Solve Division with Mixed Numbers: 492 ÷ (20½ × 4)

To solve this mathematical problem, let's follow a structured approach:

Step 1: Convert the Mixed Number to an Improper Fraction

The first part of the problem is to convert $20\frac{1}{2}$ into an improper fraction. To do this, follow the standard conversion method:

• Multiply the denominator of the fractional part by the integer part. Here, $2 \times 20 = 40$.
• Add the numerator of the fractional part. So, $40 + 1 = 41$.
• This results in the improper fraction $\frac{41}{2}$.

Step 2: Perform the Multiplication

Next, we need to multiply the improper fraction $\frac{41}{2}$ by 4. Treat 4 as a fraction $\frac{4}{1}$, and multiply:

• Numerator: $41 \times 4 = 164$.
• Denominator: $2 \times 1 = 2$.
• The result of the multiplication is $\frac{164}{2}$.

Next, simplify the fraction $\frac{164}{2}$ to find the product:

• $\frac{164}{2} = 82$.

Step 3: Perform the Division

Finally, divide 492 by the result from step 2:

• $492 \div 82 = 6$.

Thus, the final result of the given expression $492: (20\frac{1}{2} \times 4)$ is $\boxed{6}$.