Write $\frac{4 K M^2}{12 K}$ In Simplest Form:A. $\frac{4 K M^2}{3 K}$ B. \$\frac{2 M^2}{6}$[/tex\] C. $\frac{1}{3}$ D. $\frac{m^2}{3}$

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for any math enthusiast. In this article, we will focus on simplifying a specific algebraic expression, $\frac{4 k m^2}{12 k}$, and explore the different options provided.

Understanding the Expression

Before we dive into simplifying the expression, let's break it down and understand its components. The expression consists of two parts: the numerator and the denominator. The numerator is $4 k m^2$, and the denominator is $12 k$.

Simplifying the Expression

To simplify the expression, we need to find the greatest common factor (GCF) of the numerator and the denominator. The GCF is the largest number that divides both the numerator and the denominator without leaving a remainder.

In this case, the GCF of $4 k m^2$ and $12 k$ is $4 k$. We can simplify the expression by dividing both the numerator and the denominator by the GCF.

4km212k=4km2÷4k12k÷4k=m23k\frac{4 k m^2}{12 k} = \frac{4 k m^2 \div 4 k}{12 k \div 4 k} = \frac{m^2}{3 k}

Analyzing the Options

Now that we have simplified the expression, let's analyze the options provided:

  • A. $\frac{4 k m^2}{3 k}$
  • B. $\frac{2 m^2}{6}$
  • C. $\frac{1}{3}$
  • D. $\frac{m^2}{3}$

Option A: $\frac{4 k m^2}{3 k}$

Option A is incorrect because we simplified the expression to $\frac{m^2}{3 k}$, not $\frac{4 k m^2}{3 k}$.

Option B: $\frac{2 m^2}{6}$

Option B is incorrect because we simplified the expression to $\frac{m^2}{3 k}$, not $\frac{2 m^2}{6}$.

Option C: $\frac{1}{3}$

Option C is incorrect because we simplified the expression to $\frac{m^2}{3 k}$, not $\frac{1}{3}$.

Option D: $\frac{m^2}{3}$

Option D is correct because we simplified the expression to $\frac{m^2}{3 k}$, which can be further simplified to $\frac{m^2}{3}$ by canceling out the common factor of $k$.

Conclusion

In conclusion, the correct answer is D. $\frac{m^2}{3}$. Simplifying algebraic expressions is an essential skill in mathematics, and understanding the concept of greatest common factor (GCF) is crucial in simplifying expressions.

Tips and Tricks

  • Always look for the greatest common factor (GCF) of the numerator and the denominator.
  • Simplify the expression by dividing both the numerator and the denominator by the GCF.
  • Cancel out common factors to simplify the expression further.

Practice Problems

  • Simplify the expression $\frac{6 x^2 y}{12 x y}$.
  • Simplify the expression $\frac{9 a^2 b}{27 a b}$.
  • Simplify the expression $\frac{4 m^2 n}{8 m n}$.

References

About the Author

Introduction

In our previous article, we explored the concept of simplifying algebraic expressions and provided a step-by-step guide on how to simplify the expression $\frac{4 k m^2}{12 k}$. In this article, we will answer some frequently asked questions (FAQs) related to simplifying algebraic expressions.

Q&A

Q: What is the greatest common factor (GCF)?

A: The greatest common factor (GCF) is the largest number that divides both the numerator and the denominator of an algebraic expression without leaving a remainder.

Q: How do I find the GCF of two numbers?

A: To find the GCF of two numbers, you can list the factors of each number and find the greatest common factor. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, and the factors of 18 are 1, 2, 3, 6, 9, and 18. The greatest common factor of 12 and 18 is 6.

Q: Can I simplify an algebraic expression by canceling out common factors?

A: Yes, you can simplify an algebraic expression by canceling out common factors. For example, if you have the expression $\frac{6 x^2 y}{12 x y}$, you can cancel out the common factor of 6 to simplify the expression to $\frac{x^2 y}{2 x y}$.

Q: What is the difference between simplifying an algebraic expression and factoring an algebraic expression?

A: Simplifying an algebraic expression involves canceling out common factors to reduce the expression to its simplest form. Factoring an algebraic expression involves expressing the expression as a product of simpler expressions.

Q: Can I simplify an algebraic expression with variables?

A: Yes, you can simplify an algebraic expression with variables. For example, if you have the expression $\frac{4 k m^2}{12 k}$, you can simplify the expression by canceling out the common factor of 4k to get $\frac{m^2}{3}$.

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

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

  • Not canceling out common factors
  • Not simplifying the expression to its simplest form
  • Not checking for common factors in the numerator and denominator

Tips and Tricks

  • Always look for the greatest common factor (GCF) of the numerator and the denominator.
  • Simplify the expression by canceling out common factors.
  • Check for common factors in the numerator and denominator.
  • Simplify the expression to its simplest form.

Practice Problems

  • Simplify the expression $\frac{9 a^2 b}{27 a b}$.
  • Simplify the expression $\frac{4 m^2 n}{8 m n}$.
  • Simplify the expression $\frac{6 x^2 y}{12 x y}$.

References

About the Author

The author is a mathematics enthusiast with a passion for simplifying algebraic expressions. They have a strong background in mathematics and enjoy sharing their knowledge with others.