Question

Remove the brackets and simplify: $\frac{1}{2}(a-3b)-\frac{2}{3}(\frac{1}{4}a-\frac{4}{3}b)$

Answer 1

SImplifying the algebraic expression

Simplification rule: If there is a $"-"$ sign before a bracket, then the signs of all the terms inside the bracket changes but if there is a $“+”$ sign before the bracket, then no change of signs.

$\begin{array}{rcl}\frac{1}{2}(a-3b)-\frac{2}{3}(\frac{1}{4}a-\frac{4}{3}b)& =& \frac{a}{2}-\frac{3b}{2}-\frac{2a}{12}+\frac{8b}{9}\\ & =& \frac{a}{2}-\frac{2a}{12}+\frac{8b}{9}-\frac{3b}{2}\\ & =& \frac{6a-2a}{12}+\frac{16b-27b}{18}\\ & =& \frac{4a}{12}-\frac{11b}{18}\\ & =& \frac{a}{3}-\frac{11b}{18}\end{array}$

Therefore, the simplified result is $\frac{a}{3}-\frac{11b}{18}$.