Select The Best Answer For The Question.4. Simplify This Expression: $13 + (-12) - (-5) =$ ?A. -30 B. 30 C. -6 D. 6
Introduction
Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for students and professionals alike. In this article, we will focus on simplifying a specific type of algebraic expression, which involves adding and subtracting integers with different signs. We will use a step-by-step approach to simplify the expression and arrive at the correct answer.
Understanding the Expression
The given expression is:
This expression involves three terms: 13, -12, and -5. The first term is a positive integer, while the second and third terms are negative integers. Our goal is to simplify this expression by combining the terms and arriving at a final answer.
Step 1: Simplify the Negative Terms
The second and third terms are negative integers, which means they have opposite signs. To simplify the expression, we need to combine these two terms by adding them together.
So, the expression now becomes:
Step 2: Combine the Terms
Now that we have simplified the negative terms, we can combine them with the first term. To do this, we need to add 13 and -17.
Therefore, the simplified expression is:
Conclusion
In conclusion, the simplified expression is:
This answer is not among the options provided in the question. However, we can see that the correct answer is not A, B, C, or D. The correct answer is actually E, which is not provided in the question. But if we look at the options, we can see that the closest answer is C, which is -6. However, this is not the correct answer.
Answer Key
The correct answer is not among the options provided in the question. However, if we look at the options, we can see that the closest answer is C, which is -6. But the correct answer is actually -4.
Why is this Important?
Simplifying algebraic expressions is an essential skill in mathematics, and it has numerous applications in real-life situations. For example, in physics, algebraic expressions are used to describe the motion of objects, while in economics, they are used to model the behavior of markets. Therefore, it is crucial to understand how to simplify algebraic expressions to solve problems in various fields.
Tips and Tricks
Here are some tips and tricks to help you simplify algebraic expressions:
- Combine like terms: When simplifying an expression, combine like terms by adding or subtracting them.
- Use the order of operations: When simplifying an expression, use the order of operations (PEMDAS) to evaluate the expression.
- Simplify negative terms: When simplifying an expression, simplify negative terms by adding them together.
- Check your work: When simplifying an expression, check your work to ensure that the answer is correct.
Conclusion
Q: What is an algebraic expression?
A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. It is a way to represent a mathematical relationship between variables and constants.
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 simplifying an expression. The order of operations is:
- 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 simplify a negative term?
A: To simplify a negative term, you need to add it to another negative term. For example, if you have the expression -12 + (-5), you can simplify it by adding the two negative terms together: -12 + (-5) = -17.
Q: What is the difference between a variable and a constant?
A: A variable is a letter or symbol that represents a value that can change. A constant is a value that does not change.
Q: How do I combine like terms?
A: To combine like terms, you need to add or subtract terms that have the same variable and exponent. For example, if you have the expression 2x + 3x, you can combine the two terms by adding them together: 2x + 3x = 5x.
Q: What is the importance of simplifying algebraic expressions?
A: Simplifying algebraic expressions is important because it helps us to:
- Solve equations and inequalities
- Graph functions
- Model real-world situations
- Make predictions and decisions
Q: How do I check my work when simplifying an algebraic expression?
A: To check your work, you need to:
- Plug in values for the variables
- Simplify the expression using the order of operations
- Check that the answer is correct
Q: What are some common mistakes to avoid when simplifying algebraic expressions?
A: Some common mistakes to avoid when simplifying algebraic expressions include:
- Forgetting to combine like terms
- Not following the order of operations
- Making errors when simplifying negative terms
- Not checking your work
Q: How can I practice simplifying algebraic expressions?
A: You can practice simplifying algebraic expressions by:
- Working through practice problems
- Using online resources and tools
- Asking a teacher or tutor for help
- Joining a study group or math club
Conclusion
In conclusion, simplifying algebraic expressions is an essential skill in mathematics, and it has numerous applications in real-life situations. By following the steps outlined in this article, you can simplify algebraic expressions and arrive at the correct answer. Remember to combine like terms, use the order of operations, simplify negative terms, and check your work to ensure that the answer is correct.