Simplify: ${ \frac{8}{9} \div \frac{2}{3} }$

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Introduction

Understanding Division of Fractions When dealing with division of fractions, it's essential to remember that it's the same as multiplying by the reciprocal of the divisor. This concept is crucial in simplifying complex fraction problems. In this article, we will delve into the world of fractions and explore how to simplify the given expression: $\frac{8}{9} \div \frac{2}{3}$.

The Concept of Division of Fractions

Division of fractions is a fundamental concept in mathematics that can be a bit tricky to grasp at first. However, with a clear understanding of the concept, it becomes relatively straightforward. When we divide one fraction by another, we are essentially multiplying the first fraction by the reciprocal of the second fraction. This means that we need to flip the second fraction and change the division sign to a multiplication sign.

Applying the Concept to the Given Expression

Now that we have a clear understanding of the concept of division of fractions, let's apply it to the given expression: $\frac{8}{9} \div \frac{2}{3}$. To simplify this expression, we need to multiply $\frac{8}{9}$ by the reciprocal of $\frac{2}{3}$, which is $\frac{3}{2}$.

Simplifying the Expression

To simplify the expression, we need to multiply the numerators and denominators of the two fractions. This means that we need to multiply $8$ by $3$ and $9$ by $2$. The resulting expression is:

$$\frac{8}{9} \div \frac{2}{3} = \frac{8 \times 3}{9 \times 2}$$

Evaluating the Expression

Now that we have simplified the expression, let's evaluate it. To do this, we need to multiply the numerators and denominators of the fraction. This means that we need to multiply $8$ by $3$ and $9$ by $2$. The resulting expression is:

$$\frac{8 \times 3}{9 \times 2} = \frac{24}{18}$$

Further Simplification

The resulting expression $\frac{24}{18}$ can be further simplified by dividing both the numerator and denominator by their greatest common divisor (GCD). The GCD of $24$ and $18$ is $6$. Dividing both the numerator and denominator by $6$ gives us:

$$\frac{24}{18} = \frac{24 \div 6}{18 \div 6} = \frac{4}{3}$$

Conclusion

In conclusion, simplifying the expression $\frac{8}{9} \div \frac{2}{3}$ involves applying the concept of division of fractions and simplifying the resulting expression. By multiplying the first fraction by the reciprocal of the second fraction and simplifying the resulting expression, we arrive at the final answer: $\frac{4}{3}$.

Frequently Asked Questions

• What is the concept of division of fractions? Division of fractions is a fundamental concept in mathematics that involves multiplying the first fraction by the reciprocal of the second fraction.
• How do I simplify a division of fractions expression? To simplify a division of fractions expression, you need to multiply the first fraction by the reciprocal of the second fraction and simplify the resulting expression.
• What is the final answer to the expression $\frac{8}{9} \div \frac{2}{3}$? The final answer to the expression $\frac{8}{9} \div \frac{2}{3}$ is $\frac{4}{3}$.

Additional Resources

• Mathematics textbooks: For a comprehensive understanding of division of fractions and other mathematical concepts, refer to a mathematics textbook.
• Online resources: Websites such as Khan Academy and Mathway offer interactive lessons and exercises to help you practice and improve your math skills.
• Math tutors: If you need additional help or guidance, consider hiring a math tutor who can provide one-on-one instruction and support.
  

Introduction

Division of fractions can be a complex and confusing topic, especially for those who are new to mathematics. However, with a clear understanding of the concept and some practice, it becomes relatively straightforward. In this article, we will answer some of the most frequently asked questions about division of fractions.

Q&A

Q: What is the concept of division of fractions?

A: Division of fractions is a fundamental concept in mathematics that involves multiplying the first fraction by the reciprocal of the second fraction. When we divide one fraction by another, we are essentially multiplying the first fraction by the reciprocal of the second fraction. This means that we need to flip the second fraction and change the division sign to a multiplication sign.

Q: How do I simplify a division of fractions expression?

A: To simplify a division of fractions expression, you need to multiply the first fraction by the reciprocal of the second fraction and simplify the resulting expression. This involves multiplying the numerators and denominators of the two fractions and simplifying the resulting expression.

Q: What is the final answer to the expression $\frac{8}{9} \div \frac{2}{3}$?

A: The final answer to the expression $\frac{8}{9} \div \frac{2}{3}$ is $\frac{4}{3}$. This is obtained by multiplying the first fraction by the reciprocal of the second fraction and simplifying the resulting expression.

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

A: Division of fractions is the same as multiplying by the reciprocal of the divisor. This means that when we divide one fraction by another, we are essentially multiplying the first fraction by the reciprocal of the second fraction.

Q: How do I handle negative fractions when dividing?

A: When dividing negative fractions, you need to multiply the first fraction by the reciprocal of the second fraction and change the sign of the result. This means that if the first fraction is negative and the second fraction is positive, the result will be negative.

Q: Can I simplify a division of fractions expression by canceling out common factors?

A: Yes, you can simplify a division of fractions expression by canceling out common factors. This involves identifying the common factors in the numerator and denominator and canceling them out.

Q: What is the greatest common divisor (GCD) and how do I use it to simplify a division of fractions expression?

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and denominator of a fraction. To simplify a division of fractions expression, you need to divide both the numerator and denominator by their GCD.

Conclusion

In conclusion, division of fractions can be a complex and confusing topic, but with a clear understanding of the concept and some practice, it becomes relatively straightforward. By answering some of the most frequently asked questions about division of fractions, we hope to have provided you with a better understanding of this important mathematical concept.

Additional Resources

• Mathematics textbooks: For a comprehensive understanding of division of fractions and other mathematical concepts, refer to a mathematics textbook.
• Online resources: Websites such as Khan Academy and Mathway offer interactive lessons and exercises to help you practice and improve your math skills.
• Math tutors: If you need additional help or guidance, consider hiring a math tutor who can provide one-on-one instruction and support.

Frequently Asked Questions: Division of Fractions - Part 2

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

A: Dividing fractions and dividing decimals are two different operations. Dividing fractions involves multiplying the first fraction by the reciprocal of the second fraction, while dividing decimals involves moving the decimal point and dividing the numbers.

Q: Can I divide a fraction by a whole number?

A: Yes, you can divide a fraction by a whole number. This involves multiplying the fraction by the reciprocal of the whole number.

Q: How do I handle mixed numbers when dividing?

A: When dividing mixed numbers, you need to convert them to improper fractions and then divide. This involves converting the mixed number to an improper fraction and then dividing the fractions.

Q: What is the final answer to the expression $\frac{3}{4} \div 2$?

A: The final answer to the expression $\frac{3}{4} \div 2$ is $\frac{3}{8}$. This is obtained by multiplying the fraction by the reciprocal of the whole number and simplifying the resulting expression.

Q: Can I simplify a division of fractions expression by canceling out common factors?

A: Yes, you can simplify a division of fractions expression by canceling out common factors. This involves identifying the common factors in the numerator and denominator and canceling them out.

Q: What is the greatest common divisor (GCD) and how do I use it to simplify a division of fractions expression?

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and denominator of a fraction. To simplify a division of fractions expression, you need to divide both the numerator and denominator by their GCD.

Conclusion

In conclusion, division of fractions can be a complex and confusing topic, but with a clear understanding of the concept and some practice, it becomes relatively straightforward. By answering some of the most frequently asked questions about division of fractions, we hope to have provided you with a better understanding of this important mathematical concept.