Simplify The Expression: \left(4x+\frac{3}{4}\right)+\left(-3x-\frac{5}{12}\right ]

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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, which involves combining like terms and handling fractions. By the end of this guide, you will be able to simplify complex algebraic expressions with ease.

Understanding the Expression

The given expression is (4x+34)+(−3x−512)\left(4x+\frac{3}{4}\right)+\left(-3x-\frac{5}{12}\right). This expression consists of two terms, each containing a variable xx and a fraction. Our goal is to simplify this expression by combining like terms and handling the fractions.

Combining Like Terms

Like terms are terms that have the same variable raised to the same power. In this expression, we have two terms with the variable xx: 4x4x and −3x-3x. These terms are like terms because they both have the variable xx raised to the power of 1.

To combine like terms, we add or subtract the coefficients of the terms. In this case, we add the coefficients of xx: 4x+(−3x)=(4−3)x=x4x + (-3x) = (4 - 3)x = x.

Handling Fractions

The expression also contains fractions: 34\frac{3}{4} and 512\frac{5}{12}. To handle these fractions, we need to find a common denominator. The least common multiple (LCM) of 4 and 12 is 12.

We can rewrite the fraction 34\frac{3}{4} with a denominator of 12 by multiplying the numerator and denominator by 3: 34=3×34×3=912\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}.

Simplifying the Expression

Now that we have combined like terms and handled the fractions, we can simplify the expression.

(4x+34)+(−3x−512)\left(4x+\frac{3}{4}\right)+\left(-3x-\frac{5}{12}\right)

=x+912−512= x + \frac{9}{12} - \frac{5}{12}

=x+412= x + \frac{4}{12}

=x+13= x + \frac{1}{3}

Conclusion

Simplifying algebraic expressions is an essential skill for any math enthusiast. By combining like terms and handling fractions, we can simplify complex expressions and make them easier to work with. In this article, we simplified the expression (4x+34)+(−3x−512)\left(4x+\frac{3}{4}\right)+\left(-3x-\frac{5}{12}\right) and arrived at the simplified expression x+13x + \frac{1}{3}.

Tips and Tricks

  • When combining like terms, make sure to add or subtract the coefficients of the terms.
  • When handling fractions, find a common denominator and rewrite the fractions with that denominator.
  • Simplify the expression by combining like terms and handling fractions.

Real-World Applications

Simplifying algebraic expressions has many real-world applications. For example, in physics, we use algebraic expressions to describe the motion of objects. By simplifying these expressions, we can make predictions about the motion of objects and understand the underlying physics.

In engineering, we use algebraic expressions to design and optimize systems. By simplifying these expressions, we can make the systems more efficient and effective.

Final Thoughts

Simplifying algebraic expressions is a fundamental skill that has many real-world applications. By combining like terms and handling fractions, we can simplify complex expressions and make them easier to work with. Whether you are a math enthusiast or a professional in a field that uses algebraic expressions, this skill is essential for success.

Frequently Asked Questions

Q: What is the difference between like terms and unlike terms?

A: Like terms are terms that have the same variable raised to the same power. Unlike terms are terms that have different variables or variables raised to different powers.

Q: How do I find a common denominator for fractions?

A: To find a common denominator, find the least common multiple (LCM) of the denominators. Then, rewrite the fractions with that denominator.

Q: Can I simplify an expression with variables and fractions?

A: Yes, you can simplify an expression with variables and fractions by combining like terms and handling fractions.

Q: What are some real-world applications of simplifying algebraic expressions?

A: Simplifying algebraic expressions has many real-world applications, including physics, engineering, and computer science.

Q: How do I know if an expression is simplified?

A: An expression is simplified when there are no like terms that can be combined and no fractions that can be handled.

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Introduction

In our previous article, we discussed the basics of simplifying algebraic expressions. However, we know that math can be a complex and confusing subject, and sometimes it's helpful to have a Q&A guide to clarify any doubts. In this article, we will answer some of the most frequently asked questions about simplifying algebraic expressions.

Q&A

Q: What is the difference between like terms and unlike terms?

A: Like terms are terms that have the same variable raised to the same power. Unlike terms are terms that have different variables or variables raised to different powers.

Example: 2x2x and 3x3x are like terms because they both have the variable xx raised to the power of 1. However, 2x2x and 3y3y are unlike terms because they have different variables.

