To solve \( \frac{10 \times 21}{\frac{5}{7}} \), we follow these steps:

### Step 1: Multiply 10 by 21
\[
10 \times 21 = 210
\]

### Step 2: Divide by \( \frac{5}{7} \)
Dividing by a fraction is the same as multiplying by its reciprocal. So, instead of dividing by \( \frac{5}{7} \), we multiply by \( \frac{7}{5} \):
\[
210 \div \frac{5}{7} = 210 \times \frac{7}{5}
\]

### Step 3: Multiply and simplify
\[
210 \times \frac{7}{5} = \frac{210 \times 7}{5} = \frac{1470}{5} = 294
\]

Thus, the answer is \( 294 \).

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### Related Questions:
1. How do you multiply and divide fractions?
2. What is the method for simplifying complex fractions?
3. Can you explain why dividing by a fraction is the same as multiplying by its reciprocal?
4. How does changing the order of operations affect the result in a complex division problem?
5. What are some practical examples of dividing by fractions?

**Tip:** When dividing by a fraction, always multiply by its reciprocal to simplify calculations.

Learn how to solve the math problem '10 times 21 divided by 5/7' with a detailed solution. This problem involves multiplication, division by fractions, and the reciprocal theorem, making it suitable for students in Grades 6-8.

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