Question

Solve the following expression:
$\frac{3}{5}$ × -$\frac{1}{2}$ - $\frac{3}{7}$ + $\frac{1}{14}$ × $\frac{3}{5}$

• A. 27/35
• B. -9/7
• C. 15/21
• D. -24/35

Answer 1

The correct option is D -24/35

Given: $\frac{3}{5}$ × -$\frac{1}{2}$ - $\frac{3}{7}$ + $\frac{1}{14}$ × $\frac{3}{5}$

Firstly, let's group the like rational terms together,

$\frac{3}{5}$ × -$\frac{1}{2}$ + $\frac{1}{14}$ × $\frac{3}{5}$ - $\frac{3}{7}$

= $\frac{3}{5}$ × [-$\frac{1}{2}$ + $\frac{1}{14}$] -$\frac{3}{7}$

= $\frac{3}{5}$ × [ $\frac{-7+1}{14}$] - $\frac{3}{7}$

= $\frac{3}{5}$ × [ $\frac{-6}{14}$] - $\frac{3}{7}$

= $\frac{3}{5}$ × [$\frac{-3}{7}$] - $\frac{3}{7}$

= -$\frac{9}{35}$ - $\frac{3}{7}$

= $\frac{-9-15}{35}$

= - $\frac{24}{35}$

Therefore, option (d) is the correct answer.