The Concept of Double Negative

Oct 13, 2025 by leolavanderia.com.br 71 views

Understanding the Problem

When dealing with negative numbers, it's essential to understand the concept of the "double negative." A double negative occurs when two negative signs are present in an expression. In this case, we have the expression $-14 - (-20)$ , which involves a double negative.

The Concept of Double Negative

A double negative is a mathematical concept where two negative signs are present in an expression. When a negative number is subtracted from another negative number, the result is a positive number. This is because the two negative signs cancel each other out, resulting in a positive value.

Evaluating the Expression

To evaluate the expression $-14 - (-20)$ , we need to follow the order of operations (PEMDAS):

Parentheses: Evaluate the expression inside the parentheses.
Exponents: None in this case.
Multiplication and Division: None in this case.
Addition and Subtraction: Perform the subtraction operation.

Step 1: Evaluate the Expression Inside the Parentheses

The expression inside the parentheses is $-20$ . This is already simplified, so we can move on to the next step.

Step 2: Perform the Subtraction Operation

Now, we need to perform the subtraction operation: $-14 - (-20)$ . To do this, we need to follow the rule of double negatives. When a negative number is subtracted from another negative number, the result is a positive number.

Step 3: Apply the Rule of Double Negatives

When we subtract a negative number from another negative number, we need to change the sign of the second number. In this case, we change the sign of $-20$ to positive, resulting in $20$ . Now, we can perform the subtraction operation: $-14 - 20$ .

Step 4: Perform the Subtraction Operation

Now, we need to perform the subtraction operation: $-14 - 20$ . To do this, we need to subtract $20$ from $-14$ . This results in a negative value.

Step 5: Simplify the Expression

The final result of the expression $-14 - (-20)$ is $-34$ .

Conclusion

In conclusion, the expression $-14 - (-20)$ can be evaluated by following the order of operations and applying the rule of double negatives. The final result of the expression is $-34$ .

Example Use Case

The expression $-14 - (-20)$ can be used in various mathematical problems, such as:

Evaluating the value of an expression with double negatives
Understanding the concept of double negatives in mathematics
Applying the rule of double negatives to simplify expressions

Tips and Tricks

When dealing with double negatives, it's essential to follow the rule of double negatives. This rule states that when a negative number is subtracted from another negative number, the result is a positive number. By applying this rule, you can simplify expressions with double negatives and arrive at the correct solution.

Common Mistakes

When dealing with double negatives, it's common to make mistakes. Some common mistakes include:

Not following the order of operations
Not applying the rule of double negatives
Not simplifying the expression correctly

Real-World Applications

The concept of double negatives has real-world applications in various fields, such as:

Finance: When dealing with debt and credit, double negatives can be used to simplify expressions and arrive at the correct solution.
Science: In physics and chemistry, double negatives can be used to simplify expressions and arrive at the correct solution.
Engineering: In engineering, double negatives can be used to simplify expressions and arrive at the correct solution.

Final Thoughts

In conclusion, the expression $-14 - (-20)$ can be evaluated by following the order of operations and applying the rule of double negatives. The final result of the expression is $-34$ . By understanding the concept of double negatives and applying the rule, you can simplify expressions and arrive at the correct solution.

Frequently Asked Questions

Q: What is a double negative in mathematics?

A: A double negative is a mathematical concept where two negative signs are present in an expression. When a negative number is subtracted from another negative number, the result is a positive number.

Q: How do I evaluate an expression with a double negative?

A: To evaluate an expression with a double negative, you need to follow the order of operations (PEMDAS) and apply the rule of double negatives. The rule states that when a negative number is subtracted from another negative number, the result is a positive number.

Q: What is the rule of double negatives?

A: The rule of double negatives states that when a negative number is subtracted from another negative number, the result is a positive number. This means that you need to change the sign of the second number to positive before performing the subtraction operation.

Q: Can you give an example of evaluating an expression with a double negative?

A: Yes, let's consider the expression $-14 - (-20)$ . To evaluate this expression, we need to follow the order of operations and apply the rule of double negatives. First, we change the sign of $-20$ to positive, resulting in $20$ . Then, we perform the subtraction operation: $-14 - 20 = -34$ .

