Question

solve 3/8 + (-1/5) - 5/8 + 3/10 using appropriate property​

Answer 1

Answer:

$\begin{aligned} -\frac{2}{3} \times \frac{3}{5}+\frac{5}{2}-\frac{3}{5} \times \frac{1}{6} & \\ =-\frac{2}{3} \times \frac{3}{5}-\frac{3}{5} \times \frac{1}{6}+\frac{5}{2} & \text { (by commutativity) } \end{aligned}$

$\begin{array}{l} =\frac{3}{5}\left(\frac{-2}{3}-\frac{1}{6}\right)+\frac{5}{2} \\ =\frac{3}{5}\left(\frac{-4-1}{6}\right)+\frac{5}{2} \\ =\frac{3}{5}\left(\frac{-5}{6}\right)+\frac{5}{2} \\ =\frac{-15}{30}+\frac{5}{2} \\ =\frac{-1}{2}+\frac{5}{2} \\ =\frac{4}{2} \\ =2 \end{array}$

(ii)

$\begin{array}{c} \frac{2}{5} \times\left(-\frac{3}{7}\right)-\frac{1}{6} \times \frac{3}{2}+\frac{1}{14} \times \frac{2}{5} \\ =\frac{2}{5} \times\left(-\frac{3}{7}\right)-\frac{1}{6} \times \frac{3}{2}+\frac{1}{14} \times \frac{2}{5} \\ =\frac{2}{5} \times\left(-\frac{3}{7}\right)+\frac{1}{14} \times \frac{2}{5}-\left(\frac{1}{6} \times \frac{3}{2}\right) \text { (by commutativity) } \end{array}</p><p>$

$</p><p>\begin{array}{l} =\frac{2}{5} \times\left(-\frac{3}{7}+\frac{1}{14}\right)-\frac{3}{12} \\ =\frac{2}{5} \times\left(\frac{-6+1}{14}\right)-\frac{1}{4} \\ =\frac{2}{5} \times\left(\frac{-6+1}{14}\right)-\frac{1}{4} \\ =\frac{2}{5} \times\left(\frac{-5}{14}\right)-\frac{1}{4} \\ =\frac{2}{5} \times\left(\frac{-5}{14}\right)-\frac{1}{4} \\ =\left(\frac{-10}{70}\right)-\frac{1}{4} \\ =\frac{-1}{7}-\frac{1}{4} \\ =\frac{-4-7}{28} \end{array}$

$\huge\pink{\textsf{MichRUHI}}$