Question

Using appropriate properties find:

(i) $-\frac{2}{3}\times \frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times \frac{1}{6}$

(ii) $\frac{2}{5}\times [-\frac{3}{7}]-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}$

Answer 1

(i) $-\frac{2}{3}\times \frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times \frac{1}{6}$

$=-\frac{2}{3}\times \frac{3}{5}-\frac{3}{5}\times \frac{1}{6}+\frac{5}{2}$ [Using commutative property of addition for rational numbers]

$=(-\frac{3}{5})\times (\frac{2}{3}+\frac{1}{6})+\frac{5}{2}$ [Using Distributive property of multiplication over addition for rational numbers]

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

$=(-\frac{3}{5})\times \left(\frac{5}{6}\right)+\frac{5}{2}$

$=(-\frac{1}{2})+\frac{5}{2}$

$=\left(\frac{-1+5}{2}\right)$

$=\frac{4}{2}=2$

(ii) $\frac{2}{5}\times [-\frac{3}{7}]-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}$

$=\frac{2}{5}\times (-\frac{3}{7})+\frac{1}{14}\times \frac{2}{5}-\frac{1}{6}\times \frac{3}{2}$ [Using commutative property of addition for rational numbers]]

$=\frac{2}{5}\times (-\frac{3}{7}+\frac{1}{14})-\frac{1}{4}$ [Using Distributive property of multiplication over addition for rational numbers]]

$=\frac{2}{5}\times \left(\frac{-3\times 2+1}{14}\right)-\frac{1}{4}$

$=\frac{2}{5}\times \left(\frac{-5}{14}\right)-\frac{1}{4}$

$=-\frac{1}{7}-\frac{1}{4}$

$=\frac{-4-7}{28}=\frac{-11}{28}$