1 6/7 * 3 5/10 = ?

Let's solve the expression step by step:

1. First, convert the mixed numbers to improper fractions:
$$1\frac{6}{7} = \frac{1 \times 7 + 6}{7} = \frac{7 + 6}{7} = \frac{13}{7}$$
$$3\frac{5}{10} = \frac{3 \times 10 + 5}{10} = \frac{30 + 5}{10} = \frac{35}{10}$$

2. Now, multiply the two fractions:
$$\frac{13}{7} \times \frac{35}{10} = \frac{13 \times 35}{7 \times 10} = \frac{455}{70}$$

3. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 35:
$$\frac{455}{70} = \frac{455 \div 35}{70 \div 35} = \frac{13}{2}$$

4. Convert the improper fraction $$\frac{13}{2}$$ to a mixed number:
$$\frac{13}{2} = 6\frac{1}{2}$$

So, the result of the expression is:
$$1\frac{6}{7} \times 3\frac{5}{10} = 6\frac{1}{2}$$

Answer: 6 1/2