Find The Quotient.$\frac{3}{15} \div \frac{4}{9} = $

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Introduction

When it comes to dividing fractions, many of us struggle to understand the concept and apply it correctly. However, with a clear understanding of the rules and a step-by-step approach, dividing fractions can be a breeze. In this article, we will delve into the world of fraction division and explore the concept of finding the quotient.

What is a Quotient?

A quotient is the result of a division operation. When we divide one number by another, the result is the quotient. In the context of fractions, the quotient is the result of dividing one fraction by another.

Dividing Fractions: A Step-by-Step Guide

To divide fractions, we need to follow a simple step-by-step process. Here's how to do it:

Step 1: Invert the Second Fraction

The first step in dividing fractions is to invert the second fraction. This means that we flip the numerator and denominator of the second fraction. For example, if we have the fraction 49\frac{4}{9}, we would invert it to become 94\frac{9}{4}.

Step 2: Multiply the Fractions

Once we have inverted the second fraction, we can multiply the two fractions together. This means that we multiply the numerators together and the denominators together.

Step 3: Simplify the Result

After multiplying the fractions, we need to simplify the result. This means that we need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD.

Example: Find the Quotient of 315÷49\frac{3}{15} \div \frac{4}{9}

Let's use the example given in the problem to illustrate the concept of dividing fractions. We need to find the quotient of 315÷49\frac{3}{15} \div \frac{4}{9}.

Step 1: Invert the Second Fraction

The second fraction is 49\frac{4}{9}. We need to invert it to become 94\frac{9}{4}.

Step 2: Multiply the Fractions

Now that we have inverted the second fraction, we can multiply the two fractions together. We multiply the numerators together and the denominators together:

315×94=2760\frac{3}{15} \times \frac{9}{4} = \frac{27}{60}

Step 3: Simplify the Result

We need to simplify the result by finding the GCD of the numerator and denominator. The GCD of 27 and 60 is 3. We divide both numbers by 3 to get:

2760=920\frac{27}{60} = \frac{9}{20}

Conclusion

Dividing fractions may seem like a daunting task, but with a clear understanding of the rules and a step-by-step approach, it can be a breeze. By following the steps outlined in this article, you can find the quotient of any fraction division problem. Remember to invert the second fraction, multiply the fractions together, and simplify the result.

Frequently Asked Questions

Q: What is the quotient of 12÷34\frac{1}{2} \div \frac{3}{4}?

A: To find the quotient, we need to invert the second fraction and multiply the fractions together. The result is 12×43=23\frac{1}{2} \times \frac{4}{3} = \frac{2}{3}.

Q: What is the quotient of 23÷56\frac{2}{3} \div \frac{5}{6}?

A: To find the quotient, we need to invert the second fraction and multiply the fractions together. The result is 23×65=45\frac{2}{3} \times \frac{6}{5} = \frac{4}{5}.

Tips and Tricks

  • When dividing fractions, always invert the second fraction.
  • Multiply the fractions together by multiplying the numerators together and the denominators together.
  • Simplify the result by finding the GCD of the numerator and denominator.

Final Thoughts

Dividing fractions is an essential concept in mathematics, and with practice, you can become proficient in finding the quotient of any fraction division problem. Remember to follow the steps outlined in this article, and you'll be dividing fractions like a pro in no time.

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Introduction

Dividing fractions can be a challenging concept for many students. However, with practice and a clear understanding of the rules, it can become second nature. In this article, we will answer some of the most frequently asked questions about dividing fractions.

Q&A: Dividing Fractions

Q: What is the quotient of 12÷34\frac{1}{2} \div \frac{3}{4}?

A: To find the quotient, we need to invert the second fraction and multiply the fractions together. The result is 12×43=23\frac{1}{2} \times \frac{4}{3} = \frac{2}{3}.

Q: What is the quotient of 23÷56\frac{2}{3} \div \frac{5}{6}?

A: To find the quotient, we need to invert the second fraction and multiply the fractions together. The result is 23×65=45\frac{2}{3} \times \frac{6}{5} = \frac{4}{5}.

Q: How do I divide fractions with unlike denominators?

A: To divide fractions with unlike denominators, we need to find the least common multiple (LCM) of the denominators. Then, we can multiply the fractions together by multiplying the numerators together and the denominators together.

Q: What is the quotient of 38÷512\frac{3}{8} \div \frac{5}{12}?

A: To find the quotient, we need to invert the second fraction and multiply the fractions together. The result is 38×125=910\frac{3}{8} \times \frac{12}{5} = \frac{9}{10}.

Q: How do I simplify the result of a fraction division problem?

A: To simplify the result, we need to find the greatest common divisor (GCD) of the numerator and denominator. Then, we can divide both numbers by the GCD.

Q: What is the quotient of 49÷23\frac{4}{9} \div \frac{2}{3}?

A: To find the quotient, we need to invert the second fraction and multiply the fractions together. The result is 49×32=23\frac{4}{9} \times \frac{3}{2} = \frac{2}{3}.

Q: Can I divide fractions with zero in the numerator or denominator?

A: No, you cannot divide fractions with zero in the numerator or denominator. Division by zero is undefined.

Q: What is the quotient of 01÷23\frac{0}{1} \div \frac{2}{3}?

A: Since the numerator is zero, we cannot divide the fractions. The result is undefined.

Q: How do I handle negative fractions in a division problem?

A: When dividing fractions with negative numbers, we need to follow the rules of division. If the signs of the fractions are the same, the result is positive. If the signs are different, the result is negative.

Q: What is the quotient of −34÷23-\frac{3}{4} \div \frac{2}{3}?

A: To find the quotient, we need to invert the second fraction and multiply the fractions together. The result is −34×32=−98-\frac{3}{4} \times \frac{3}{2} = -\frac{9}{8}.

Conclusion

Dividing fractions can be a challenging concept, but with practice and a clear understanding of the rules, it can become second nature. By following the steps outlined in this article, you can answer any fraction division problem with confidence.

Final Thoughts

Dividing fractions is an essential concept in mathematics, and with practice, you can become proficient in finding the quotient of any fraction division problem. Remember to follow the steps outlined in this article, and you'll be dividing fractions like a pro in no time.

Additional Resources

Glossary

  • Quotient: The result of a division operation.
  • Invert: To flip the numerator and denominator of a fraction.
  • Multiply: To multiply the numerators together and the denominators together.
  • Simplify: To find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD.
  • Least Common Multiple (LCM): The smallest multiple that two or more numbers have in common.
  • Greatest Common Divisor (GCD): The largest number that divides two or more numbers without leaving a remainder.