Problem 33 - Fundamentals of Mathematics

Question

Determine each of the values. $$ |-(2 \cdot 3)| $$

Step-by-Step Solution

Answer

The value is 6.

Step 1: Solve the Expression Inside the Absolute Value

To determine the value of \[| -(2 \cdot 3) | \]first, solve the expression inside the parentheses. Multiply 2 and 3 to get:\[2 \cdot 3 = 6\]

Step 2: Apply the Negative Sign

After calculating the value inside the parentheses, apply the negative sign:\[-(6) = -6\]

Step 3: Take the Absolute Value

Now, take the absolute value of -6. Remember that the absolute value of a number is its distance from 0 on a number line, which is always positive.Hence, \[|-6| = 6\]

Key Concepts

Integer Operations

Integer operations involve various mathematical calculations using whole numbers, which can be either positive, negative, or zero. In the context of our exercise, we leverage the basic operations, particularly multiplication and negation.

• Negation: This operation changes the sign of a number. For example, the negation of a positive number becomes negative and vice versa.
• Multiplication: Here, two numbers are multiplied to get a product. In our problem, we multiply 2 and 3 to get the product of 6.

Understanding these operations allows us to combine numbers in different ways to solve more complex problems effectively.

Number Line

A number line is a visual representation of numbers laid out in a straight line. This concept is crucial for understanding absolute value and operations involving integers. Every point on the number line corresponds to a number.

• The center of the number line is zero.
• Numbers to the right of zero are positive, while numbers to the left are negative.
• Absolute value is the distance a number is from zero, regardless of its direction on the number line.

In the exercise, finding \(|-6|\) involves locating -6 on the number line and determining its distance from zero, which is 6.

Multiplication

Multiplication is an arithmetic operation where we find the total of one number added repeatedly as many times as the other number indicates. In our exercise, multiplication is used to simplify the expression inside the absolute value.

Let's look at how multiplication works:

• Identify the two numbers to be multiplied: In our example, we have 2 and 3.
• Calculation: Multiply these numbers to find the product. Here, 2 times 3 equals 6.
• The result: is used for further calculations such as negation or finding the absolute value.

Multiplying accurately lays the foundation for handling more advanced mathematical tasks and ensures our solutions are precise, guiding us through to the final result.