To multiply the mixed numbers \(6 \frac{7}{10}\) and \(14 \frac{2}{7}\), we first need to convert them to improper fractions.

1. Convert \(6 \frac{7}{10}\):
   \[
   6 \frac{7}{10} = \frac{6 \times 10 + 7}{10} = \frac{60 + 7}{10} = \frac{67}{10}
   \]

2. Convert \(14 \frac{2}{7}\):
   \[
   14 \frac{2}{7} = \frac{14 \times 7 + 2}{7} = \frac{98 + 2}{7} = \frac{100}{7}
   \]

Now, multiply the two improper fractions:
\[
\frac{67}{10} \times \frac{100}{7}
\]

Multiply the numerators and denominators:
\[
\frac{67 \times 100}{10 \times 7} = \frac{6700}{70}
\]

Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor (GCD), which is 10:
\[
\frac{6700 \div 10}{70 \div 10} = \frac{670}{7}
\]

Convert the improper fraction back to a mixed number:
\[
670 \div 7 = 95 \quad \text{remainder} \quad 5
\]

Thus:
\[
\frac{670}{7} = 95 \frac{5}{7}
\]

So, \(6 \frac{7}{10} \times 14 \frac{2}{7} = 95 \frac{5}{7}\).

Would you like more details or have any questions?

Here are some related questions to expand on this topic:
1. How do you convert a mixed number to an improper fraction?
2. What is the process for multiplying two fractions?
3. How do you simplify a fraction?
4. What is the method for converting an improper fraction back to a mixed number?
5. Can you multiply mixed numbers directly without converting to improper fractions?

**Tip:** Always simplify fractions whenever possible to make calculations easier and results clearer.

Learn how to multiply the mixed numbers 6 7/10 and 14 2/7 by converting them to improper fractions, performing the multiplication, and simplifying the result. This problem involves converting between mixed and improper fractions, multiplying fractions, and simplifying results. Suitable for students in Grades 6-8.

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