1. **State the problem:** We need to find by how much the sum of $3\frac{1}{2}$ and $2\frac{3}{4}$ is less than 7. 2. **Convert mixed numbers to improper fractions:** - $3\frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2}$ - $2\frac{3}{4} = 2 + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4}$ 3. **Find the sum:** $$\frac{7}{2} + \frac{11}{4} = \frac{14}{4} + \frac{11}{4} = \frac{25}{4}$$ 4. **Convert sum to decimal or mixed number:** $$\frac{25}{4} = 6\frac{1}{4} = 6.25$$ 5. **Calculate how much less than 7:** $$7 - 6.25 = 0.75$$ **Final answer:** The sum is $0.75$ less than 7.