Simplify The Following Expression:$\[ \frac{\frac{2}{5u} - \frac{1}{u}}{4} \\]

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Introduction

In this article, we will simplify the given expression, which involves fractions and algebraic manipulation. The expression is 25u−1u4\frac{\frac{2}{5u} - \frac{1}{u}}{4}. We will break down the solution into manageable steps, making it easier to understand and follow along.

Step 1: Simplify the Expression Inside the Parentheses

To simplify the expression, we first need to focus on the part inside the parentheses, which is 25u−1u\frac{2}{5u} - \frac{1}{u}. We can start by finding a common denominator for the two fractions. The common denominator is 5u5u, so we can rewrite the second fraction as 5u5u⋅1u=55u\frac{5u}{5u} \cdot \frac{1}{u} = \frac{5}{5u}.

from fractions import Fraction

# Define the variables
u = 'u'  # variable
num1 = Fraction(2, 5*u)
num2 = Fraction(1, u)

# Find the common denominator
common_denominator = 5*u

# Rewrite the second fraction
num2_rewritten = Fraction(5, common_denominator)

Step 2: Subtract the Two Fractions

Now that we have the two fractions with a common denominator, we can subtract them. The expression becomes 25u−55u=2−55u=−35u\frac{2}{5u} - \frac{5}{5u} = \frac{2-5}{5u} = \frac{-3}{5u}.

# Subtract the two fractions
result = num1 - num2_rewritten
print(result)

Step 3: Simplify the Expression

Now that we have simplified the expression inside the parentheses, we can rewrite the original expression as −35u4\frac{\frac{-3}{5u}}{4}. We can simplify this expression by multiplying the numerator and denominator by −1-1, which gives us −320u\frac{-3}{20u}.

# Simplify the expression
simplified_expression = result / 4
print(simplified_expression)

Conclusion

In this article, we simplified the given expression 25u−1u4\frac{\frac{2}{5u} - \frac{1}{u}}{4} by breaking it down into manageable steps. We found a common denominator for the two fractions inside the parentheses, subtracted them, and then simplified the resulting expression. The final simplified expression is −320u\frac{-3}{20u}.

Final Answer

The final answer is −320u\boxed{\frac{-3}{20u}}.

Related Topics

  • Simplifying expressions with fractions
  • Algebraic manipulation
  • Common denominators

Further Reading

For more information on simplifying expressions and algebraic manipulation, check out the following resources:

  • Khan Academy: Simplifying Expressions
  • Mathway: Algebraic Manipulation
  • Wolfram Alpha: Simplifying Expressions

FAQs

  • Q: What is the final simplified expression? A: The final simplified expression is −320u\frac{-3}{20u}.
  • Q: How do I simplify expressions with fractions? A: To simplify expressions with fractions, find a common denominator and then perform the necessary operations.
  • Q: What is algebraic manipulation? A: Algebraic manipulation is the process of simplifying and rearranging algebraic expressions using various techniques, such as factoring, combining like terms, and canceling common factors.

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Introduction

In this article, we will address some of the most frequently asked questions related to simplifying expressions. Whether you're a student, teacher, or simply someone looking to brush up on their math skills, this article is for you.

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

A: Simplifying an expression involves reducing it to its simplest form, often by combining like terms, canceling common factors, or rearranging the terms. Solving an expression, on the other hand, involves finding the value of the expression for a given input or variable.

Q: How do I simplify an expression with multiple fractions?

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

  1. Find a common denominator for all the fractions.
  2. Rewrite each fraction with the common denominator.
  3. Add or subtract the fractions as needed.
  4. Simplify the resulting expression.

Q: What is the order of operations when simplifying expressions?

A: The order of operations when simplifying expressions is:

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

Q: How do I simplify an expression with negative exponents?

A: To simplify an expression with negative exponents, follow these steps:

  1. Rewrite the expression with positive exponents by moving the negative exponent to the other side of the fraction.
  2. Simplify the resulting expression.

Q: What is the difference between a variable and a constant?

A: A variable is a symbol that represents a value that can change, such as x or y. A constant, on the other hand, is a value that does not change, such as 2 or 5.

Q: How do I simplify an expression with variables and constants?

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

  1. Combine like terms by adding or subtracting variables and constants with the same exponent.
  2. Simplify the resulting expression.

Q: What is the final simplified expression for the given problem?

A: The final simplified expression for the given problem is −320u\frac{-3}{20u}.

Q: How do I check my work when simplifying expressions?

A: To check your work when simplifying expressions, follow these steps:

  1. Plug in a value for the variable and evaluate the expression.
  2. Simplify the resulting expression.
  3. Compare the simplified expression to the original expression.

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

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

  • Forgetting to find a common denominator when simplifying fractions.
  • Not following the order of operations.
  • Not combining like terms.
  • Not simplifying the expression fully.

Conclusion

In this article, we addressed some of the most frequently asked questions related to simplifying expressions. Whether you're a student, teacher, or simply someone looking to brush up on their math skills, this article is for you. Remember to follow the order of operations, find a common denominator, and combine like terms to simplify expressions effectively.

Final Answer

The final answer is −320u\boxed{\frac{-3}{20u}}.

Related Topics

  • Simplifying expressions with fractions
  • Algebraic manipulation
  • Common denominators

Further Reading

For more information on simplifying expressions and algebraic manipulation, check out the following resources:

  • Khan Academy: Simplifying Expressions
  • Mathway: Algebraic Manipulation
  • Wolfram Alpha: Simplifying Expressions

FAQs

  • Q: What is the difference between simplifying and solving an expression? A: Simplifying an expression involves reducing it to its simplest form, often by combining like terms, canceling common factors, or rearranging the terms. Solving an expression, on the other hand, involves finding the value of the expression for a given input or variable.
  • Q: How do I simplify an expression with multiple fractions? A: To simplify an expression with multiple fractions, follow these steps: Find a common denominator for all the fractions, rewrite each fraction with the common denominator, add or subtract the fractions as needed, and simplify the resulting expression.
  • Q: What is the order of operations when simplifying expressions? A: The order of operations when simplifying expressions is: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.