Evaluate The Following: { -3 + (-15)$}$A. -18 B. 12 C. -12 D. 45 E. None Of These.
Understanding the Problem
In this problem, we are given an expression to evaluate: -3 + (-15). Our goal is to simplify this expression and determine its value. We will use basic arithmetic operations to solve this problem.
The Order of Operations
Before we start evaluating the expression, it's essential to understand the order of operations. The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is as follows:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Evaluating the Expression
Now that we understand the order of operations, let's evaluate the expression -3 + (-15).
- Parentheses: There are no parentheses in this expression, so we can move on to the next step.
- Exponents: There are no exponential expressions in this expression, so we can move on to the next step.
- Multiplication and Division: There are no multiplication or division operations in this expression, so we can move on to the next step.
- Addition and Subtraction: Now we can evaluate the addition and subtraction operations. We have two negative numbers: -3 and -15. When we add two negative numbers, we add their absolute values and then apply the negative sign to the result.
Absolute Value
The absolute value of a number is its distance from zero on the number line. For example, the absolute value of -3 is 3, and the absolute value of -15 is 15.
Adding Absolute Values
Now that we have the absolute values of the two numbers, we can add them together: 3 + 15 = 18.
Applying the Negative Sign
Finally, we apply the negative sign to the result: -18.
Conclusion
In conclusion, the value of the expression -3 + (-15) is -18.
Answer
The correct answer is A. -18.
Explanation
The other options are incorrect because they do not follow the order of operations or do not apply the correct arithmetic operations.
- B. 12 is incorrect because it does not follow the order of operations and does not apply the correct arithmetic operations.
- C. -12 is incorrect because it does not follow the order of operations and does not apply the correct arithmetic operations.
- D. 45 is incorrect because it does not follow the order of operations and does not apply the correct arithmetic operations.
- E. None of these is incorrect because A. -18 is the correct answer.
Final Answer
Q&A: Evaluating Expressions
Q: What is the order of operations?
A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is as follows:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I evaluate an expression with parentheses?
A: To evaluate an expression with parentheses, you need to follow the order of operations. First, evaluate the expression inside the parentheses. Then, evaluate any exponential expressions, followed by any multiplication and division operations, and finally any addition and subtraction operations.
Q: What is the difference between absolute value and negative numbers?
A: The absolute value of a number is its distance from zero on the number line. For example, the absolute value of -3 is 3. A negative number is a number that is less than zero. For example, -3 is a negative number.
Q: How do I add two negative numbers?
A: To add two negative numbers, you need to add their absolute values and then apply the negative sign to the result. For example, to add -3 and -15, you would first add their absolute values: 3 + 15 = 18. Then, you would apply the negative sign to the result: -18.
Q: What is the value of the expression -3 + (-15)?
A: The value of the expression -3 + (-15) is -18.
Q: What is the correct answer to the expression -3 + (-15)?
A: The correct answer is A. -18.
Q: Why is option B incorrect?
A: Option B is incorrect because it does not follow the order of operations and does not apply the correct arithmetic operations.
Q: Why is option C incorrect?
A: Option C is incorrect because it does not follow the order of operations and does not apply the correct arithmetic operations.
Q: Why is option D incorrect?
A: Option D is incorrect because it does not follow the order of operations and does not apply the correct arithmetic operations.
Q: Why is option E incorrect?
A: Option E is incorrect because A. -18 is the correct answer.
Final Answer
The final answer is A. -18.
Common Mistakes
- Not following the order of operations
- Not applying the correct arithmetic operations
- Not evaluating expressions inside parentheses first
- Not evaluating exponential expressions next
- Not evaluating multiplication and division operations from left to right
- Not evaluating addition and subtraction operations from left to right
Tips and Tricks
- Always follow the order of operations
- Evaluate expressions inside parentheses first
- Evaluate exponential expressions next
- Evaluate multiplication and division operations from left to right
- Evaluate addition and subtraction operations from left to right
- Use absolute values to help you evaluate expressions with negative numbers
Conclusion
Evaluating expressions can be a challenging task, but by following the order of operations and applying the correct arithmetic operations, you can simplify even the most complex expressions. Remember to always evaluate expressions inside parentheses first, followed by exponential expressions, multiplication and division operations, and finally addition and subtraction operations. With practice and patience, you will become a master of evaluating expressions in no time!