0.6m+\frac{1}{3}=18\frac{1}{3}

Explanation:

Step1: Convert decimal to fraction

$0.6m=\frac{6}{10}m=\frac{3}{5}m$, and rewrite the equation as $\frac{3}{5}m+\frac{1}{3}=18\frac{1}{3}$. Convert the mixed - number $18\frac{1}{3}$ to an improper fraction: $18\frac{1}{3}=\frac{18\times3 + 1}{3}=\frac{55}{3}$. So the equation becomes $\frac{3}{5}m+\frac{1}{3}=\frac{55}{3}$.

Step2: Subtract $\frac{1}{3}$ from both sides

$\frac{3}{5}m+\frac{1}{3}-\frac{1}{3}=\frac{55}{3}-\frac{1}{3}$. $\frac{3}{5}m=\frac{55 - 1}{3}=\frac{54}{3}=18$.

Step3: Solve for $m$

Multiply both sides by $\frac{5}{3}$ (the reciprocal of $\frac{3}{5}$) to isolate $m$. $m = 18\times\frac{5}{3}$. $m=\frac{18\times5}{3}=30$.

Answer:

$m = 30$