Simplify The Following Expression: $35 + (-13) + (+8) - (-6$\].A) 36 B) 50 C) 44 D) 24

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 algebraic expression: $35 + (-13) + (+8) - (-6)$. We will break down the expression step by step, using basic arithmetic operations and mathematical concepts to arrive at the final answer.

Understanding the Expression

Before we dive into simplifying the expression, let's take a closer look at what it represents. The expression consists of four terms:

1. $35$: A positive integer
2. $(-13)$: A negative integer
3. $(+8)$: A positive integer
4. $(-6)$: A negative integer

The expression involves addition and subtraction operations, which can be performed in a specific order to simplify the expression.

Step 1: Simplifying the Expression

To simplify the expression, we need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

In this case, we don't have any parentheses, exponents, or multiplication and division operations, so we can skip those steps. We are left with addition and subtraction operations.

Step 2: Combining Like Terms

The expression contains two positive integers ($35$ and $8$) and two negative integers ($-13$ and $-6$). We can combine like terms by adding or subtracting the coefficients of the same variable.

In this case, we have:

• $35 + 8 = 43$ (combining the two positive integers)
• $-13 - (-6) = -13 + 6 = -7$ (combining the two negative integers)

Now, we can rewrite the expression as:

$43 - 7$

Step 3: Evaluating the Expression

Finally, we can evaluate the expression by performing the subtraction operation:

$43 - 7 = 36$

Conclusion

In this article, we simplified the algebraic expression $35 + (-13) + (+8) - (-6)$ step by step, using basic arithmetic operations and mathematical concepts. We broke down the expression into smaller parts, combined like terms, and finally evaluated the expression to arrive at the final answer: $36$.

Answer

The correct answer is:

A) 36

Additional Tips and Resources

• To simplify algebraic expressions, always follow the order of operations (PEMDAS).
• Combine like terms by adding or subtracting the coefficients of the same variable.
• Use basic arithmetic operations to evaluate the expression.

For more information on simplifying algebraic expressions, check out the following resources:

• Khan Academy: Algebraic Expressions
• Mathway: Simplifying Algebraic Expressions
• Wolfram Alpha: Algebraic Expressions

Introduction

In our previous article, we simplified the algebraic expression $35 + (-13) + (+8) - (-6)$ step by step, using basic arithmetic operations and mathematical concepts. However, we know that algebraic expressions can be complex and challenging to simplify. In this article, we will address some common questions and concerns that students and professionals may have when it comes to simplifying algebraic expressions.

Q&A

Q: What is the order of operations (PEMDAS)?

A: The order of operations is a set of rules that dictates the order in which mathematical operations should be performed. PEMDAS stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an algebraic expression with multiple terms?

A: To simplify an algebraic expression with multiple terms, follow these steps:

1. Combine like terms by adding or subtracting the coefficients of the same variable.
2. Evaluate any parentheses or exponents.
3. Perform any multiplication and division operations from left to right.
4. Finally, perform any addition and subtraction operations from left to right.

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. For example, x or y. A constant is a value that does not change. For example, 5 or 10.

Q: How do I simplify an expression with negative numbers?

A: When simplifying an expression with negative numbers, remember that:

• A negative number multiplied by a negative number is a positive number.
• A negative number added to a positive number is a negative number.
• A negative number subtracted from a positive number is a positive number.

Q: What is the difference between an expression and an equation?

A: An expression is a group of numbers, variables, and mathematical operations that are combined to form a value. For example, 2x + 3. An equation is a statement that says two expressions are equal. For example, 2x + 3 = 5.

Q: How do I simplify an expression with fractions?

A: When simplifying an expression with fractions, remember that:

• To add or subtract fractions, they must have the same denominator.
• To multiply fractions, multiply the numerators and denominators separately.
• To divide fractions, invert the second fraction and multiply.

Q: What are some common mistakes to avoid when simplifying algebraic expressions?

A: Some common mistakes to avoid when simplifying algebraic expressions include:

• Not following the order of operations (PEMDAS)
• Not combining like terms
• Not evaluating parentheses or exponents
• Not performing multiplication and division operations from left to right
• Not performing addition and subtraction operations from left to right

Conclusion

Simplifying algebraic expressions can be challenging, but with practice and patience, you can become proficient in simplifying even the most complex expressions. Remember to follow the order of operations (PEMDAS), combine like terms, and evaluate any parentheses or exponents. By avoiding common mistakes and using the tips and resources provided in this article, you can simplify algebraic expressions with confidence.

Additional Tips and Resources

• Practice simplifying algebraic expressions with online resources such as Khan Academy, Mathway, and Wolfram Alpha.
• Use a calculator to check your work and ensure that you are simplifying expressions correctly.
• Review the order of operations (PEMDAS) and practice simplifying expressions with multiple terms.
• Watch video tutorials and online lectures to gain a deeper understanding of algebraic expressions and simplification techniques.

By following these tips and resources, you can become proficient in simplifying algebraic expressions and tackle more complex mathematical problems with confidence.