What is the product of (-5)(7)?

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notgoodjay223 notgoodjay223

04-11-2026
Mathematics

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What is the product of (-5)(7)?

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-04T15:52:37-05:00

Identify the factors in the product: \(-5\) and \(7\).
Recognize that the product of a negative number and a positive number is negative.
Calculate the product of the absolute values, \(| -5 | \times | 7 | = 35\), and negate it to get \(-35\).
Final Answer: \(\boxed{-35}\).

Explanation

Analysis of the Product Calculation

The problem asks us to determine the product of \(-5\) and \(7\), and confirms that the result is \(-35\). To solve this, we rely on the fundamental rules of integer multiplication, specifically those involving numbers with different signs. Multiplying two numbers with opposite signs results in a negative product. Therefore, we first find the product of their absolute values and then apply the negative sign to the result.

Execution of the Multiplication

To calculate the product, we take the absolute value of each integer: \(\lvert -5 \rvert = 5\) and \(\lvert 7 \rvert = 7\). Next, we find the product of these absolute values: \(5 \times 7 = 35\). Applying the rule for signs, where a negative number multiplied by a positive number yields a negative result, we arrive at the final value: \(- (5 \times 7) = -35\). This confirms the equality stated in the problem: \((-5)(7) = -35\).

Examples

In real-life scenarios, multiplication of signed integers is essential for tracking changes. For example, if a company loses 5 dollars per hour (represented as -5) and operates for 7 hours, the total change in their balance over those 7 hours would be \(-5 \times 7 = -35\) dollars. This helps in understanding debts, temperature drops, or any situation involving a consistent negative change over time.