1. The problem asks to convert the mixed number $4 \frac{3}{4}$ into an improper fraction, which is a fraction greater than one. 2. Recall the formula to convert a mixed number $a \frac{b}{c}$ to an improper fraction is: $$\text{Improper fraction} = \frac{a \times c + b}{c}$$ where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator. 3. For $4 \frac{3}{4}$, identify $a=4$, $b=3$, and $c=4$. 4. Substitute these values into the formula: $$\frac{4 \times 4 + 3}{4}$$ 5. Calculate the numerator: $$4 \times 4 = 16$$ $$16 + 3 = 19$$ 6. So the improper fraction is: $$\frac{19}{4}$$ 7. This fraction is greater than one because the numerator (19) is greater than the denominator (4). Final answer: $\boxed{\frac{19}{4}}$