Evaluate $6 \frac{2}{5} \div 2 \frac{6}{7}$.$6 \frac{2}{5} \div 2 \frac{6}{7} = $Enter Your Next Step Here.

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Introduction to Mixed Numbers and Division

In mathematics, mixed numbers are a combination of a whole number and a fraction. They are often used to represent quantities that have both a whole and a fractional part. The division of mixed numbers is a bit more complex than the division of whole numbers or fractions, but it can be simplified using a step-by-step approach.

To evaluate the expression $6 \frac{2}{5} \div 2 \frac{6}{7}$, we need to follow the order of operations (PEMDAS) and convert the mixed numbers to improper fractions. This will allow us to perform the division and simplify the expression.

Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, we need to multiply the whole number by the denominator and then add the numerator. The result is then written as a fraction with the original denominator.

For example, to convert the mixed number $6 \frac{2}{5}$ to an improper fraction, we multiply the whole number (6) by the denominator (5) and add the numerator (2):

6×5=306 \times 5 = 30

30+2=3230 + 2 = 32

So, the improper fraction equivalent of $6 \frac{2}{5}$ is $\frac{32}{5}$.

Similarly, to convert the mixed number $2 \frac{6}{7}$ to an improper fraction, we multiply the whole number (2) by the denominator (7) and add the numerator (6):

2×7=142 \times 7 = 14

14+6=2014 + 6 = 20

So, the improper fraction equivalent of $2 \frac{6}{7}$ is $\frac{20}{7}$.

Dividing Improper Fractions

Now that we have converted the mixed numbers to improper fractions, we can perform the division.

To divide two fractions, we need to invert the second fraction (i.e., flip the numerator and denominator) and then multiply the two fractions.

So, to evaluate the expression $\frac{32}{5} \div \frac{20}{7}$, we invert the second fraction and multiply:

325×720\frac{32}{5} \times \frac{7}{20}

Multiplying Fractions

To multiply two fractions, we need to multiply the numerators and denominators separately.

So, to evaluate the expression $\frac{32}{5} \times \frac{7}{20}$, we multiply the numerators and denominators:

32×75×20\frac{32 \times 7}{5 \times 20}

Simplifying the Expression

Now that we have multiplied the fractions, we can simplify the expression by dividing the numerator and denominator by their greatest common divisor (GCD).

The GCD of 224 and 100 is 4, so we can divide both the numerator and denominator by 4:

224÷4100÷4\frac{224 \div 4}{100 \div 4}

5625\frac{56}{25}

Conclusion

In conclusion, to evaluate the expression $6 \frac{2}{5} \div 2 \frac{6}{7}$, we need to convert the mixed numbers to improper fractions, perform the division, and simplify the expression.

By following the order of operations and using the steps outlined above, we can simplify the expression and arrive at the final answer.

Final Answer

The final answer is: 5625\boxed{\frac{56}{25}}

Introduction

Evaluating mixed numbers can be a challenging task, especially when it comes to division. In our previous article, we walked through the steps to evaluate the expression $6 \frac{2}{5} \div 2 \frac{6}{7}$. However, we understand that some readers may still have questions or need further clarification. In this article, we will address some of the most frequently asked questions about evaluating mixed numbers.

Q&A

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction with a numerator that is greater than or equal to the denominator.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and then add the numerator. The result is then written as a fraction with the original denominator.

Q: What is the order of operations when evaluating mixed numbers?

A: When evaluating mixed numbers, you need to follow the order of operations (PEMDAS):

  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 divide mixed numbers?

A: To divide mixed numbers, you need to convert them to improper fractions, invert the second fraction, and then multiply the two fractions.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder. When simplifying fractions, you need to divide the numerator and denominator by their GCD.

Q: How do I simplify a fraction?

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

Q: What is the final answer to the expression $6 \frac{2}{5} \div 2 \frac{6}{7}$?

A: The final answer to the expression $6 \frac{2}{5} \div 2 \frac{6}{7}$ is $\frac{56}{25}$.

Common Mistakes to Avoid

When evaluating mixed numbers, it's easy to make mistakes. Here are some common mistakes to avoid:

  • Not converting mixed numbers to improper fractions before performing operations.
  • Not following the order of operations (PEMDAS).
  • Not inverting the second fraction when dividing mixed numbers.
  • Not simplifying fractions by dividing the numerator and denominator by their GCD.

Conclusion

Evaluating mixed numbers can be a challenging task, but with practice and patience, you can become proficient. Remember to follow the order of operations (PEMDAS), convert mixed numbers to improper fractions, and simplify fractions by dividing the numerator and denominator by their GCD. By avoiding common mistakes and following these steps, you can confidently evaluate mixed numbers and arrive at the correct answer.

Final Tips

  • Practice, practice, practice: The more you practice evaluating mixed numbers, the more comfortable you will become with the process.
  • Use visual aids: Visual aids such as diagrams and charts can help you understand the concept of mixed numbers and how to evaluate them.
  • Break down complex problems: When faced with a complex problem, break it down into smaller, more manageable parts. This will help you stay organized and avoid mistakes.

By following these tips and avoiding common mistakes, you can become a master of evaluating mixed numbers and tackle even the most challenging problems with confidence.