$1 \frac{3}{4} \div 2$

Step 1 ：Convert the mixed number $1 \frac{3}{4}$ to an improper fraction. The formula to convert a mixed number to an improper fraction is \(\text{whole number} \times \text{denominator} + \text{numerator}\). So, $1 \times 4 + 3 = 7$. Therefore, $1 \frac{3}{4}$ is equivalent to the improper fraction $\frac{7}{4}$.

Step 2 ：Next, divide the fractions by multiplying the first fraction by the reciprocal of the second fraction. The reciprocal of 2 is $\frac{1}{2}$. So, $\frac{7}{4} \times \frac{1}{2} = \frac{7}{8}$.

Step 3 ：Finally, convert the fraction $\frac{7}{8}$ to a decimal by dividing the numerator by the denominator. So, $7 \div 8 = 0.875$.

Step 4 ：\(\boxed{0.875}\) is the final answer.