Verified Answer :

  • The division of a negative number by a positive number, \(-24 \div 8\), yields \(-3\).
  • The product of two negative numbers, \(-2 \times (-7)\), yields \(14\).
  • The final answers are \(\boxed{-3}\) and \(\boxed{14}\).

Explanation

  1. Analyzing the Problem

We are asked to evaluate two mathematical expressions involving integers: \(-24 \div 8\) and \(-2 \times (-7)\). The first expression is a division of a negative number by a positive number, while the second expression is a multiplication of two negative numbers. We will follow standard arithmetic rules for signs.

  1. Evaluating the First Expression

For the expression \(-24 \div 8\), we note that when dividing a negative number by a positive number, the result is negative. We divide the absolute values: \(| -24 | \div | 8 | = 24 \div 8 = 3\). Applying the negative sign gives \(-3\). So, \(-24 \div 8 = -3\).

  1. Evaluating the Second Expression

For the expression \(-2 \times (-7)\), we note that when multiplying two negative numbers, the result is positive. We multiply the absolute values: \(| -2 | \times | -7 | = 2 \times 7 = 14\). Thus, \(-2 \times (-7) = 14\).

  1. Conclusion

Based on our analysis, we have evaluated both expressions:

  • \(-24 \div 8 = -3\)
  • \(-2 \times (-7) = 14\)

The final results are \(-3\) and \(14\).

Examples

In everyday life, these basic operations are useful for managing budgets. For example, if you have a debt of \$24 spread over 8 payments, your monthly change is @@MATH_TOKEN_19@@ dollars. Conversely, if you have two charges of \$7 each canceled (e.g., refunds), the total effect is \(-2 \times (-7) = 14\) dollars added back to your balance. Mastering signs is crucial for tracking financial transactions correctly.

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