Problem 13 - Beginning and Intermediate Algebra

Question

Find each product. \(-5(-6)\)

Step-by-Step Solution

Answer

The product is 30.

Step 1 - Understand the problem

Identify that the problem is asking to find the product of (-5) and (-6). This means we need to multiply these two negative numbers.

Step 2 - Multiply the absolute values

First, ignore the signs and just multiply the absolute values of the numbers. The absolute value of -5 is 5 and the absolute value of -6 is 6. So, multiply 5 and 6 to get 30.

Step 3 - Determine the sign of the product

When multiplying two negative numbers, the product is positive. Therefore, the product of (-5) and (-6) is positive 30.

Key Concepts

absolute value

Understanding the concept of absolute value is crucial when working with negative numbers. The absolute value of a number is its distance from 0 on a number line, regardless of direction. For instance, the absolute value of both 5 and -5 is 5.

In other words, when you see the absolute value, you are considering the number's magnitude without worrying about its sign. For the given problem \(-5(-6)\), we first find the absolute values:

• The absolute value of -5 is 5
• The absolute value of -6 is 6

Knowing this helps us to focus on the actual multiplication first, ignoring the negative signs temporarily.

product of numbers

The product of numbers refers to the result you get when you multiply them together. Multiplication is a fundamental arithmetic operation that combines quantities.

When finding the product of \(-5(-6)\), you ignore the negative signs momentarily and focus on multiplying the absolute values of the numbers first. In this case:

• Multiply the absolute value of -5, which is 5
• By the absolute value of -6, which is 6

So, 5 multiplied by 6 equals 30.

After finding the product of the absolute values, the next step is to determine the sign of the final result.

negative and positive signs

Understanding how negative and positive signs affect multiplication is essential for solving problems like \(-5(-6)\). Here's a quick rule to remember:

• When multiplying two numbers with the same sign (both positive or both negative), the product is positive.
• When multiplying two numbers with different signs (one positive and one negative), the product is negative.

In this problem, both numbers we are multiplying are negative (-5 and -6). Therefore, according to the rule, the product of two negative numbers is positive. So, the product of \(-5(-6)\) is positive 30.

This rule is essentially rooted in the way integers behave under multiplication and helps ensure you get the correct sign for the product.