1. The problem is to find the sum of $\frac{3}{4} + \frac{1}{10}$.\n\n2. To add fractions, we need a common denominator. The denominators are 4 and 10. The least common denominator (LCD) is the least common multiple of 4 and 10, which is 20.\n\n3. Convert each fraction to an equivalent fraction with denominator 20:\n$$\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}$$\n$$\frac{1}{10} = \frac{1 \times 2}{10 \times 2} = \frac{2}{20}$$\n\n4. Now add the fractions with the common denominator:\n$$\frac{15}{20} + \frac{2}{20} = \frac{15 + 2}{20} = \frac{17}{20}$$\n\n5. The sum of $\frac{3}{4} + \frac{1}{10}$ is $\frac{17}{20}$.\n\nFinal answer: $\frac{17}{20}$