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Chapter 0: Problem 65

Find each product. $$ -8(-5) $$

Short Answer

Expert verified
40

Step by step solution

01

Identify the Numbers

The exercise asks to find the product of two numbers: \(-8\) and \(-5\).
02

Apply the Multiplication Rule for Negatives

Recall that the product of two negative numbers is a positive number. Therefore, multiplying \(-8\) and \(-5\) will result in a positive product.
03

Multiply the Absolute Values

Calculate the product of the absolute values of the numbers: \(8 \times 5 = 40\).
04

Assign the Correct Sign

Since both numbers were negative, the product is positive. Therefore, the product of \(-8\) and \(-5\) is \(+40\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Absolute Value
When dealing with negative numbers, it's useful to understand the concept of absolute value. The absolute value of a number is its distance from zero on the number line, regardless of direction. For example, the absolute values of \(-8\) and \(-5\) are 8 and 5 respectively. Absolute value helps simplify the calculation by removing the negative signs before the multiplication process. In this exercise, we took the absolute value of both numbers: \(8\) and \(5\).
Product
The product in mathematics refers to the result of multiplying two or more numbers together. To find the product of \(-8\) and \(-5\), we start by ignoring the signs and multiplying the absolute values of the numbers. This gives us \(8 \times 5 = 40\). After calculating the magnitude (absolute value), we consider the signs to determine the final product's sign.
Multiplication Rules
Understanding multiplication rules is crucial, especially when dealing with negative numbers:
  • When you multiply two positive numbers, the product is positive.
  • When you multiply a positive number by a negative number, the product is negative.
  • When you multiply two negative numbers, the product is positive because the negatives cancel each other out.
In our example, multiplying \(-8\) by \(-5\) follows the rule that two negatives make a positive, hence the result is \(+40\).
Always remember, these rules help determine the sign of the product after you multiply the absolute values of the numbers.

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