Question

Which expression is equivalent to 2f-1/3(2g-3f)-1/3g?

Answer 1

The given expression is :

$2f-\frac{1}{3}(2g-3f)-\frac{1}{3}g$

Simplify by the BODMAS rule

B-Brackets, O- Of, D-Division, M-Multiplication, A-Add & S - SUbtract

Step 1 : Open the brackets

$2f-\frac{1}{3}(2g-3f)-\frac{1}{3}g=2f-\frac{2}{3}g+\frac{3}{3}f-\frac{1}{3}g$

Step 2 : Simplify the similar term together

$\begin{gathered} 2f-\frac{1}{3}(2g-3f)-\frac{1}{3}g=2f+\frac{3}{3}f-\frac{1}{3}g-\frac{2}{3}g \\ 2f-\frac{1}{3}(2g-3f)-\frac{1}{3}g=2f+f-\frac{1}{3}g-\frac{2}{3}g \\ 2f-\frac{1}{3}(2g-3f)-\frac{1}{3}g=f(2+1)-g(\frac{1}{3}+\frac{2}{3}) \\ 2f-\frac{1}{3}(2g-3f)-\frac{1}{3}g=f(3)-g(\frac{3}{3}) \\ 2f-\frac{1}{3}(2g-3f)-\frac{1}{3}g=f(3)-g(1) \\ 2f-\frac{1}{3}(2g-3f)-\frac{1}{3}g=3f-g \end{gathered}$

Answer : A) 3f - g