Calculate The Following Expression: $\[ 6.89 \times 0.2 \div 0.08 \\]

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Introduction

In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Calculating expressions is an essential skill that helps us solve problems in various fields, including science, engineering, and finance. In this article, we will focus on calculating a specific expression: ${ 6.89 \times 0.2 \div 0.08 }$. We will break down the expression into smaller parts, apply the order of operations, and arrive at the final result.

Understanding the Order of Operations

The order of operations is a set of rules that helps us evaluate expressions with multiple operations. The acronym PEMDAS is commonly used to remember the order of operations:

  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.

Breaking Down the Expression

Let's break down the given expression into smaller parts:

6.89×0.2÷0.08{ 6.89 \times 0.2 \div 0.08 }

We can rewrite the expression as:

(6.89×0.2)÷0.08{ (6.89 \times 0.2) \div 0.08 }

Now, we can apply the order of operations:

  1. Evaluate the expression inside the parentheses: 6.89×0.26.89 \times 0.2
  2. Divide the result by 0.080.08

Evaluating the Expression Inside the Parentheses

To evaluate the expression inside the parentheses, we need to multiply 6.896.89 by 0.20.2:

6.89×0.2=1.378{ 6.89 \times 0.2 = 1.378 }

Dividing the Result by 0.08

Now, we need to divide the result by 0.080.08:

1.378÷0.08=17.225{ 1.378 \div 0.08 = 17.225 }

Rounding the Result

The result of the expression is 17.22517.225. However, we can round the result to a specific number of decimal places, depending on the context of the problem.

Conclusion

Calculating expressions is an essential skill in mathematics. By following the order of operations and breaking down the expression into smaller parts, we can arrive at the final result. In this article, we calculated the expression ${ 6.89 \times 0.2 \div 0.08 }$ and arrived at the result 17.22517.225. We also discussed the importance of rounding the result to a specific number of decimal places.

Real-World Applications

Calculating expressions has numerous real-world applications, including:

  • Finance: Calculating interest rates, investment returns, and loan payments.
  • Science: Calculating distances, velocities, and forces in physics and engineering.
  • Business: Calculating profits, losses, and expenses in accounting and finance.

Tips and Tricks

Here are some tips and tricks to help you calculate expressions:

  • Use parentheses: Use parentheses to group numbers and operations together, making it easier to evaluate the expression.
  • Follow the order of operations: Remember the acronym PEMDAS to evaluate expressions with multiple operations.
  • Check your work: Double-check your calculations to ensure accuracy.

Common Mistakes

Here are some common mistakes to avoid when calculating expressions:

  • Forgetting to use parentheses: Failing to use parentheses can lead to incorrect results.
  • Misapplying the order of operations: Misapplying the order of operations can lead to incorrect results.
  • Rounding errors: Rounding errors can occur when rounding the result to a specific number of decimal places.

Final Thoughts

Calculating expressions is an essential skill in mathematics. By following the order of operations and breaking down the expression into smaller parts, we can arrive at the final result. Remember to use parentheses, follow the order of operations, and check your work to ensure accuracy. With practice and patience, you can become proficient in calculating expressions and apply them to real-world problems.

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Introduction

In our previous article, we discussed how to calculate expressions using the order of operations. However, we know that practice makes perfect, and there's no better way to learn than by asking questions and getting answers. In this article, we'll provide a Q&A guide to help you understand and apply the concepts of calculating expressions.

Q&A: Calculating Expressions

Q: What is the order of operations?

A: The order of operations is a set of rules that helps us evaluate expressions with multiple operations. The acronym PEMDAS is commonly used to remember the order of operations:

  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 evaluate expressions with multiple operations?

A: To evaluate expressions with multiple operations, follow the order of operations:

  1. Evaluate expressions inside parentheses first.
  2. Evaluate any exponential expressions next.
  3. Evaluate multiplication and division operations from left to right.
  4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both operations that involve numbers, but they have different effects on the result. Multiplication involves adding a number a certain number of times, while division involves sharing a number into equal parts.

Q: How do I handle fractions in expressions?

A: Fractions can be handled in expressions by following the order of operations. When a fraction is present, evaluate the numerator and denominator separately, and then perform the operation.

Q: What is the importance of using parentheses?

A: Using parentheses is essential in expressions to group numbers and operations together, making it easier to evaluate the expression. Without parentheses, the order of operations may be unclear, leading to incorrect results.

Q: How do I round results to a specific number of decimal places?

A: To round results to a specific number of decimal places, follow these steps:

  1. Evaluate the expression.
  2. Count the number of decimal places required.
  3. Round the result to the specified number of decimal places.

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

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

  • Forgetting to use parentheses.
  • Misapplying the order of operations.
  • Rounding errors.

Conclusion

Calculating expressions is an essential skill in mathematics. By following the order of operations and breaking down the expression into smaller parts, we can arrive at the final result. Remember to use parentheses, follow the order of operations, and check your work to ensure accuracy. With practice and patience, you can become proficient in calculating expressions and apply them to real-world problems.

Real-World Applications

Calculating expressions has numerous real-world applications, including:

  • Finance: Calculating interest rates, investment returns, and loan payments.
  • Science: Calculating distances, velocities, and forces in physics and engineering.
  • Business: Calculating profits, losses, and expenses in accounting and finance.

Tips and Tricks

Here are some tips and tricks to help you calculate expressions:

  • Use parentheses: Use parentheses to group numbers and operations together, making it easier to evaluate the expression.
  • Follow the order of operations: Remember the acronym PEMDAS to evaluate expressions with multiple operations.
  • Check your work: Double-check your calculations to ensure accuracy.

Common Mistakes

Here are some common mistakes to avoid when calculating expressions:

  • Forgetting to use parentheses: Failing to use parentheses can lead to incorrect results.
  • Misapplying the order of operations: Misapplying the order of operations can lead to incorrect results.
  • Rounding errors: Rounding errors can occur when rounding the result to a specific number of decimal places.

Final Thoughts

Calculating expressions is an essential skill in mathematics. By following the order of operations and breaking down the expression into smaller parts, we can arrive at the final result. Remember to use parentheses, follow the order of operations, and check your work to ensure accuracy. With practice and patience, you can become proficient in calculating expressions and apply them to real-world problems.