Verified Answer :

  • Identify that the product involves two negative numbers, which will result in a positive value.
  • Determine the absolute values of the numbers: \(|-11| = 11\) and \(|-30| = 30\).
  • Multiply the absolute values: \(11 \times 30 = 330\).
  • Conclude that the product is positive: \((-11) \times (-30) = \boxed{330}\).

Explanation

  1. Understanding the Operation

The problem asks for the product of two negative integers, \(-11\) and \(-30\). We are dealing with an expression of the form \((-a) \times (-b)\), where \(a = 11\) and \(b = 30\). In mathematics, when we multiply two negative numbers, the result is always a positive number. This is because the operation effectively negates the magnitude of the product of their absolute values.

  1. Calculating the Product

To find the product of \(-11\) and \(-30\), we first find the product of their absolute values:
\[|-11| \times |-30| = 11 \times 30\]
To compute \(11 \times 30\), we can observe that \(11 \times 3 = 33\), and then multiply by \(10\):
\[11 \times 30 = 330\]
Since the product of two negative numbers is positive, the result is positive \(330\).

  1. Final Result

Combining these steps, we see that the product of the two negative integers is:
\[(-11) \times (-30) = 330\]
Thus, the final answer is \(\boxed{330}\).

Examples

Imagine a bank account where a specific recurring deduction of \$11 is cancelled for 30 months. If you had previously accounted for these deductions as negative changes (representing a decrease in balance), cancelling a "negative" deduction for 30 months actually results in a "positive" gain of \$330 back into your account. Multiplication of negative numbers helps us understand how removing debt or reversing negative trends leads to a positive outcome.

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