Simplify 3 4 X − 1 3 X \frac{3}{4}x - \frac{1}{3}x 4 3 ​ X − 3 1 ​ X .A. 2 3 X \frac{2}{3}x 3 2 ​ X B. 5 12 X \frac{5}{12}x 12 5 ​ X C. 3 5 X \frac{3}{5}x 5 3 ​ X D. 2 12 \frac{2}{12} 12 2 ​

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for students and professionals alike. In this article, we will focus on simplifying a specific algebraic expression, $\frac{3}{4}x - \frac{1}{3}x$. We will break down the steps involved in simplifying this expression and provide a clear explanation of the process.

Understanding the Expression

The given expression is $\frac{3}{4}x - \frac{1}{3}x$. This expression consists of two terms, each of which is a fraction multiplied by a variable $x$. To simplify this expression, we need to find a common denominator for the two fractions.

Finding a Common Denominator

A common denominator is the least common multiple (LCM) of the denominators of the two fractions. In this case, the denominators are 4 and 3. The LCM of 4 and 3 is 12.

Rewriting the Expression with a Common Denominator

To rewrite the expression with a common denominator, we need to multiply the numerator and denominator of each fraction by the necessary factors. For the first fraction, we need to multiply the numerator and denominator by 3, and for the second fraction, we need to multiply the numerator and denominator by 4.

$\frac{3}{4}x - \frac{1}{3}x = \frac{3 \cdot 3}{4 \cdot 3}x - \frac{1 \cdot 4}{3 \cdot 4}x$

Simplifying the fractions, we get:

$\frac{9}{12}x - \frac{4}{12}x$

Combining Like Terms

Now that we have a common denominator, we can combine the two fractions by adding or subtracting their numerators.

$\frac{9}{12}x - \frac{4}{12}x = \frac{9 - 4}{12}x$

Simplifying the numerator, we get:

$\frac{5}{12}x$

Conclusion

In conclusion, the simplified form of the expression $\frac{3}{4}x - \frac{1}{3}x$ is $\frac{5}{12}x$. This expression is a simplified version of the original expression, and it is easier to work with than the original expression.

Answer

The correct answer is B. $\frac{5}{12}x$.

Tips and Tricks

• When simplifying algebraic expressions, it is essential to find a common denominator for the fractions.
• Use the least common multiple (LCM) of the denominators to find the common denominator.
• Multiply the numerator and denominator of each fraction by the necessary factors to rewrite the expression with a common denominator.
• Combine like terms by adding or subtracting the numerators.

Common Mistakes

• Failing to find a common denominator for the fractions.
• Not multiplying the numerator and denominator of each fraction by the necessary factors.
• Not combining like terms.

Real-World Applications

Simplifying algebraic expressions is an essential skill in many real-world applications, including:

• Physics: Simplifying algebraic expressions is crucial in physics, where equations often involve fractions and variables.
• Engineering: Engineers use algebraic expressions to model and analyze complex systems.
• Economics: Economists use algebraic expressions to model and analyze economic systems.

Conclusion

Introduction

In our previous article, we discussed the steps involved in simplifying algebraic expressions. In this article, we will provide a Q&A guide to help you better understand the concepts and techniques involved in simplifying algebraic expressions.

Q: What is the first step in simplifying an algebraic expression?

A: The first step in simplifying an algebraic expression is to identify the like terms. Like terms are terms that have the same variable raised to the same power.

Q: How do I identify like terms?

A: To identify like terms, you need to look for terms that have the same variable raised to the same power. For example, in the expression $2x + 3x$, the terms $2x$ and $3x$ are like terms because they both have the variable $x$ raised to the power of 1.

Q: What is the next step in simplifying an algebraic expression?

A: The next step in simplifying an algebraic expression is to combine the like terms. To combine like terms, you need to add or subtract their coefficients.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract their coefficients. For example, in the expression $2x + 3x$, the coefficients are 2 and 3. To combine these terms, you need to add their coefficients: $2 + 3 = 5$. Therefore, the simplified expression is $5x$.

Q: What is the role of the distributive property in simplifying algebraic expressions?

A: The distributive property is a fundamental concept in algebra that allows you to multiply a single term by multiple terms. The distributive property is used to simplify algebraic expressions by multiplying a single term by multiple terms.

Q: How do I use the distributive property to simplify an algebraic expression?

A: To use the distributive property to simplify an algebraic expression, you need to multiply a single term by multiple terms. For example, in the expression $2(x + 3)$, you need to multiply the term $2$ by the terms $x$ and $3$. Therefore, the simplified expression is $2x + 6$.

Q: What is the role of the commutative property in simplifying algebraic expressions?

A: The commutative property is a fundamental concept in algebra that allows you to rearrange the order of terms in an expression. The commutative property is used to simplify algebraic expressions by rearranging the order of terms.

Q: How do I use the commutative property to simplify an algebraic expression?

A: To use the commutative property to simplify an algebraic expression, you need to rearrange the order of terms in the expression. For example, in the expression $x + 3$, you can rearrange the order of terms to get $3 + x$.

Q: What is the role of the associative property in simplifying algebraic expressions?

A: The associative property is a fundamental concept in algebra that allows you to regroup terms in an expression. The associative property is used to simplify algebraic expressions by regrouping terms.

Q: How do I use the associative property to simplify an algebraic expression?

A: To use the associative property to simplify an algebraic expression, you need to regroup terms in the expression. For example, in the expression $(x + 2) + 3$, you can regroup the terms to get $x + (2 + 3)$.

Conclusion

In conclusion, simplifying algebraic expressions is an essential skill that requires attention to detail and a clear understanding of the concepts involved. By following the steps outlined in this article, you can simplify complex algebraic expressions and make them easier to work with.

Common Mistakes

• Failing to identify like terms.
• Not combining like terms.
• Not using the distributive property to simplify expressions.
• Not using the commutative property to simplify expressions.
• Not using the associative property to simplify expressions.

Real-World Applications

Simplifying algebraic expressions is an essential skill in many real-world applications, including:

• Physics: Simplifying algebraic expressions is crucial in physics, where equations often involve fractions and variables.
• Engineering: Engineers use algebraic expressions to model and analyze complex systems.
• Economics: Economists use algebraic expressions to model and analyze economic systems.

Tips and Tricks

• Always identify like terms before combining them.
• Use the distributive property to simplify expressions.
• Use the commutative property to simplify expressions.
• Use the associative property to simplify expressions.
• Practice simplifying algebraic expressions to become proficient in the skill.