1. The problem asks to convert the mixed number $3 \frac{5}{6}$ into an improper fraction. 2. Recall that a mixed number $a \frac{b}{c}$ can be converted to an improper fraction using the formula: $$\text{Improper fraction} = \frac{a \times c + b}{c}$$ 3. Here, $a=3$, $b=5$, and $c=6$. Substitute these values: $$\frac{3 \times 6 + 5}{6}$$ 4. Calculate the numerator: $$3 \times 6 = 18$$ $$18 + 5 = 23$$ 5. So the improper fraction is: $$\frac{23}{6}$$ 6. This fraction is greater than one, as the numerator is larger than the denominator. 7. Therefore, Charlie uses $\frac{23}{6}$ cups of onions in the recipe.