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Let's work out the problem step by step.

### Problem:
\[
3 \frac{2}{7} \times \frac{1}{10}
\]

### Step 1: Convert the mixed fraction to an improper fraction.
To convert \(3 \frac{2}{7}\) to an improper fraction, use the following rule:
\[
\text{Improper fraction} = \left( \text{Whole number} \times \text{Denominator} + \text{Numerator} \right) \div \text{Denominator}
\]
For \(3 \frac{2}{7}\):
\[
3 \frac{2}{7} = \frac{(3 \times 7) + 2}{7} = \frac{21 + 2}{7} = \frac{23}{7}
\]

### Step 2: Perform the multiplication.
Now, multiply \(\frac{23}{7}\) by \(\frac{1}{10}\):
\[
\frac{23}{7} \times \frac{1}{10} = \frac{23 \times 1}{7 \times 10} = \frac{23}{70}
\]

### Step 3: Simplify the fraction.
The fraction \(\frac{23}{70}\) is already in its simplest form because 23 and 70 have no common factors other than 1.

### Final Answer:
\[
\frac{23}{70}
\]

Would you like more details on any part of this? Here are some related questions to explore further:

1. How do you convert between mixed fractions and improper fractions?
2. Why is it important to simplify fractions?
3. Can improper fractions always be converted back to mixed numbers?
4. How do you multiply two fractions together?
5. What are the rules for finding the least common denominator?

**Tip:** Always double-check if your fraction can be simplified by finding the greatest common divisor (GCD) of the numerator and denominator.

Work out 3 2/7 × 1/10. Give your answer as a fraction in its simplest form.

Learn how to solve the multiplication of a mixed number and a fraction with the example 3 2/7 × 1/10. This problem covers key concepts such as converting mixed numbers to improper fractions, multiplying fractions, and simplifying the result. Suitable for students in Grades 6-8.

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