Question

Using appropriate properties, find:

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

ii) $\frac{2}{5}\times \left(\begin{array}{c}-\frac{3}{7}\end{array}\right)-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}$

• A. $2;\frac{-11}{28}$
• B. $3;\frac{-12}{29}$
• C. $2;\frac{3}{10}$
• D. $4;-3$

Answer 1

The correct option is A $2;\frac{-11}{28}$

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 ]

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

$=\left(\begin{array}{c}-\frac{3}{5}\end{array}\right)\times \left(\begin{array}{c}\frac{2}{3}+\frac{1}{6}\end{array}\right)+\frac{5}{2}$ [Using Distributive Property]

$=\left(\begin{array}{c}-\frac{3}{5}\end{array}\right)\times \left(\frac{4+1}{6}\right)+\frac{5}{2}$

$=-\frac{3}{5}\times \frac{5}{6}+\frac{5}{2}$

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

$=\frac{-1+5}{2}=\frac{4}{2}=2$.

ii) $\frac{2}{5}\times \left(\begin{array}{c}-\frac{3}{7}\end{array}\right)-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}$

$=\frac{2}{5}\times \left(\begin{array}{c}-\frac{3}{7}\end{array}\right)+\frac{1}{14}\times \frac{2}{5}-\frac{1}{6}\times \frac{3}{2}$ [Using Commutative property ]

$=\frac{2}{5}\times \left(\begin{array}{c}-\frac{3}{7}\end{array}\right)+\frac{2}{5}\times \frac{1}{14}-\frac{1}{6}\times \frac{3}{2}$

$=\frac{2}{5}\times \left[\begin{array}{c}\left(\begin{array}{c}-\frac{3}{7}\end{array}\right)+\frac{1}{14}\end{array}\right]-\frac{1}{6}\times \frac{3}{2}$ [Using Distributive Property]

$=\frac{2}{5}\times \left(\begin{array}{c}\frac{-6+1}{14}\end{array}\right)-\frac{3}{12}$

$=\frac{2}{5}\times \frac{-5}{14}-\frac{1}{4}=\frac{-1}{7}-\frac{1}{4}$

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