Q: What are some common mistakes to avoid when evaluating expressions with double negatives?

A: Some common mistakes to avoid when evaluating expressions with double negatives include:

Not following the order of operations
Not applying the rule of double negatives
Not simplifying the expression correctly

Q: Can you give an example of a real-world application of double negatives?

A: Yes, let's consider a financial example. Suppose you have a debt of $-14 and you receive a credit of $-20. To find the net result, you need to evaluate the expression $-14 - (-20)$ . By applying the rule of double negatives, you can simplify the expression and arrive at the correct solution.

Q: How do I simplify an expression with a double negative?

A: To simplify an expression with a double negative, you need to follow the order of operations and apply the rule of double negatives. The rule states that when a negative number is subtracted from another negative number, the result is a positive number. By changing the sign of the second number to positive, you can simplify the expression and arrive at the correct solution.

Q: Can you give an example of a scientific application of double negatives?

A: Yes, let's consider a physics example. Suppose you have a force of $-14 N and you apply a force of $-20 N in the opposite direction. To find the net force, you need to evaluate the expression $-14 - (-20)$ . By applying the rule of double negatives, you can simplify the expression and arrive at the correct solution.

Q: How do I apply the rule of double negatives in a word problem?

A: To apply the rule of double negatives in a word problem, you need to identify the negative numbers and the operation involved. Then, you need to follow the order of operations and apply the rule of double negatives. The rule states that when a negative number is subtracted from another negative number, the result is a positive number. By changing the sign of the second number to positive, you can simplify the expression and arrive at the correct solution.

Q: Can you give an example of a mathematical proof involving double negatives?

A: Yes, let's consider a mathematical proof involving double negatives. Suppose we want to prove that $-a - (-b) = a + b$ . To prove this, we need to follow the order of operations and apply the rule of double negatives. By changing the sign of $-b$ to positive, we can simplify the expression and arrive at the correct solution.

Q: How do I use double negatives in algebra?

A: To use double negatives in algebra, you need to follow the order of operations and apply the rule of double negatives. The rule states that when a negative number is subtracted from another negative number, the result is a positive number. By changing the sign of the second number to positive, you can simplify the expression and arrive at the correct solution.

Q: Can you give an example of a mathematical puzzle involving double negatives?

A: Yes, let's consider a mathematical puzzle involving double negatives. Suppose we have a puzzle that states: "Tom has $-14 and he receives a gift of $-20. How much money does Tom have now?" To solve this puzzle, we need to evaluate the expression $-14 - (-20)$ . By applying the rule of double negatives, we can simplify the expression and arrive at the correct solution.

Q: How do I use double negatives in calculus?

A: To use double negatives in calculus, you need to follow the order of operations and apply the rule of double negatives. The rule states that when a negative number is subtracted from another negative number, the result is a positive number. By changing the sign of the second number to positive, you can simplify the expression and arrive at the correct solution.

Q: Can you give an example of a real-world application of double negatives in finance?

Q: How do I use double negatives in statistics?

A: To use double negatives in statistics, you need to follow the order of operations and apply the rule of double negatives. The rule states that when a negative number is subtracted from another negative number, the result is a positive number. By changing the sign of the second number to positive, you can simplify the expression and arrive at the correct solution.

Q: Can you give an example of a mathematical proof involving double negatives in geometry?

A: Yes, let's consider a mathematical proof involving double negatives in geometry. Suppose we want to prove that the sum of the interior angles of a triangle is $180^\circ$ . To prove this, we need to follow the order of operations and apply the rule of double negatives. By changing the sign of the second number to positive, we can simplify the expression and arrive at the correct solution.

Q: How do I use double negatives in computer science?

A: To use double negatives in computer science, you need to follow the order of operations and apply the rule of double negatives. The rule states that when a negative number is subtracted from another negative number, the result is a positive number. By changing the sign of the second number to positive, you can simplify the expression and arrive at the correct solution.

Q: Can you give an example of a real-world application of double negatives in engineering?

A: Yes, let's consider an engineering example. Suppose you have a force of $-14 N and you apply a force of $-20 N in the opposite direction. To find the net force, you need to evaluate the expression $-14 - (-20)$ . By applying the rule of double negatives, you can simplify the expression and arrive at the correct solution.