Question

Simplify the expression: $\frac{1}{2}a-\frac{2}{3}b-4c+\frac{2}{3}a+2b-\frac{1}{2}c+5b-\frac{1}{3}a$

Answer 1

The given expression is: $\frac{1}{2}a-\frac{2}{3}b-4c+\frac{2}{3}a+2b-\frac{1}{2}c+5b-\frac{1}{3}a$

Simplifying the expression:

To simplify an expression, all the like terms to be grouped and added.

So, the given expression $\frac{1}{2}a-\frac{2}{3}b-4c+\frac{2}{3}a+2b-\frac{1}{2}c+5b-\frac{1}{3}a$ can be written as:

$=(\frac{1}{2}a+\frac{2}{3}a-\frac{1}{3}a)+(-\frac{2}{3}b+2b+5b)+(-\frac{1}{2}c-4c)$

$=$$\left(\frac{3a+4a-2a}{6}\right)+\left(\frac{-2b+6b+15b}{3}\right)+\left(\frac{-c-8c}{2}\right)$

$=$$\frac{5a}{6}+\frac{19b}{3}-\frac{9c}{2}$

$=$$\frac{5a+76b-54c}{12}$

Therefore, the simplified expression is .