Evaluate The Expression:$\[ 2 \times \frac{3}{5} + \frac{1}{5} \\]

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Introduction

In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Evaluating an expression involves simplifying it to a single value. In this article, we will evaluate the expression 2 × 3/5 + 1/5. This expression involves multiplication and addition of fractions.

Understanding the Expression

The given expression is 2 × 3/5 + 1/5. To evaluate this expression, we need to follow the order of operations (PEMDAS):

  1. Parentheses: None in this expression
  2. Exponents: None in this expression
  3. Multiplication and Division: Evaluate from left to right
  4. Addition and Subtraction: Evaluate from left to right

Evaluating the Expression

To evaluate the expression, we will follow the order of operations:

  1. Multiply 2 and 3/5: 2×35=2×35=65{ 2 \times \frac{3}{5} = \frac{2 \times 3}{5} = \frac{6}{5} }

  2. Add 1/5 to the result: 65+15=6+15=75{ \frac{6}{5} + \frac{1}{5} = \frac{6 + 1}{5} = \frac{7}{5} }

Simplifying the Result

The result of the expression is 7/5. This fraction can be simplified further by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 1.

Conclusion

In conclusion, the expression 2 × 3/5 + 1/5 can be evaluated by following the order of operations. The result of the expression is 7/5, which cannot be simplified further.

Real-World Applications

Evaluating expressions like 2 × 3/5 + 1/5 is essential in various real-world applications, such as:

  • Finance: When calculating interest rates or investment returns, expressions involving fractions and multiplication are common.
  • Science: In physics and engineering, expressions involving fractions and multiplication are used to calculate quantities like velocity, acceleration, and force.
  • Everyday Life: When shopping or cooking, expressions involving fractions and multiplication are used to calculate quantities like prices and ingredient ratios.

Tips and Tricks

Here are some tips and tricks to help you evaluate expressions like 2 × 3/5 + 1/5:

  • Use a calculator: If you're struggling to evaluate an expression, use a calculator to check your work.
  • Simplify fractions: Before evaluating an expression, simplify any fractions in the expression.
  • Follow the order of operations: Always follow the order of operations (PEMDAS) when evaluating an expression.

Common Mistakes

Here are some common mistakes to avoid when evaluating expressions like 2 × 3/5 + 1/5:

  • 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 make it difficult to evaluate an expression.
  • Not using a calculator: Failing to use a calculator can lead to errors in calculation.

Final Thoughts

Evaluating expressions like 2 × 3/5 + 1/5 is an essential skill in mathematics. By following the order of operations and simplifying fractions, you can evaluate expressions accurately and efficiently. Remember to use a calculator when necessary and avoid common mistakes like not following the order of operations. With practice and patience, you'll become proficient in evaluating expressions like a pro!

Introduction

In our previous article, we evaluated the expression 2 × 3/5 + 1/5. In this article, we will answer some frequently asked questions (FAQs) related to evaluating expressions like this one.

Q&A

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when evaluating an expression. The order of operations 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 fractions?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator. Then, divide both the numerator and the denominator by the GCD.

Q: What is the difference between multiplication and addition of fractions?

A: When multiplying fractions, you multiply the numerators and denominators separately. When adding fractions, you need to find a common denominator and then add the numerators.

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 work 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
  • Not simplifying fractions
  • Not using a calculator when necessary
  • Not checking your work by hand

Q: How do I evaluate expressions with negative numbers?

A: To evaluate expressions with negative numbers, you need to follow the same order of operations as before. However, when multiplying or dividing negative numbers, you need to remember that a negative times a negative is a positive, and a negative divided by a negative is a positive.

Q: Can I use a calculator to evaluate expressions with variables?

A: Yes, you can use a calculator to evaluate expressions with variables. However, you need to make sure that the calculator is set to the correct mode (e.g., algebraic mode) and that you enter the expression correctly.

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

A: Evaluating expressions is essential in various real-world applications, such as:

  • Finance: When calculating interest rates or investment returns
  • Science: In physics and engineering, when calculating quantities like velocity, acceleration, and force
  • Everyday Life: When shopping or cooking, when calculating quantities like prices and ingredient ratios

Conclusion

Evaluating expressions like 2 × 3/5 + 1/5 is an essential skill in mathematics. By following the order of operations and simplifying fractions, you can evaluate expressions accurately and efficiently. Remember to use a calculator when necessary and avoid common mistakes like not following the order of operations. With practice and patience, you'll become proficient in evaluating expressions like a pro!

Final Thoughts

Evaluating expressions is a fundamental concept in mathematics that has numerous real-world applications. By mastering the skills of evaluating expressions, you'll be able to solve problems in finance, science, and everyday life with ease. So, keep practicing and stay confident in your ability to evaluate expressions like a pro!