Problem 22 - Elementary Algebra

Question

Determine each of the values, |-4|

Step-by-Step Solution

Answer

Answer: The absolute value of |-4| is 4.

Step 1: Identify the number inside the absolute value symbols

We have |-4|, and the number inside the absolute value symbols is -4.

Step 2: Determine the absolute value

Since the number inside the absolute value symbols is negative (-4), the absolute value of |-4| is the positive version of it, which is 4.

Step 3: Write the final answer

The absolute value of |-4| is 4.

Key Concepts

Numeric Expressions

In mathematics, a numeric expression is a combination of numbers and operational symbols that represent a particular value. This includes expressions like \(-4\), \(3 + 2\), or even just a single number like \(7\). Simplifying numeric expressions often entails performing operations such as addition, subtraction, multiplication, or division.

• An example of a numeric expression is \( -4 + 6 \).
• This expression can be simplified by performing the addition to yield \(2\).

By understanding numeric expressions, we can solve mathematical problems and make complex calculations simpler by working through operations step by step.

Negative Numbers

Negative numbers are numbers less than zero and are represented with a minus sign in front of them, such as \(-4\) or \(-10\). They are crucial in areas like temperature, altitude below sea level, and financial losses.

• Negative numbers appear on the left side of zero on a number line.
• When adding negative numbers, the value becomes more negative. For example, \(-4 + -3 = -7\).
• To subtract a negative number, you add its positive value: \(-4 - (-3) = -4 + 3 = -1\).

Learning how to work with negative numbers helps us handle a range of practical problems.

Positive Numbers

Positive numbers are greater than zero, and they appear without any sign (or with a \(+\) sign) in front of them, like \(3\) or \(15\). Positive numbers are used in various applications, from counting quantities to measuring distances.

• On a number line, positive numbers sit right of zero.
• Adding positive numbers increases the total value: \(4 + 5 = 9\).
• Subtracting a smaller positive number from a larger one decreases the total: \(9 - 5 = 4\).

Understanding positive numbers is fundamental for carrying out arithmetic operations and solving everyday math problems.

Mathematical Operations

Mathematical operations are the processes we use to solve numeric expressions. These include addition, subtraction, multiplication, and division. Each operation has rules that dictate how they combine numbers to produce results.

• Addition combines two or more numbers into a single sum. For example, \(+4 + 3 = 7\).
• Subtraction involves taking one number away from another: \(9 - 5 = 4\).
• Multiplication finds the product by adding a number to itself a certain number of times: \(3 \times 4 = 12\).
• Division splits a number into equal parts: \(12 \/ 4 = 3\).

Recognizing how these operations work is essential for evaluating and simplifying expressions, which is crucial in mathematics as well as in everyday scenarios.