Which Of The Following Is Equal To The Expression 6(11 + 3)? A 6 × 14 B 33 + 3 C 66 + 3 D 6(11 × 3)
Introduction
Algebraic expressions are a fundamental concept in mathematics, and solving them requires a clear understanding of the order of operations and the properties of numbers. In this article, we will explore the concept of algebraic expressions and provide a step-by-step guide on how to solve them. We will also examine a specific problem, which is equal to the expression 6(11 + 3), and determine the correct answer among the given options.
Understanding Algebraic Expressions
An algebraic expression is a mathematical statement that contains variables, constants, and mathematical operations. It is a way of representing a mathematical relationship between variables and constants. Algebraic expressions can be simple or complex, and they can be used to solve a wide range of mathematical problems.
Order of Operations
When solving algebraic expressions, it is essential to follow the order of operations, which is a set of rules that dictate the order in which mathematical operations should be performed. 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.
Solving the Expression 6(11 + 3)
To solve the expression 6(11 + 3), we need to follow the order of operations. The first step is to evaluate the expression inside the parentheses, which is 11 + 3.
Step 1: Evaluate the Expression Inside the Parentheses
11 + 3 = 14
Step 2: Multiply 6 by the Result
Now that we have evaluated the expression inside the parentheses, we can multiply 6 by the result.
6 × 14 = 84
Step 3: Determine the Correct Answer
Based on the calculation above, the correct answer is A 6 × 14.
Why is Option B Incorrect?
Option B is incorrect because it does not follow the order of operations. The expression 33 + 3 is not equal to 6(11 + 3).
Why is Option C Incorrect?
Option C is incorrect because it does not follow the order of operations. The expression 66 + 3 is not equal to 6(11 + 3).
Why is Option D Incorrect?
Option D is incorrect because it does not follow the order of operations. The expression 6(11 × 3) is not equal to 6(11 + 3).
Conclusion
In conclusion, solving algebraic expressions requires a clear understanding of the order of operations and the properties of numbers. By following the order of operations, we can evaluate complex algebraic expressions and determine the correct answer. In this article, we have examined a specific problem, which is equal to the expression 6(11 + 3), and determined the correct answer among the given options.
Final Answer
The final answer is A 6 × 14.
Additional Tips and Resources
- To improve your algebraic expression-solving skills, practice solving a wide range of problems, including simple and complex expressions.
- Use online resources, such as Khan Academy and Mathway, to help you understand and solve algebraic expressions.
- Review the order of operations and practice applying it to different types of algebraic expressions.
Common Algebraic Expression Mistakes
- Failing to follow the order of operations
- Not evaluating expressions inside parentheses first
- Not multiplying or dividing numbers correctly
- Not adding or subtracting numbers correctly
Algebraic Expression Practice Problems
- Solve the expression 3(2 + 5)
- Solve the expression 2 × (7 - 3)
- Solve the expression 5 + 2 × 3
- Solve the expression 10 - 3 × 2
Frequently Asked Questions: Algebraic Expressions =====================================================
Q: What is an algebraic expression?
A: An algebraic expression is a mathematical statement that contains variables, constants, and mathematical operations. It is a way of representing 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 dictate the order in which mathematical operations should be performed. 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 algebraic expression?
A: To evaluate an algebraic expression, follow the order of operations. First, evaluate any expressions inside parentheses. Next, evaluate any exponential expressions. Then, evaluate any multiplication and division operations from left to right. Finally, evaluate 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. A constant is a value that does not change.
Q: How do I simplify an algebraic expression?
A: To simplify an algebraic expression, combine like terms. Like terms are terms that have the same variable and exponent.
Q: What is a like term?
A: A like term is a term that has the same variable and exponent.
Q: How do I combine like terms?
A: To combine like terms, add or subtract the coefficients of the like terms.
Q: What is a coefficient?
A: A coefficient is a number that is multiplied by a variable.
Q: How do I evaluate an expression with parentheses?
A: To evaluate an expression with parentheses, first evaluate the expression inside the parentheses. Then, evaluate the expression outside the parentheses.
Q: What is the difference between an equation and an expression?
A: An equation is a statement that says two expressions are equal. An expression is a mathematical statement that contains variables, constants, and mathematical operations.
Q: How do I solve an equation?
A: To solve an equation, isolate the variable. This means getting the variable by itself on one side of the equation.
Q: What is the difference between a linear equation and a quadratic equation?
A: A linear equation is an equation that can be written in the form ax + b = c, where a, b, and c are constants. A quadratic equation is an equation that can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants.
Q: How do I solve a linear equation?
A: To solve a linear equation, isolate the variable. This means getting the variable by itself on one side of the equation.
Q: How do I solve a quadratic equation?
A: To solve a quadratic equation, use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a.
Q: What is the quadratic formula?
A: The quadratic formula is a formula that is used to solve quadratic equations. It is: x = (-b ± √(b^2 - 4ac)) / 2a.
Q: How do I use the quadratic formula?
A: To use the quadratic formula, plug in the values of a, b, and c into the formula. Then, simplify the expression and solve for x.
Additional Tips and Resources
- To improve your algebraic expression-solving skills, practice solving a wide range of problems, including simple and complex expressions.
- Use online resources, such as Khan Academy and Mathway, to help you understand and solve algebraic expressions.
- Review the order of operations and practice applying it to different types of algebraic expressions.
Common Algebraic Expression Mistakes
- Failing to follow the order of operations
- Not evaluating expressions inside parentheses first
- Not multiplying or dividing numbers correctly
- Not adding or subtracting numbers correctly
Algebraic Expression Practice Problems
- Solve the expression 3(2 + 5)
- Solve the expression 2 × (7 - 3)
- Solve the expression 5 + 2 × 3
- Solve the expression 10 - 3 × 2