Reducing the Answer to its Lowest Fraction

Oct 13, 2025 by miodeya.com 8 views

Introduction

In mathematics, division is a fundamental operation that involves finding the quotient of two numbers. When dealing with fractions, division can be a bit more complex, but with the right approach, it can be simplified. In this article, we will explore how to find the quotient of $$5 / 31$$ divided by $$31 / 23$$ and reduce the answer to its lowest fraction.

Understanding the Problem

To find the quotient of $$5 / 31$$ divided by $$15 / 23$$, we need to follow the order of operations (PEMDAS):

Divide $$5$$ by $$31$$
Divide $$15$$ by $$23$$
Divide the result of step 1 by the result of step 2

Step 1: Divide $$5$$ by $$31$$

To divide $$5$$ by $$31$$, we can simply write the fraction as $$\frac{5}{31}$$.

Step 2: Divide $$15$$ by $$23$$

To divide $$15$$ by $$23$$, we can simply write the fraction as $$\frac{15}{23}$$.

Step 3: Divide the Result of Step 1 by the Result of Step 2

Now, we need to divide the result of step 1 by the result of step 2. To do this, we can multiply the numerator of the first fraction by the denominator of the second fraction, and then divide the result by the product of the two denominators.

\frac{5}{31} \div \frac{15}{23} = \frac{5 \times 23}{31 \times 15} = \frac{115}{465}

Reducing the Answer to its Lowest Fraction

To reduce the answer to its lowest fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of $$115$$ and $$465$$ is $$5$$.

\frac{115}{465} = \frac{115 \div 5}{465 \div 5} = \frac{23}{93}

Conclusion

In conclusion, the quotient of $$5 / 31$$ divided by $$15 / 23$$ is $$\frac{23}{93}$$. This can also be written as $$4 \frac{1}{23}$$.

Final Answer

The final answer is: $\boxed{\frac{23}{93}}$

Frequently Asked Questions

Q: What is the quotient of $$5 / 31$$ divided by $$15 / 23$$? A: The quotient of $$5 / 31$$ divided by $$15 / 23$$ is $$\frac{23}{93}$$.

Q: How do I reduce a fraction to its lowest form? A: To reduce a fraction to its lowest form, you need to find the greatest common divisor (GCD) of the numerator and the denominator, and then divide both numbers by the GCD.

Additional Resources

For more information on division with fractions, please refer to the following resources:

Khan Academy: Division with Fractions
Mathway: Division with Fractions
Wolfram Alpha: Division with Fractions

Introduction

In our previous article, we explored how to find the quotient of $$5 / 31$$ divided by $$15 / 23$$ and reduce the answer to its lowest fraction. In this article, we will answer some frequently asked questions related to this topic.

Q&A

Q: What is the quotient of $$5 / 31$$ divided by $$15 / 23$$?

A: The quotient of $$5 / 31$$ divided by $$15 / 23$$ is $$\frac{23}{93}$$.

Q: How do I divide fractions?

A: To divide fractions, you need to follow the order of operations (PEMDAS):

Invert the second fraction (i.e., flip the numerator and denominator)
Multiply the two fractions

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

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder. For example, the GCD of $$115$$ and $$465$$ is $$5$$.

Q: How do I reduce a fraction to its lowest form?

A: To reduce a fraction to its lowest form, you need to find the greatest common divisor (GCD) of the numerator and the denominator, and then divide both numbers by the GCD.

For example, to reduce $$\frac{115}{465}$$ to its lowest form, you would find the GCD of $$115$$ and $$465$$, which is $$5$$, and then divide both numbers by $$5$$ to get $$\frac{23}{93}$$.

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

A: Dividing fractions is the opposite of multiplying fractions. When you divide fractions, you invert the second fraction and then multiply the two fractions. When you multiply fractions, you multiply the numerators and denominators separately.

For example, to divide $$\frac{5}{31}$$ by $$\frac{15}{23}$$, you would invert the second fraction to get $$\frac{23}{15}$$, and then multiply the two fractions to get $$\frac{5 \times 23}{31 \times 15}$$. To multiply $$\frac{5}{31}$$ by $$\frac{15}{23}$$, you would multiply the numerators and denominators separately to get $$\frac{5 \times 15}{31 \times 23}$$.

Q: Can I use a calculator to divide fractions?

A: Yes, you can use a calculator to divide fractions. However, it's always a good idea to understand the concept behind dividing fractions and to practice dividing fractions by hand to build your math skills.

Conclusion

In conclusion, dividing fractions can be a bit tricky, but with the right approach, it can be simplified. We hope this Q&A article has helped you understand how to divide fractions and reduce the answer to its lowest form.

Final Answer

The final answer is: $\boxed{\frac{23}{93}}$

Frequently Asked Questions

Q: What is the quotient of $$5 / 31$$ divided by $$15 / 23$$? A: The quotient of $$5 / 31$$ divided by $$15 / 23$$ is $$\frac{23}{93}$$.

Q: How do I divide fractions? A: To divide fractions, you need to follow the order of operations (PEMDAS): invert the second fraction and then multiply the two fractions.

Q: What is the greatest common divisor (GCD) of two numbers? A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder.

Additional Resources

For more information on division with fractions, please refer to the following resources:

Khan Academy: Division with Fractions
Mathway: Division with Fractions
Wolfram Alpha: Division with Fractions