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

By distributive rule:

$\Rightarrow \frac{3}{5}[\frac{(–5)}{6}]+\frac{5}{2}$

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.

$$\begin{gathered} \Rightarrow \frac{-15}{30}+\frac{5}{2} \\ \Rightarrow \frac{-1}{2}+\frac{5}{2} \\ \Rightarrow \frac{(-1+5)}{2} \\ \Rightarrow \frac{4}{2} \\ =2 \end{gathered}$$

Hence, $-\frac{2}{3}\times \frac{3}{5}+\frac{5}{2}–\frac{3}{5}\times \frac{1}{6}=2$