Given: A = − 1 11 B = 1 7 A = -\frac{1}{11} \quad B = \frac{1}{7} A = − 11 1 ​ B = 7 1 ​ Calculate: 11 A + 12 B 11a + 12b 11 A + 12 B

Introduction

Algebraic expressions are a fundamental concept in mathematics, and solving them is an essential skill for students and professionals alike. In this article, we will focus on calculating the value of a given algebraic expression, $11a + 12b$, where $a = -\frac{1}{11}$ and $b = \frac{1}{7}$. We will break down the solution into manageable steps, making it easy to understand and follow.

Understanding the Given Values

Before we dive into the solution, let's take a closer look at the given values of $a$ and $b$.

• Value of $a$: $a = -\frac{1}{11}$
• Value of $b$: $b = \frac{1}{7}$

These values will be used to calculate the final result of the expression $11a + 12b$.

Step 1: Multiply $11$ with $a$

To calculate the value of $11a$, we need to multiply $11$ with the value of $a$.

• Value of $a$: $a = -\frac{1}{11}$
• Multiplication: $11 \times a = 11 \times -\frac{1}{11}$
• Result: $-1$

So, the value of $11a$ is $-1$.

Step 2: Multiply $12$ with $b$

Next, we need to calculate the value of $12b$ by multiplying $12$ with the value of $b$.

• Value of $b$: $b = \frac{1}{7}$
• Multiplication: $12 \times b = 12 \times \frac{1}{7}$
• Result: $\frac{12}{7}$

So, the value of $12b$ is $\frac{12}{7}$.

Step 3: Add the Results of $11a$ and $12b$

Now that we have the values of $11a$ and $12b$, we can add them together to get the final result.

• Value of $11a$: $-1$
• Value of $12b$: $\frac{12}{7}$
• Addition: $-1 + \frac{12}{7}$

To add these two values, we need to find a common denominator, which is $7$ in this case.

• Equivalent fraction for $-1$: $-\frac{7}{7}$
• Addition: $-\frac{7}{7} + \frac{12}{7}$
• Result: $\frac{5}{7}$

So, the final result of the expression $11a + 12b$ is $\frac{5}{7}$.

Conclusion

In this article, we calculated the value of the algebraic expression $11a + 12b$, where $a = -\frac{1}{11}$ and $b = \frac{1}{7}$. We broke down the solution into manageable steps, making it easy to understand and follow. By multiplying $11$ with $a$ and $12$ with $b$, and then adding the results, we arrived at the final answer of $\frac{5}{7}$. This problem demonstrates the importance of following the order of operations and using equivalent fractions to simplify expressions.

Frequently Asked Questions

• What is the value of $11a + 12b$?
  • The final result is $\frac{5}{7}$.
• How do I calculate the value of $11a + 12b$?
  • Multiply $11$ with $a$ and $12$ with $b$, and then add the results.
• What is the order of operations for solving algebraic expressions?
  • Follow the order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Additional Resources

• Algebraic Expressions: A comprehensive guide to algebraic expressions, including definitions, examples, and practice problems.
• Order of Operations: A detailed explanation of the order of operations, including examples and practice problems.
• Equivalent Fractions: A tutorial on equivalent fractions, including definitions, examples, and practice problems.
  Algebraic Expressions Q&A: Frequently Asked Questions =====================================================

Introduction

Algebraic expressions are a fundamental concept in mathematics, and solving them is an essential skill for students and professionals alike. In this article, we will answer some of the most frequently asked questions about algebraic expressions, including definitions, examples, and practice problems.

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 value or a relationship between values using mathematical symbols and notation.

Q: What are the basic components of an algebraic expression?

A: The basic components of an algebraic expression are:

• Variables: Letters or symbols that represent unknown values or quantities.
• Constants: Numbers that do not change value.
• Mathematical operations: Symbols that represent addition, subtraction, multiplication, and division.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, follow these steps:

1. Combine like terms: Combine terms that have the same variable and coefficient.
2. Simplify fractions: Simplify fractions by dividing the numerator and denominator by their greatest common divisor.
3. Remove parentheses: Remove parentheses by distributing the terms inside the parentheses to the terms outside.
4. Simplify exponents: Simplify exponents by applying the rules of exponents.

Q: What is the order of operations for solving algebraic expressions?

A: The order of operations for solving algebraic expressions is:

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

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, follow these steps:

1. Substitute values: Substitute the given values into the expression.
2. Simplify the expression: Simplify the expression by combining like terms, simplifying fractions, removing parentheses, and simplifying exponents.
3. Evaluate the expression: Evaluate the expression by applying the order of operations.

Q: What are some common algebraic expressions?

A: Some common algebraic expressions include:

• Linear expressions: Expressions of the form $ax + b$, where $a$ and $b$ are constants.
• Quadratic expressions: Expressions of the form $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants.
• Polynomial expressions: Expressions of the form $a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0$, where $a_n$, $a_{n-1}$, $\ldots$, $a_1$, and $a_0$ are constants.

Q: How do I graph an algebraic expression?

A: To graph an algebraic expression, follow these steps:

1. Determine the type of graph: Determine the type of graph that the expression will produce, such as a linear, quadratic, or polynomial graph.
2. Find the x-intercepts: Find the x-intercepts of the graph by setting the expression equal to zero and solving for x.
3. Find the y-intercept: Find the y-intercept of the graph by substituting x = 0 into the expression.
4. Plot the graph: Plot the graph by using the x-intercepts and y-intercept to create a graph.

Conclusion

Algebraic expressions are a fundamental concept in mathematics, and solving them is an essential skill for students and professionals alike. By understanding the basic components of an algebraic expression, simplifying expressions, and evaluating expressions, you can solve a wide range of algebraic problems. Remember to follow the order of operations and use equivalent fractions to simplify expressions. With practice and patience, you can become proficient in solving algebraic expressions and graphing them.

Frequently Asked Questions

• What is an algebraic expression?
  • An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations.
• How do I simplify an algebraic expression?
  • Combine like terms, simplify fractions, remove parentheses, and simplify exponents.
• What is the order of operations for solving algebraic expressions?
  • Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
• How do I evaluate an algebraic expression?
  • Substitute values, simplify the expression, and evaluate the expression.

Additional Resources

• Algebraic Expressions: A comprehensive guide to algebraic expressions, including definitions, examples, and practice problems.
• Order of Operations: A detailed explanation of the order of operations, including examples and practice problems.
• Graphing Algebraic Expressions: A tutorial on graphing algebraic expressions, including examples and practice problems.