To evaluate the absolute value of a negative number

Oct 13, 2025 by magicalceylontours.com 41 views

Introduction to Absolute Value

Absolute value is a mathematical concept that represents the distance of a number from zero on the number line. It is denoted by two vertical lines on either side of the number, such as $|x|$ . The absolute value of a number is always non-negative, and it can be positive or zero. In this article, we will simplify the expression $|-14| + |4| - 5 + (-2)$ using the concept of absolute value.

Understanding Absolute Value of Negative Numbers

When we have a negative number inside the absolute value, we need to find its distance from zero. This means we need to change the sign of the number to make it positive. For example, $|-14|$ is equal to $14$ because the distance of $-14$ from zero is $14$ . Similarly, $|4|$ is equal to $4$ because the distance of $4$ from zero is $4$ .

Simplifying the Expression

Now that we understand the concept of absolute value, let's simplify the expression $|-14| + |4| - 5 + (-2)$ . We can start by evaluating the absolute values:

$|-14| = 14$ $|4| = 4$

Now, we can substitute these values back into the expression:

$14 + 4 - 5 + (-2)$

Evaluating the Expression

Next, we need to evaluate the expression by following the order of operations (PEMDAS):

Parentheses: None
Exponents: None
Multiplication and Division: None
Addition and Subtraction: From left to right

We can start by adding $14$ and $4$ :

$14 + 4 = 18$

Now, we can subtract $5$ from $18$ :

$18 - 5 = 13$

Finally, we can add $-2$ to $13$ :

$13 + (-2) = 11$

Conclusion

In this article, we simplified the expression $|-14| + |4| - 5 + (-2)$ using the concept of absolute value. We evaluated the absolute values and then followed the order of operations to simplify the expression. The final result is $11$ . We hope this article has helped you understand how to simplify expressions involving absolute value.

Frequently Asked Questions

What is absolute value?
How do you evaluate absolute value of negative numbers?
What is the order of operations (PEMDAS)?
How do you simplify expressions involving absolute value?

Answer to Frequently Asked Questions

What is absolute value? Absolute value is a mathematical concept that represents the distance of a number from zero on the number line.
How do you evaluate absolute value of negative numbers? To evaluate the absolute value of a negative number, you need to change the sign of the number to make it positive.
What is the order of operations (PEMDAS)? The order of operations is a set of rules that tells you which operations to perform first when you have multiple operations in an expression. The order is: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
How do you simplify expressions involving absolute value? To simplify expressions involving absolute value, you need to evaluate the absolute values first and then follow the order of operations.

Additional Resources

Final Answer

The final answer is: $\boxed{11}$

Introduction

In our previous article, we simplified the expression $|-14| + |4| - 5 + (-2)$ using the concept of absolute value. In this article, we will answer some frequently asked questions related to absolute value simplification.

Q&A

Q1: What is absolute value?

A1: Absolute value is a mathematical concept that represents the distance of a number from zero on the number line. It is denoted by two vertical lines on either side of the number, such as $|x|$ . The absolute value of a number is always non-negative, and it can be positive or zero.

Q2: How do you evaluate absolute value of negative numbers?

A2: To evaluate the absolute value of a negative number, you need to change the sign of the number to make it positive. For example, $|-14|$ is equal to $14$ because the distance of $-14$ from zero is $14$ .

Q3: What is the order of operations (PEMDAS)?

A3: The order of operations is a set of rules that tells you which operations to perform first when you have multiple operations in an expression. The order is: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q4: How do you simplify expressions involving absolute value?

A4: To simplify expressions involving absolute value, you need to evaluate the absolute values first and then follow the order of operations. For example, to simplify the expression $|-14| + |4| - 5 + (-2)$ , you need to evaluate the absolute values first and then follow the order of operations.

Q5: What is the difference between absolute value and distance?

A5: Absolute value and distance are related but not exactly the same thing. Absolute value represents the distance of a number from zero on the number line, while distance represents the actual length between two points on the number line.

Q6: Can absolute value be negative?

A6: No, absolute value cannot be negative. The absolute value of a number is always non-negative, and it can be positive or zero.

Q7: How do you handle absolute value in fractions?

A7: To handle absolute value in fractions, you need to evaluate the absolute value of the numerator and the denominator separately. For example, to simplify the expression $\frac{|-14|}{|4|}$ , you need to evaluate the absolute values of the numerator and the denominator separately.

Q8: Can absolute value be used with other mathematical operations?

A8: Yes, absolute value can be used with other mathematical operations such as addition, subtraction, multiplication, and division. For example, to simplify the expression $|-14| + |4| - 5 + (-2)$ , you need to use absolute value with addition and subtraction.