Simplify The Expression:$\[ \frac{5-3}{7-4} \\]$\[ \frac{5-3}{7-4} = \square \\](Type An Integer Or A Fraction. Simplify Your Answer.)

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Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently. It involves reducing complex expressions to their simplest form, making it easier to understand and work with. In this article, we will focus on simplifying the expression 5−37−4\frac{5-3}{7-4}.

Understanding the Expression

The given expression is 5−37−4\frac{5-3}{7-4}. To simplify this expression, we need to follow the order of operations (PEMDAS):

  1. Evaluate the expressions inside the parentheses.
  2. Simplify the fraction.

Evaluating Expressions Inside Parentheses

Let's start by evaluating the expressions inside the parentheses:

5−37−4=23\frac{5-3}{7-4} = \frac{2}{3}

Simplifying the Fraction

Now that we have evaluated the expressions inside the parentheses, we can simplify the fraction:

23\frac{2}{3}

Why Simplify the Expression?

Simplifying the expression 5−37−4\frac{5-3}{7-4} is important because it helps us:

  • Reduce complexity: Simplifying the expression reduces its complexity, making it easier to understand and work with.
  • Improve accuracy: Simplifying the expression helps us avoid errors that can occur when working with complex expressions.
  • Enhance problem-solving skills: Simplifying the expression is a crucial skill that helps us solve problems efficiently.

Real-World Applications

Simplifying expressions has numerous real-world applications, including:

  • Science and engineering: Simplifying expressions is essential in science and engineering, where complex calculations are often involved.
  • Finance: Simplifying expressions is crucial in finance, where complex financial calculations are often required.
  • Computer programming: Simplifying expressions is essential in computer programming, where complex algorithms are often involved.

Conclusion

In conclusion, simplifying the expression 5−37−4\frac{5-3}{7-4} is a crucial skill that helps us solve problems efficiently. By following the order of operations and simplifying the fraction, we can reduce the complexity of the expression and improve accuracy. Simplifying expressions has numerous real-world applications, including science and engineering, finance, and computer programming.

Frequently Asked Questions

Q: Why is simplifying expressions important?

A: Simplifying expressions is important because it helps us reduce complexity, improve accuracy, and enhance problem-solving skills.

Q: How do I simplify an expression?

A: To simplify an expression, follow the order of operations (PEMDAS) and simplify the fraction.

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

A: Simplifying expressions has numerous real-world applications, including science and engineering, finance, and computer programming.

Final Answer

The final answer is: 23\boxed{\frac{2}{3}}

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Introduction

In our previous article, we discussed how to simplify the expression 5−37−4\frac{5-3}{7-4}. In this article, we will provide a Q&A guide to help you understand the concept of simplifying expressions better.

Q&A Guide

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that helps us evaluate mathematical expressions in the correct order. PEMDAS stands for:

  • 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 a fraction?

A: To simplify a fraction, follow these steps:

  1. Find the greatest common divisor (GCD): Find the greatest common divisor of the numerator and denominator.
  2. Divide both numbers by the GCD: Divide both the numerator and denominator by the GCD.
  3. Simplify the fraction: The resulting fraction is the simplified form of the original fraction.

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

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

  • Not following the order of operations: Failing to follow the order of operations can lead to incorrect results.
  • Not simplifying fractions: Failing to simplify fractions can lead to complex and difficult-to-work-with expressions.
  • Not checking for errors: Failing to check for errors can lead to incorrect results.

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

A: To determine if an expression is already simplified, follow these steps:

  1. Check for any common factors: Check if the numerator and denominator have any common factors.
  2. Simplify the fraction: If there are any common factors, simplify the fraction by dividing both numbers by the common factor.
  3. Check if the fraction is in its simplest form: If the fraction cannot be simplified further, it is in its simplest form.

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

A: Simplifying expressions has numerous real-world applications, including:

  • Science and engineering: Simplifying expressions is essential in science and engineering, where complex calculations are often involved.
  • Finance: Simplifying expressions is crucial in finance, where complex financial calculations are often required.
  • Computer programming: Simplifying expressions is essential in computer programming, where complex algorithms are often involved.

Conclusion

In conclusion, simplifying expressions is a crucial skill that helps us solve problems efficiently. By following the order of operations and simplifying fractions, we can reduce the complexity of expressions and improve accuracy. This Q&A guide provides a comprehensive overview of the concept of simplifying expressions and helps you understand the common mistakes to avoid.

Frequently Asked Questions

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

A: Simplifying an expression involves reducing it to its simplest form, while evaluating an expression involves finding its value.

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

A: To determine if an expression is already simplified, check for any common factors and simplify the fraction.

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

A: Some common mistakes to avoid when simplifying expressions include not following the order of operations, not simplifying fractions, and not checking for errors.

Final Answer

The final answer is: 23\boxed{\frac{2}{3}}