1. The problem asks to rewrite the mixed number $1 \frac{1}{4}$ as an improper fraction. 2. A mixed number consists of a whole number and a fraction. To convert it to an improper fraction, multiply the whole number by the denominator of the fraction and add the numerator. 3. The formula is: $$\text{Improper fraction} = \frac{(\text{whole number} \times \text{denominator}) + \text{numerator}}{\text{denominator}}$$ 4. For $1 \frac{1}{4}$, the whole number is 1, the numerator is 1, and the denominator is 4. 5. Calculate the numerator of the improper fraction: $$1 \times 4 + 1 = 4 + 1 = 5$$ 6. So the improper fraction is: $$\frac{5}{4}$$ 7. Therefore, $1 \frac{1}{4}$ rewritten as an improper fraction is $\frac{5}{4}$.