( -1 ) - ( -9 )=?? ( -15 ) - ( -4 )
( -15 ) - ( -4 )
Understanding the Problem
When dealing with negative numbers, it's essential to remember the rules of subtraction. In this case, we have two expressions to evaluate: ( -1 ) - ( -9 ) and ( -15 ) - ( -4 ). To solve these problems, we need to apply the correct order of operations and understand the concept of subtracting negative numbers.
Subtracting Negative Numbers
Subtracting a negative number is equivalent to adding a positive number. This is because when we subtract a negative number, we are essentially adding its opposite, which is a positive number. For example, ( -1 ) - ( -9 ) is equivalent to ( -1 ) + 9.
Evaluating the First Expression
Let's start by evaluating the first expression: ( -1 ) - ( -9 ). As mentioned earlier, subtracting a negative number is equivalent to adding a positive number. Therefore, ( -1 ) - ( -9 ) is equal to ( -1 ) + 9.
Applying the Order of Operations
When we add 9 to -1, we need to follow the order of operations. In this case, we simply add the numbers together. So, ( -1 ) + 9 is equal to 8.
Evaluating the Second Expression
Now, let's evaluate the second expression: ( -15 ) - ( -4 ). Again, subtracting a negative number is equivalent to adding a positive number. Therefore, ( -15 ) - ( -4 ) is equal to ( -15 ) + 4.
Applying the Order of Operations
When we add 4 to -15, we need to follow the order of operations. In this case, we simply add the numbers together. So, ( -15 ) + 4 is equal to -11.
Conclusion
In conclusion, when dealing with negative numbers, it's essential to remember the rules of subtraction. Subtracting a negative number is equivalent to adding a positive number. By applying the correct order of operations, we can evaluate expressions involving negative numbers.
Examples and Practice
Here are a few examples to help you practice subtracting negative numbers:
- ( -2 ) - ( -6 ) = ?
- ( -8 ) - ( -3 ) = ?
- ( -12 ) - ( -9 ) = ?
Solution to Examples
- ( -2 ) - ( -6 ) = ( -2 ) + 6 = 4
- ( -8 ) - ( -3 ) = ( -8 ) + 3 = -5
- ( -12 ) - ( -9 ) = ( -12 ) + 9 = -3
Tips and Tricks
When dealing with negative numbers, it's essential to remember the following tips and tricks:
- Subtracting a negative number is equivalent to adding a positive number.
- When adding or subtracting negative numbers, always follow the order of operations.
- Use parentheses to clarify the order of operations when dealing with multiple negative numbers.
Common Mistakes
Here are a few common mistakes to avoid when dealing with negative numbers:
- Forgetting to change the sign when subtracting a negative number.
- Not following the order of operations when adding or subtracting multiple negative numbers.
- Not using parentheses to clarify the order of operations.
Final Thoughts
In conclusion, subtracting negative numbers is a fundamental concept in mathematics. By understanding the rules of subtraction and applying the correct order of operations, we can evaluate expressions involving negative numbers with confidence. Remember to practice regularly and use the tips and tricks provided to avoid common mistakes.
( -15 ) - ( -4 )
Q&A: Subtracting Negative Numbers
Q: What is the rule for subtracting negative numbers?
A: The rule for subtracting negative numbers is that subtracting a negative number is equivalent to adding a positive number. For example, ( -1 ) - ( -9 ) is equal to ( -1 ) + 9.
Q: How do I evaluate expressions involving negative numbers?
A: To evaluate expressions involving negative numbers, you need to follow the order of operations. This means that you need to subtract the negative numbers first, and then add or subtract the remaining numbers.
Q: What is the difference between subtracting a negative number and adding a positive number?
A: Subtracting a negative number is equivalent to adding a positive number. For example, ( -1 ) - ( -9 ) is equal to ( -1 ) + 9.
Q: Can you provide examples of subtracting negative numbers?
A: Here are a few examples:
- ( -2 ) - ( -6 ) = ?
- ( -8 ) - ( -3 ) = ?
- ( -12 ) - ( -9 ) = ?
Q: How do I solve these examples?
A: To solve these examples, you need to follow the rule for subtracting negative numbers. Here are the solutions:
- ( -2 ) - ( -6 ) = ( -2 ) + 6 = 4
- ( -8 ) - ( -3 ) = ( -8 ) + 3 = -5
- ( -12 ) - ( -9 ) = ( -12 ) + 9 = -3
Q: What are some common mistakes to avoid when dealing with negative numbers?
A: Here are a few common mistakes to avoid:
- Forgetting to change the sign when subtracting a negative number.
- Not following the order of operations when adding or subtracting multiple negative numbers.
- Not using parentheses to clarify the order of operations.
Q: How can I practice subtracting negative numbers?
A: You can practice subtracting negative numbers by working through examples and exercises. You can also use online resources or math apps to help you practice.
Q: What are some real-world applications of subtracting negative numbers?
A: Subtracting negative numbers has many real-world applications, including:
- Calculating financial losses or gains
- Determining the cost of a product or service
- Understanding the concept of debt or credit
Q: Can you provide more examples of subtracting negative numbers?
A: Here are a few more examples:
- ( -5 ) - ( -2 ) = ?
- ( -10 ) - ( -7 ) = ?
- ( -15 ) - ( -12 ) = ?
Q: How do I solve these examples?
A: To solve these examples, you need to follow the rule for subtracting negative numbers. Here are the solutions:
- ( -5 ) - ( -2 ) = ( -5 ) + 2 = -3
- ( -10 ) - ( -7 ) = ( -10 ) + 7 = -3
- ( -15 ) - ( -12 ) = ( -15 ) + 12 = -3
Q: What is the final answer to the original problem?
A: The final answer to the original problem is:
( -1 ) - ( -9 ) = 8 ( -15 ) - ( -4 ) = -11