Evaluate:$-14 - (-20)$
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Introduction
When dealing with mathematical expressions, it's essential to understand the rules of operations, especially when it comes to negative numbers. In this article, we will evaluate the expression $-14 - (-20)$ and explore the concept of subtracting negative numbers.
Understanding Negative Numbers
Negative numbers are a fundamental concept in mathematics, and they play a crucial role in various mathematical operations. A negative number is a number that is less than zero. For example, -5 is a negative number because it is less than zero. When we see a negative number, we know that it is the opposite of a positive number. In other words, -5 is the opposite of 5.
Subtracting Negative Numbers
Subtracting negative numbers can be a bit tricky, but it's essential to understand the concept. When we subtract a negative number, we are essentially adding the opposite of that number. For example, subtracting -3 from 5 is the same as adding 3 to 5.
Evaluating the Expression
Now that we have a basic understanding of negative numbers and subtracting negative numbers, let's evaluate the expression $-14 - (-20)$. To evaluate this expression, we need to follow the order of operations (PEMDAS):
- Evaluate the expressions inside the parentheses: $-14 - (-20)$
- Subtract the negative number from the first number: $-14 + 20$
Step-by-Step Evaluation
Let's break down the evaluation process step by step:
- Evaluate the expressions inside the parentheses: $-14 - (-20)$ The expression inside the parentheses is $-20$, which is a negative number. When we see a negative number inside the parentheses, we know that it is the opposite of a positive number. In this case, $-20$ is the opposite of $20$.
- Subtract the negative number from the first number: $-14 + 20$ Now that we have evaluated the expression inside the parentheses, we can subtract the negative number from the first number. When we subtract a negative number, we are essentially adding the opposite of that number. In this case, we are adding $20$ to $-14$.
Final Evaluation
Let's perform the final evaluation:
Therefore, the final answer to the expression $-14 - (-20)$ is $6$.
Conclusion
In conclusion, evaluating the expression $-14 - (-20)$ requires a basic understanding of negative numbers and subtracting negative numbers. By following the order of operations (PEMDAS) and breaking down the evaluation process step by step, we can arrive at the final answer. Remember, when subtracting a negative number, we are essentially adding the opposite of that number.
Frequently Asked Questions
Q: What is the difference between subtracting a negative number and adding a positive number?
A: When we subtract a negative number, we are essentially adding the opposite of that number. For example, subtracting -3 from 5 is the same as adding 3 to 5.
Q: How do I evaluate an expression with multiple negative numbers?
A: To evaluate an expression with multiple negative numbers, follow the order of operations (PEMDAS) and break down the evaluation process step by step. For example, to evaluate the expression $-14 - (-20) - (-30)$, first evaluate the expressions inside the parentheses, then subtract the negative numbers from the first number.
Q: What is the final answer to the expression $-14 - (-20)$?
A: The final answer to the expression $-14 - (-20)$ is $6$.
Additional Resources
For more information on negative numbers and subtracting negative numbers, check out the following resources:
- Khan Academy: Negative Numbers
- Mathway: Subtracting Negative Numbers
- Wolfram Alpha: Negative Numbers and Subtracting Negative Numbers
Final Thoughts
Evaluating the expression $-14 - (-20)$ requires a basic understanding of negative numbers and subtracting negative numbers. By following the order of operations (PEMDAS) and breaking down the evaluation process step by step, we can arrive at the final answer. Remember, when subtracting a negative number, we are essentially adding the opposite of that number.
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Introduction
In our previous article, we evaluated the expression $-14 - (-20)$ and explored the concept of subtracting negative numbers. In this article, we will answer some frequently asked questions about negative numbers and subtracting negative numbers.
Q&A
Q: What is the difference between subtracting a negative number and adding a positive number?
A: When we subtract a negative number, we are essentially adding the opposite of that number. For example, subtracting -3 from 5 is the same as adding 3 to 5.
Q: How do I evaluate an expression with multiple negative numbers?
A: To evaluate an expression with multiple negative numbers, follow the order of operations (PEMDAS) and break down the evaluation process step by step. For example, to evaluate the expression $-14 - (-20) - (-30)$, first evaluate the expressions inside the parentheses, then subtract the negative numbers from the first number.
Q: What is the rule for subtracting negative numbers?
A: The rule for subtracting negative numbers is to change the subtraction sign to an addition sign and change the sign of the second number. For example, subtracting -3 from 5 is the same as adding 3 to 5.
Q: Can I use a calculator to evaluate expressions with negative numbers?
A: Yes, you can use a calculator to evaluate expressions with negative numbers. However, it's essential to understand the concept of subtracting negative numbers to avoid making mistakes.
Q: How do I simplify expressions with negative numbers?
A: To simplify expressions with negative numbers, follow the order of operations (PEMDAS) and break down the evaluation process step by step. For example, to simplify the expression $-14 - (-20)$, first evaluate the expressions inside the parentheses, then subtract the negative numbers from the first number.
Q: What is the final answer to the expression $-14 - (-20)$?
A: The final answer to the expression $-14 - (-20)$ is $6$.
Q: Can I use a graphing calculator to visualize expressions with negative numbers?
A: Yes, you can use a graphing calculator to visualize expressions with negative numbers. Graphing calculators can help you understand the behavior of expressions with negative numbers and make it easier to evaluate them.
Q: How do I evaluate expressions with negative numbers and fractions?
A: To evaluate expressions with negative numbers and fractions, follow the order of operations (PEMDAS) and break down the evaluation process step by step. For example, to evaluate the expression $-\frac{1}{2} - (-\frac{3}{4})$, first evaluate the expressions inside the parentheses, then subtract the negative numbers from the first number.
Additional Resources
For more information on negative numbers and subtracting negative numbers, check out the following resources:
- Khan Academy: Negative Numbers
- Mathway: Subtracting Negative Numbers
- Wolfram Alpha: Negative Numbers and Subtracting Negative Numbers
Final Thoughts
Evaluating expressions with negative numbers requires a basic understanding of negative numbers and subtracting negative numbers. By following the order of operations (PEMDAS) and breaking down the evaluation process step by step, we can arrive at the final answer. Remember, when subtracting a negative number, we are essentially adding the opposite of that number.
Common Mistakes
When evaluating expressions with negative numbers, it's essential to avoid making common mistakes. Some common mistakes include:
- Forgetting to change the subtraction sign to an addition sign when subtracting a negative number
- Forgetting to change the sign of the second number when subtracting a negative number
- Not following the order of operations (PEMDAS)
- Not breaking down the evaluation process step by step
Conclusion
In conclusion, evaluating expressions with negative numbers requires a basic understanding of negative numbers and subtracting negative numbers. By following the order of operations (PEMDAS) and breaking down the evaluation process step by step, we can arrive at the final answer. Remember, when subtracting a negative number, we are essentially adding the opposite of that number.