Q: How do I find a common denominator for fractions?

A: To find a common denominator, find the least common multiple (LCM) of the denominators. Then, rewrite the fractions with that denominator.

Example: To find the common denominator of 14\frac{1}{4} and 16\frac{1}{6}, we need to find the LCM of 4 and 6, which is 12. We can then rewrite the fractions as 312\frac{3}{12} and 212\frac{2}{12}.

Q: Can I simplify an expression with variables and fractions?

A: Yes, you can simplify an expression with variables and fractions by combining like terms and handling fractions.

Example: The expression (2x+14)+(3x−16)\left(2x+\frac{1}{4}\right)+\left(3x-\frac{1}{6}\right) can be simplified by combining like terms and handling fractions.

Q: What are some real-world applications of simplifying algebraic expressions?

A: Simplifying algebraic expressions has many real-world applications, including:

  • Physics: Algebraic expressions are used to describe the motion of objects.
  • Engineering: Algebraic expressions are used to design and optimize systems.
  • Computer Science: Algebraic expressions are used to write algorithms and solve problems.

Q: How do I know if an expression is simplified?

A: An expression is simplified when there are no like terms that can be combined and no fractions that can be handled.

Example: The expression 2x+3y2x+3y is not simplified because it contains unlike terms. However, the expression x+3yx+3y is simplified because it contains only one variable.

Q: Can I simplify an expression with negative coefficients?

A: Yes, you can simplify an expression with negative coefficients by combining like terms and handling fractions.

Example: The expression (−2x+14)+(3x−16)\left(-2x+\frac{1}{4}\right)+\left(3x-\frac{1}{6}\right) can be simplified by combining like terms and handling fractions.

Q: How do I handle fractions with different signs?

A: To handle fractions with different signs, find a common denominator and rewrite the fractions with that denominator.

Example: To handle the fractions 14\frac{1}{4} and −16-\frac{1}{6}, we need to find a common denominator, which is 12. We can then rewrite the fractions as 312\frac{3}{12} and −212-\frac{2}{12}.

Q: Can I simplify an expression with variables and exponents?

A: Yes, you can simplify an expression with variables and exponents by combining like terms and handling fractions.

Example: The expression (2x2+14)+(3x2−16)\left(2x^2+\frac{1}{4}\right)+\left(3x^2-\frac{1}{6}\right) can be simplified by combining like terms and handling fractions.

Conclusion

Simplifying algebraic expressions is an essential skill for any math enthusiast. By understanding the basics of simplifying expressions, you can tackle complex problems with confidence. In this Q&A guide, we have answered some of the most frequently asked questions about simplifying algebraic expressions.

Tips and Tricks

  • When combining like terms, make sure to add or subtract the coefficients of the terms.
  • When handling fractions, find a common denominator and rewrite the fractions with that denominator.
  • Simplify the expression by combining like terms and handling fractions.

Final Thoughts

Simplifying algebraic expressions is a fundamental skill that has many real-world applications. By combining like terms and handling fractions, you can simplify complex expressions and make them easier to work with. Whether you are a math enthusiast or a professional in a field that uses algebraic expressions, this skill is essential for success.

Frequently Asked Questions (FAQs)

Q: What is the difference between like terms and unlike terms?

A: Like terms are terms that have the same variable raised to the same power. Unlike terms are terms that have different variables or variables raised to different powers.

Q: How do I find a common denominator for fractions?

A: To find a common denominator, find the least common multiple (LCM) of the denominators. Then, rewrite the fractions with that denominator.

Q: Can I simplify an expression with variables and fractions?

A: Yes, you can simplify an expression with variables and fractions by combining like terms and handling fractions.

Q: What are some real-world applications of simplifying algebraic expressions?

A: Simplifying algebraic expressions has many real-world applications, including physics, engineering, and computer science.

Q: How do I know if an expression is simplified?

A: An expression is simplified when there are no like terms that can be combined and no fractions that can be handled.

Q: Can I simplify an expression with negative coefficients?

A: Yes, you can simplify an expression with negative coefficients by combining like terms and handling fractions.

Q: How do I handle fractions with different signs?

A: To handle fractions with different signs, find a common denominator and rewrite the fractions with that denominator.

Q: Can I simplify an expression with variables and exponents?

A: Yes, you can simplify an expression with variables and exponents by combining like terms and handling fractions.