NCERT Solutions Class 8 Mathematics Solutions for Exercise 1.1 in Chapter 1 - Rational Numbers

Question 28 Exercise 1.1

Using appropriate properties find the value of $-\frac{2}{3}\times\frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times\frac{1}{6}$

Answer:

$\begin{aligned} &-\frac{2}{3} \times \frac{3}{5}+\frac{5}{2}-\frac{3}{5} \times \frac{1}{6}=-\frac{2}{3} \times \frac{3}{5}-\frac{3}{5} \times \frac{1}{6}+\frac{5}{2}\\ &\text { (Using commutativity of rational numbers) }\\ &=\left(-\frac{3}{5}\right) \times\left(\frac{2}{3}+\frac{1}{6}\right)+\frac{5}{2} \quad \text { (Distributivity) }\\ &=\left(-\frac{3}{5}\right) \times\left(\frac{2 \times 2+1}{6}\right)+\frac{5}{2}=\left(-\frac{3}{5}\right) \times\left(\frac{5}{6}\right)+\frac{5}{2}\\ &=\left(-\frac{3}{6}\right)+\frac{5}{2}=\left(\frac{-3+5 \times 3}{6}\right)=\left(\frac{-3+15}{6}\right)\\ &=\frac{12}{6}=2 \end{aligned}$

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