Evaluate The Expression: \[$\frac{2}{4} \times \frac{2}{6}\$\].

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Introduction

In mathematics, evaluating expressions is a fundamental concept that involves simplifying mathematical expressions by performing operations such as addition, subtraction, multiplication, and division. In this article, we will evaluate the expression 24×26\frac{2}{4} \times \frac{2}{6}, which involves multiplying two fractions together. We will break down the steps involved in evaluating this expression and provide a clear explanation of the process.

Understanding the Expression

The given expression is 24×26\frac{2}{4} \times \frac{2}{6}. To evaluate this expression, we need to understand the concept of multiplying fractions. When we multiply two fractions together, we multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom).

Multiplying Fractions

To multiply fractions, we follow these steps:

  1. Multiply the numerators together.
  2. Multiply the denominators together.
  3. Simplify the resulting fraction, if possible.

Evaluating the Expression

Now, let's apply these steps to evaluate the expression 24×26\frac{2}{4} \times \frac{2}{6}.

Step 1: Multiply the Numerators

The numerators are 2 and 2. Multiplying them together, we get:

2 × 2 = 4

Step 2: Multiply the Denominators

The denominators are 4 and 6. Multiplying them together, we get:

4 × 6 = 24

Step 3: Simplify the Resulting Fraction

Now, we have the fraction 424\frac{4}{24}. To simplify this fraction, we need to find the greatest common divisor (GCD) of 4 and 24. The GCD of 4 and 24 is 4.

To simplify the fraction, we divide both the numerator and the denominator by the GCD:

424=4÷424÷4=16\frac{4}{24} = \frac{4 ÷ 4}{24 ÷ 4} = \frac{1}{6}

Conclusion

In conclusion, the expression 24×26\frac{2}{4} \times \frac{2}{6} evaluates to 16\frac{1}{6}. We followed the steps involved in multiplying fractions, which included multiplying the numerators and denominators together and simplifying the resulting fraction.

Importance of Evaluating Expressions

Evaluating expressions is an essential skill in mathematics, as it allows us to simplify complex mathematical expressions and solve problems more efficiently. In this article, we evaluated the expression 24×26\frac{2}{4} \times \frac{2}{6}, which involved multiplying two fractions together. By following the steps involved in multiplying fractions, we were able to simplify the expression and arrive at the final answer.

Real-World Applications

Evaluating expressions has numerous real-world applications in fields such as science, engineering, and finance. For example, in physics, evaluating expressions is used to calculate quantities such as distance, velocity, and acceleration. In engineering, evaluating expressions is used to design and optimize systems such as bridges, buildings, and electronic circuits. In finance, evaluating expressions is used to calculate quantities such as interest rates, investment returns, and stock prices.

Tips for Evaluating Expressions

Here are some tips for evaluating expressions:

  • Always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).
  • Simplify fractions by finding the greatest common divisor (GCD) of the numerator and denominator.
  • Use a calculator to check your answers, if necessary.
  • Practice, practice, practice! The more you practice evaluating expressions, the more comfortable you will become with the process.

Common Mistakes to Avoid

Here are some common mistakes to avoid when evaluating expressions:

  • Not following the order of operations (PEMDAS).
  • Not simplifying fractions.
  • Not using a calculator to check your answers.
  • Not practicing regularly.

Conclusion

In conclusion, evaluating expressions is an essential skill in mathematics that involves simplifying mathematical expressions by performing operations such as addition, subtraction, multiplication, and division. In this article, we evaluated the expression 24×26\frac{2}{4} \times \frac{2}{6}, which involved multiplying two fractions together. By following the steps involved in multiplying fractions, we were able to simplify the expression and arrive at the final answer. We also discussed the importance of evaluating expressions, provided tips for evaluating expressions, and identified common mistakes to avoid.

Introduction

In our previous article, we evaluated the expression 24×26\frac{2}{4} \times \frac{2}{6}, which involved multiplying two fractions together. In this article, we will answer some frequently asked questions (FAQs) about evaluating expressions.

Q&A

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

A: The order of operations is PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. This means that you should evaluate expressions inside parentheses first, followed by exponents, then multiplication and division, and finally addition and subtraction.

Q: How do I simplify fractions when evaluating expressions?

A: To simplify fractions, you need to find the greatest common divisor (GCD) of the numerator and denominator. Once you have found the GCD, you can divide both the numerator and denominator by the GCD to simplify the fraction.

Q: What is the difference between multiplying and dividing fractions?

A: When multiplying fractions, you multiply the numerators together and multiply the denominators together. When dividing fractions, you invert the second fraction (i.e., flip the numerator and denominator) and then multiply the fractions together.

Q: Can I use a calculator to evaluate expressions?

A: Yes, you can use a calculator to evaluate expressions. However, it's always a good idea to check your answers by hand to make sure you understand the process.

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

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

  • Not following the order of operations (PEMDAS)
  • Not simplifying fractions
  • Not using a calculator to check your answers
  • Not practicing regularly

Q: How can I practice evaluating expressions?

A: There are many ways to practice evaluating expressions, including:

  • Using online resources such as Khan Academy or Mathway
  • Working with a tutor or teacher
  • Practicing with worksheets or problems
  • Using a calculator to check your answers

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

A: Evaluating expressions has numerous real-world applications in fields such as science, engineering, and finance. For example, in physics, evaluating expressions is used to calculate quantities such as distance, velocity, and acceleration. In engineering, evaluating expressions is used to design and optimize systems such as bridges, buildings, and electronic circuits. In finance, evaluating expressions is used to calculate quantities such as interest rates, investment returns, and stock prices.

Q: Can I evaluate expressions with variables?

A: Yes, you can evaluate expressions with variables. When evaluating expressions with variables, you need to follow the same steps as when evaluating expressions with numbers. However, you may need to use algebraic properties such as the distributive property or the commutative property to simplify the expression.

Q: What are some tips for evaluating expressions with variables?

A: Some tips for evaluating expressions with variables include:

  • Use algebraic properties such as the distributive property or the commutative property to simplify the expression
  • Use a calculator to check your answers
  • Practice, practice, practice! The more you practice evaluating expressions with variables, the more comfortable you will become with the process.

Conclusion

In conclusion, evaluating expressions is an essential skill in mathematics that involves simplifying mathematical expressions by performing operations such as addition, subtraction, multiplication, and division. In this article, we answered some frequently asked questions (FAQs) about evaluating expressions, including questions about the order of operations, simplifying fractions, and real-world applications. We also provided tips for evaluating expressions with variables and common mistakes to avoid.