- Perform the multiplication of the two integers: \(13 \times 6 = 78\).
- Multiply the resulting product by the fraction \(\frac{1}{2}\): \(78 \times \frac{1}{2} = 39\).
- The final value is \(\boxed{39}\).
Explanation
- Problem Analysis
The problem requires calculating the value of the expression \(A = \frac{1}{2} \times 13 \times 6\). This is a straightforward multiplication of three factors. To simplify the expression, we can multiply the integers first and then multiply by the fraction.
- Step-by-Step Calculation
To compute \(A\), first perform the multiplication of the integers \(13\) and \(6\):
\[13 \times 6 = 78\]
Now, substitute this result back into the original expression for \(A\):
\[A = \frac{1}{2} \times 78\]
Finally, divide \(78\) by \(2\):
\[A = \frac{78}{2} = 39\]
Examples
This type of calculation is very common in everyday geometry, such as finding the area of a triangle, where the formula is \(\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}\). If a triangle has a base of 13 units and a height of 6 units, the area would be \(\frac{1}{2} \times 13 \times 6 = 39\) square units. Knowing how to multiply fractions and integers efficiently helps in various fields, from construction to design.