Problem 23 - Elementary Algebra

Question

Calculate the product of 3 and -8 divided by -2 .

Step-by-Step Solution

Answer

The result is 12.

Step 1: Calculate the Product

First, we need to find the product of \(3\) and \(-8\). Multiply these two numbers: \(3 \times (-8) = -24\).

Step 2: Divide the Product

Next, we take the product from Step 1, which is \(-24\), and divide it by \(-2\). So, \(-24 \div (-2) = 12\).

Key Concepts

Understanding Multiplication

Multiplication is one of the four basic arithmetic operations. It provides a method for calculating the total of one number taken multiple times. In our exercise, we multiplied 3 by -8. To simply put it: when you multiply two numbers, you're adding the number on the left the number of times stated by the number on the right. For example, multiplying 3 by 4 (3 × 4) means you add 3 four times (3 + 3 + 3 + 3 = 12).

• When both numbers are positive, the result is positive.
• When both numbers are negative, the result is positive.
• When only one number is negative, the result is negative.

In our case, since we have 3 (positive) and -8 (negative), the product is -24 because a positive multiplied by a negative gives a negative result.

The Process of Division

Division is essentially the process of determining how many times one number is contained within another. Think of it as distributing a number into equal parts. From our solution, we needed to divide -24 by -2.

• If both numbers are positive, the result is positive.
• If both numbers are negative, the result is positive because two negatives make a positive.
• If one number is positive and the other negative, the outcome is negative.

Here, since -24 and -2 are both negative, when you divide them (\(-24 \div (-2)\)), you get 12, which is a positive number. This is because dividing two negatives results in a positive.

Working with Negative Numbers

Negative numbers are numbers less than zero and are typically represented by a minus sign. They appear in calculations involving values like debt, temperature below zero, or elevation below sea level. When working with negative numbers:

• Adding a negative is like subtracting its positive counterpart.
• Subtracting a negative is like adding its positive counterpart.
• Multiplying or dividing two negatives yields a positive.
• Multiplying or dividing a positive with a negative yields a negative.

In our exercise, understanding the behavior of negative numbers helped us solve the multiplication and division correctly. Knowing these rules ensures accurate solutions in arithmetic operations involving negatives.