Calculate The Expression:$\[ 6 \times (6 + 2) - 13 \\]
Understanding the Basics of Algebraic Expressions
Algebraic expressions are a fundamental concept in mathematics, and they play a crucial role in solving various mathematical problems. An algebraic expression is a combination of variables, constants, and mathematical operations that can be evaluated to obtain a numerical value. In this article, we will focus on solving a specific algebraic expression: 6 × (6 + 2) - 13.
The Order of Operations: A Key to Solving Algebraic Expressions
To solve 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 often remembered using the acronym PEMDAS, which stands for:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate 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 6 × (6 + 2) - 13
Now that we have a basic understanding of algebraic expressions and the order of operations, let's apply these concepts to solve the expression 6 × (6 + 2) - 13.
Step 1: Evaluate the Expression Inside the Parentheses
The first step is to evaluate the expression inside the parentheses: 6 + 2. Using the order of operations, we can evaluate this expression as follows:
6 + 2 = 8
So, the expression inside the parentheses is equal to 8.
Step 2: Multiply 6 by the Result
Next, we need to multiply 6 by the result we obtained in the previous step:
6 × 8 = 48
Step 3: Subtract 13 from the Result
Finally, we need to subtract 13 from the result we obtained in the previous step:
48 - 13 = 35
Therefore, the final result of the expression 6 × (6 + 2) - 13 is 35.
Conclusion
In this article, we have learned how to solve a specific algebraic expression using the order of operations. We have applied the rules of algebraic expressions and the order of operations to evaluate the expression 6 × (6 + 2) - 13. By following these steps, we have obtained the final result of the expression, which is 35. This article has provided a step-by-step guide to solving algebraic expressions, and it has demonstrated the importance of following the order of operations in mathematics.
Common Algebraic Expressions and Their Solutions
Here are some common algebraic expressions and their solutions:
- 2 × (3 + 4) - 5 = ?
- 5 × (2 - 3) + 4 = ?
- 3 × (4 + 2) - 2 = ?
Solution 1: 2 × (3 + 4) - 5
To solve this expression, we need to follow the order of operations:
- Evaluate the expression inside the parentheses: 3 + 4 = 7
- Multiply 2 by the result: 2 × 7 = 14
- Subtract 5 from the result: 14 - 5 = 9
Therefore, the final result of the expression 2 × (3 + 4) - 5 is 9.
Solution 2: 5 × (2 - 3) + 4
To solve this expression, we need to follow the order of operations:
- Evaluate the expression inside the parentheses: 2 - 3 = -1
- Multiply 5 by the result: 5 × -1 = -5
- Add 4 to the result: -5 + 4 = -1
Therefore, the final result of the expression 5 × (2 - 3) + 4 is -1.
Solution 3: 3 × (4 + 2) - 2
To solve this expression, we need to follow the order of operations:
- Evaluate the expression inside the parentheses: 4 + 2 = 6
- Multiply 3 by the result: 3 × 6 = 18
- Subtract 2 from the result: 18 - 2 = 16
Therefore, the final result of the expression 3 × (4 + 2) - 2 is 16.
Tips and Tricks for Solving Algebraic Expressions
Here are some tips and tricks for solving algebraic expressions:
- Always follow the order of operations.
- Evaluate expressions inside parentheses first.
- Use the correct order of operations to evaluate exponential expressions.
- Use the correct order of operations to evaluate multiplication and division operations.
- Use the correct order of operations to evaluate addition and subtraction operations.
- Check your work to ensure that you have obtained the correct result.
By following these tips and tricks, you can become proficient in solving algebraic expressions and apply these skills to a wide range of mathematical problems.
Understanding Algebraic Expressions
Algebraic expressions are a fundamental concept in mathematics, and they play a crucial role in solving various mathematical problems. In this article, we will answer some frequently asked questions about algebraic expressions.
Q: What is an algebraic expression?
A: An algebraic expression is a combination of variables, constants, and mathematical operations that can be evaluated to obtain a numerical value.
Q: What are the different types of algebraic expressions?
A: There are several types of algebraic expressions, including:
- Monomials: A monomial is a single term that consists of a variable or a constant.
- Binomials: A binomial is a two-term expression that consists of two variables or constants.
- Polynomials: A polynomial is a multi-term expression that consists of two or more variables or constants.
- Rational expressions: A rational expression is a fraction that consists of a polynomial in the numerator and a polynomial in the denominator.
Q: How do I evaluate an algebraic expression?
A: To evaluate an algebraic expression, you need 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 often remembered using the acronym PEMDAS, which stands for:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: What is the difference between an equation and an expression?
A: An equation is a statement that two expressions are equal, while an expression is a combination of variables, constants, and mathematical operations that can be evaluated to obtain a numerical value.
Q: How do I simplify an algebraic expression?
A: To simplify an algebraic expression, you need to combine like terms and eliminate any unnecessary parentheses or brackets.
Q: What is the distributive property?
A: The distributive property is a rule that allows you to multiply a single term by multiple terms. It states that:
a(b + c) = ab + ac
Q: What is the commutative property?
A: The commutative property is a rule that allows you to change the order of terms in an expression without changing the value of the expression. It states that:
a + b = b + a
Q: What is the associative property?
A: The associative property is a rule that allows you to change the order of terms in an expression without changing the value of the expression. It states that:
(a + b) + c = a + (b + c)
Q: How do I solve a linear equation?
A: To solve a linear equation, you need to isolate the variable on one side of the equation. You can do this by adding or subtracting the same value to both sides of the equation, or by multiplying or dividing both sides of the equation by the same value.
Q: How do I solve a quadratic equation?
A: To solve a quadratic equation, you need to use the quadratic formula, which is:
x = (-b ± √(b^2 - 4ac)) / 2a
Conclusion
In this article, we have answered some frequently asked questions about algebraic expressions. We have covered topics such as the definition of an algebraic expression, the different types of algebraic expressions, and how to evaluate and simplify algebraic expressions. We have also covered topics such as the distributive property, the commutative property, and the associative property, and how to solve linear and quadratic equations. By following these tips and tricks, you can become proficient in solving algebraic expressions and apply these skills to a wide range of mathematical problems.
Additional Resources
If you are looking for additional resources to help you learn about algebraic expressions, here are some suggestions:
- Textbooks: There are many textbooks available that cover algebraic expressions in detail. Some popular textbooks include "Algebra and Trigonometry" by Michael Sullivan and "College Algebra" by James Stewart.
- Online resources: There are many online resources available that provide tutorials and examples of algebraic expressions. Some popular online resources include Khan Academy, Mathway, and Wolfram Alpha.
- Practice problems: Practice problems are an essential part of learning algebraic expressions. You can find practice problems in textbooks, online resources, or by creating your own problems.
By following these tips and tricks, and by using these additional resources, you can become proficient in solving algebraic expressions and apply these skills to a wide range of mathematical problems.