Divide, And Write Your Answer In Simplified Form: 1 2 3 ÷ 6 7 1 \frac{2}{3} \div \frac{6}{7} 1 3 2 ÷ 7 6 .(Enter Your Answer As An Improper Fraction Or Whole Number.)

Mar 11, 2025 by ADMIN 171 views

$Divide, and Write Your Answer in Simplified Form: $1 \frac{2}{3} \div \frac{6}{7}$$

Understanding the Problem

To solve the division problem $1 \frac{2}{3} \div \frac{6}{7}$ , we need to first convert the mixed number $1 \frac{2}{3}$ into an improper fraction. This will make it easier to perform the division operation.

Converting Mixed Numbers to Improper Fractions

A mixed number is a combination of a whole number and a fraction. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and then add the numerator. The result is then written as the new numerator over the denominator.

For example, to convert $1 \frac{2}{3}$ to an improper fraction, we multiply 1 by 3 and add 2:

$1 \times 3 = 3$ $3 + 2 = 5$

So, $1 \frac{2}{3}$ is equal to $\frac{5}{3}$ .

Performing the Division Operation

Now that we have converted the mixed number to an improper fraction, we can perform the division operation. To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction.

The reciprocal of a fraction is obtained by swapping the numerator and the denominator. So, the reciprocal of $\frac{6}{7}$ is $\frac{7}{6}$ .

Now, we multiply $\frac{5}{3}$ by $\frac{7}{6}$ :

$\frac{5}{3} \div \frac{6}{7} = \frac{5}{3} \times \frac{7}{6}$

Multiplying Fractions

To multiply fractions, we multiply the numerators and multiply the denominators:

$\frac{5}{3} \times \frac{7}{6} = \frac{5 \times 7}{3 \times 6}$

Simplifying the Result

Now, we simplify the result by dividing the numerator and the denominator by their greatest common divisor (GCD). The GCD of 35 and 18 is 1, so we cannot simplify the fraction further.

$\frac{5 \times 7}{3 \times 6} = \frac{35}{18}$

Writing the Answer in Simplified Form

The final answer is $\frac{35}{18}$ .

Converting the Answer to a Mixed Number (Optional)

If you prefer to write the answer as a mixed number, you can divide the numerator by the denominator:

$35 \div 18 = 1 \frac{17}{18}$

So, the answer can also be written as $1 \frac{17}{18}$ .

Conclusion

In this article, we learned how to divide a mixed number by a fraction. We converted the mixed number to an improper fraction, performed the division operation, and simplified the result. The final answer is $\frac{35}{18}$ , which can also be written as $1 \frac{17}{18}$ .

Frequently Asked Questions

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 single fraction with a numerator greater than the denominator.
Q: How do I convert a mixed number to an improper fraction? A: To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. The result is then written as the new numerator over the denominator.
Q: How do I perform the division operation with fractions? A: To divide two fractions, multiply the first fraction by the reciprocal of the second fraction.

Additional Resources

Q&A: Division of Fractions

In this article, we will answer some of the most frequently asked questions about dividing fractions. Whether you are a student, a teacher, or simply someone who wants to learn more about fractions, this article is for you.

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 single fraction with a numerator greater than the denominator.

Example:

Mixed number: $1 \frac{2}{3}$
Improper fraction: $\frac{5}{3}$

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

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

Example:

$1 \frac{2}{3}$
Multiply 1 by 3: $1 \times 3 = 3$
Add 2: $3 + 2 = 5$
Write the result as an improper fraction: $\frac{5}{3}$

Q: How do I perform the division operation with fractions?

A: To divide two fractions, multiply the first fraction by the reciprocal of the second fraction.

Example:

$\frac{5}{3} \div \frac{6}{7}$
Multiply $\frac{5}{3}$ by the reciprocal of $\frac{6}{7}$ , which is $\frac{7}{6}$ :
$\frac{5}{3} \times \frac{7}{6} = \frac{5 \times 7}{3 \times 6}$

Q: What is the reciprocal of a fraction?

A: The reciprocal of a fraction is obtained by swapping the numerator and the denominator.

Example:

Reciprocal of $\frac{6}{7}$ : $\frac{7}{6}$

Q: How do I multiply fractions?

A: To multiply fractions, multiply the numerators and multiply the denominators.

Example:

$\frac{5}{3} \times \frac{7}{6} = \frac{5 \times 7}{3 \times 6}$

Q: How do I simplify a fraction?

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

Example:

$\frac{35}{18}$
GCD of 35 and 18 is 1, so the fraction cannot be simplified further.

Q: Can I write the answer as a mixed number?

A: Yes, you can write the answer as a mixed number by dividing the numerator by the denominator.

Example:

$\frac{35}{18}$
Divide 35 by 18: $35 \div 18 = 1 \frac{17}{18}$

Q: What are some common mistakes to avoid when dividing fractions?

A: Some common mistakes to avoid when dividing fractions include:

Not converting mixed numbers to improper fractions
Not multiplying the first fraction by the reciprocal of the second fraction
Not simplifying the result
Not writing the answer as a mixed number when necessary

Q: Where can I find more resources on dividing fractions?

A: You can find more resources on dividing fractions on websites such as Mathway, Khan Academy, and Wolfram Alpha.

Conclusion

In this article, we have answered some of the most frequently asked questions about dividing fractions. Whether you are a student, a teacher, or simply someone who wants to learn more about fractions, we hope this article has been helpful.