- The product of a positive number and a negative number is calculated by multiplying their absolute values and applying a negative sign.
- The absolute values are \(|9| = 9\) and \(|-9| = 9\), so their product is \(81\).
- Applying the negative sign gives \(-81\).
- The final answer is \(\boxed{-81}\).
Explanation
- Analysis of the Problem
We are given the expression \(9(-9)\). This requires finding the product of a positive integer \(9\) and a negative integer \(-9\). The multiplication rule for numbers with different signs states that the product is negative. Therefore, we calculate the product of their absolute values and then apply a negative sign to the result.
- Calculating the Product
The absolute value of \(9\) is \(|9| = 9\) and the absolute value of \(-9\) is \(|-9| = 9\). We multiply these absolute values:
\[9 \times 9 = 81.\]
Since the original numbers have opposite signs, their product must be negative:
\[9(-9) = -(9 \times 9) = -81.\]
Examples
In real life, if you lose \$9 on nine separate occasions, your total financial change can be represented by the multiplication \(9 \times (-9)\). In this case, you have lost a total of \(\$81\), which is expressed as \(-\$81\). Understanding how to handle negative numbers is essential for tracking debts, temperature drops, or any scenario involving loss and decrease.