Show step by step on solving 24π ÷ 3π/8

To solve the expression \( 24\pi \div \frac{3\pi}{8} \), follow these steps:

### Step 1: Write down the expression.
\[
24\pi \div \frac{3\pi}{8}
\]

### Step 2: Convert the division into multiplication by the reciprocal.
When dividing by a fraction, multiply by its reciprocal. The reciprocal of \(\frac{3\pi}{8}\) is \(\frac{8}{3\pi}\).
\[
24\pi \times \frac{8}{3\pi}
\]

### Step 3: Multiply the numerators and denominators.
\[
\frac{24\pi \times 8}{3\pi}
\]

### Step 4: Simplify the expression.
Notice that \(\pi\) appears in both the numerator and denominator, so it can be canceled out.
\[
\frac{24 \times 8}{3} = \frac{192}{3}
\]

### Step 5: Perform the division.
\[
\frac{192}{3} = 64
\]

### Final Answer:
\[
24\pi \div \frac{3\pi}{8} = 64
\]

Would you like any further details or have any questions?

### Related Questions:
1. How do you multiply and divide fractions?
2. What happens when dividing terms with the same variable or constant?
3. How can you simplify complex expressions with multiple fractions?
4. How do you handle operations involving \(\pi\) in expressions?
5. What are some common mistakes to avoid when solving fraction division?

### Tip:
Always look for common factors that can be canceled out early in the process to simplify calculations.

Learn how to solve the expression 24π ÷ 3π/8 step-by-step with a detailed mathematical solution. This problem involves division of fractions, multiplication by reciprocals, and cancellation of terms involving π. Suitable for students in Grades 7-9.

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