Multiply the fraction by 4

Oct 13, 2025 by miodeya.com 22 views

$Multiply the fraction by 4$

Introduction to Algebraic Manipulation

Algebraic manipulation is a crucial aspect of mathematics, and it involves simplifying complex expressions to make them easier to understand and work with. In this article, we will focus on simplifying the expression: $a - 4 \cdot \frac{21}{2}$ . This expression involves basic arithmetic operations, fractions, and variables, making it an ideal candidate for algebraic manipulation.

Understanding the Expression

Before we dive into simplifying the expression, let's break it down and understand its components. The expression consists of three main parts:

Variable: The variable $a$ represents an unknown value.
Fraction: The fraction $\frac{21}{2}$ represents a ratio of two numbers.
Multiplication: The multiplication operation $4 \cdot \frac{21}{2}$ involves multiplying a number by a fraction.

Simplifying the Fraction

To simplify the expression, we need to start by simplifying the fraction $\frac{21}{2}$ . We can do this by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 21 and 2 is 1, so the fraction is already in its simplest form.

Multiplying the Fraction by 4

Now that we have simplified the fraction, we can multiply it by 4. To do this, we need to multiply the numerator (21) by 4 and keep the denominator (2) the same.

Simplifying the Expression

Now that we have multiplied the fraction by 4, we can simplify the expression by combining the variable $a$ with the result of the multiplication.

Step-by-Step Solution

Here's a step-by-step solution to simplify the expression:

Simplify the fraction: The fraction $\frac{21}{2}$ is already in its simplest form.
Multiply the fraction by 4: Multiply the numerator (21) by 4 to get 84, and keep the denominator (2) the same.
Simplify the expression: Combine the variable $a$ with the result of the multiplication: $a - 4 \cdot \frac{21}{2} = a - 84$ .

Final Answer

The final answer to the expression $a - 4 \cdot \frac{21}{2}$ is $a - 84$ .

Conclusion

Simplifying algebraic expressions is an essential skill in mathematics, and it involves breaking down complex expressions into simpler components. In this article, we simplified the expression $a - 4 \cdot \frac{21}{2}$ by breaking it down into its components, simplifying the fraction, multiplying the fraction by 4, and combining the variable with the result of the multiplication. The final answer is $a - 84$ .

Frequently Asked Questions

What is algebraic manipulation?: Algebraic manipulation is the process of simplifying complex expressions to make them easier to understand and work with.
How do I simplify a fraction?: To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD).
How do I multiply a fraction by a number?: To multiply a fraction by a number, multiply the numerator by the number and keep the denominator the same.

Additional Resources

Algebraic Manipulation Tutorial: This tutorial provides a comprehensive guide to algebraic manipulation, including simplifying fractions, multiplying fractions, and combining variables.
Mathematics Glossary: This glossary provides definitions for key mathematical terms, including algebraic manipulation, fractions, and variables.

References

Algebraic Manipulation: This article provides a detailed explanation of algebraic manipulation, including its importance and applications.
Simplifying Fractions: This article provides a step-by-step guide to simplifying fractions, including dividing both the numerator and the denominator by their GCD.

Simplifying Algebraic Expressions: This article provides a comprehensive guide to simplifying algebraic expressions, including combining variables, simplifying fractions, and multiplying fractions.
Algebraic Manipulation Techniques: This article provides a detailed explanation of algebraic manipulation techniques, including simplifying fractions, multiplying fractions, and combining variables.

Introduction

Algebraic manipulation is a crucial aspect of mathematics, and it involves simplifying complex expressions to make them easier to understand and work with. In this article, we will provide answers to frequently asked questions about algebraic manipulation, including simplifying fractions, multiplying fractions, and combining variables.

Q&A: Algebraic Manipulation

Q: What is algebraic manipulation?

A: Algebraic manipulation is the process of simplifying complex expressions to make them easier to understand and work with. It involves breaking down complex expressions into simpler components, such as fractions, variables, and constants.

Q: How do I simplify a fraction?

A: To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD). For example, to simplify the fraction $\frac{12}{18}$ , divide both the numerator and the denominator by 6 to get $\frac{2}{3}$ .

Q: How do I multiply a fraction by a number?

A: To multiply a fraction by a number, multiply the numerator by the number and keep the denominator the same. For example, to multiply the fraction $\frac{3}{4}$ by 2, multiply the numerator by 2 to get $\frac{6}{4}$ , which can be simplified to $\frac{3}{2}$ .

Q: How do I combine variables?

A: To combine variables, add or subtract the variables as if they were numbers. For example, to combine the variables $x$ and $y$ , add them together to get $x + y$ .

Q: What is the order of operations in algebraic manipulation?

A: The order of operations in algebraic manipulation 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 an expression with multiple variables?

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

Combine like terms: Combine any like terms in the expression.
Simplify fractions: Simplify any fractions in the expression.
Combine variables: Combine any variables in the expression.
Simplify the expression: Simplify the expression by combining any remaining terms.

Q: What are some common algebraic manipulation techniques?

A: Some common algebraic manipulation techniques include:

Simplifying fractions: Simplifying fractions by dividing both the numerator and the denominator by their GCD.
Multiplying fractions: Multiplying fractions by multiplying the numerator by the number and keeping the denominator the same.
Combining variables: Combining variables by adding or subtracting them as if they were numbers.
Simplifying expressions: Simplifying expressions by combining like terms, simplifying fractions, and combining variables.

Conclusion

Algebraic manipulation is a crucial aspect of mathematics, and it involves simplifying complex expressions to make them easier to understand and work with. In this article, we provided answers to frequently asked questions about algebraic manipulation, including simplifying fractions, multiplying fractions, and combining variables. By following these steps and techniques, you can simplify complex expressions and make them easier to work with.

Frequently Asked Questions

What is algebraic manipulation?
How do I simplify a fraction?
How do I multiply a fraction by a number?
How do I combine variables?
What is the order of operations in algebraic manipulation?
How do I simplify an expression with multiple variables?
What are some common algebraic manipulation techniques?

Additional Resources

Algebraic Manipulation Tutorial: This tutorial provides a comprehensive guide to algebraic manipulation, including simplifying fractions, multiplying fractions, and combining variables.
Mathematics Glossary: This glossary provides definitions for key mathematical terms, including algebraic manipulation, fractions, and variables.
Algebraic Manipulation Techniques: This article provides a detailed explanation of algebraic manipulation techniques, including simplifying fractions, multiplying fractions, and combining variables.

References

Algebraic Manipulation: This article provides a detailed explanation of algebraic manipulation, including its importance and applications.
Simplifying Fractions: This article provides a step-by-step guide to simplifying fractions, including dividing both the numerator and the denominator by their GCD.
Multiplying Fractions: This article provides a step-by-step guide to multiplying fractions, including multiplying the numerator by the number and keeping the denominator the same.