Applying the Concept to a Problem

Oct 13, 2025 by talynt.org 59 views

In mathematics, fractions are a way to represent a part of a whole. When we multiply two fractions together, we are essentially finding the product of two parts of a whole. In this article, we will explore how to find the product of two fractions and apply this concept to a specific problem.

Understanding Fractions

A fraction is a way to represent a part of a whole. It consists of two numbers: a numerator and a denominator. The numerator represents the number of equal parts we have, and the denominator represents the total number of parts the whole is divided into. For example, the fraction 3/4 represents 3 equal parts out of a total of 4 parts.

Multiplying Fractions

To multiply two fractions together, we simply multiply the numerators together and the denominators together. This is represented by the following formula:

\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}

Where a, b, c, and d are the numerators and denominators of the two fractions.

Applying the Concept to a Problem

Now that we understand how to multiply fractions, let's apply this concept to the problem presented in the question:

What is the product of $$\frac{2}{8}$$ and $$\frac{3}{5}$$?

To find the product of these two fractions, we will multiply the numerators together and the denominators together.

\frac{2}{8} \times \frac{3}{5} = \frac{(2)(3)}{(8)(5)}

Now, let's simplify the fraction by multiplying the numerators together and the denominators together.

\frac{(2)(3)}{(8)(5)} = \frac{6}{40}

We can simplify this fraction further by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

\frac{6}{40} = \frac{3}{20}

Therefore, the product of $$\frac{2}{8}$$ and $$\frac{3}{5}$$ is $$\frac{3}{20}$$.

Conclusion

In this article, we explored how to find the product of two fractions. We learned that to multiply two fractions together, we simply multiply the numerators together and the denominators together. We then applied this concept to a specific problem and found the product of $$\frac{2}{8}$$ and $$\frac{3}{5}$$ to be $$\frac{3}{20}$$.

Answer

The correct answer is D) $$\frac{3}{20}$$.

Additional Examples

Here are a few additional examples of multiplying fractions:

$\frac{1}{2} \times \frac{3}{4} = \frac{3}{8}$
$\frac{2}{3} \times \frac{5}{6} = \frac{10}{18} = \frac{5}{9}$
$\frac{3}{4} \times \frac{2}{5} = \frac{6}{20} = \frac{3}{10}$

In the previous article, we explored how to find the product of two fractions. However, we understand that there may be some questions and concerns that you may have. In this article, we will address some of the most frequently asked questions about multiplying fractions.

Q: What is the rule for multiplying fractions?

A: The rule for multiplying fractions is to multiply the numerators together and the denominators together. This is represented by the following formula:

\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}

Where a, b, c, and d are the numerators and denominators of the two fractions.

Q: How do I simplify a fraction after multiplying?

A: To simplify a fraction after multiplying, you need to find the greatest common divisor (GCD) of the numerator and the denominator. Then, divide both the numerator and the denominator by the GCD.

Q: What if the denominators are not the same?

A: If the denominators are not the same, you need to find the least common multiple (LCM) of the two denominators. Then, multiply both the numerator and the denominator by the LCM.

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

A: Yes, you can multiply a fraction by a whole number. To do this, simply multiply the numerator by the whole number and keep the denominator the same.

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

A: Multiplying fractions involves multiplying the numerators together and the denominators together. Dividing fractions involves inverting the second fraction (i.e., flipping the numerator and the denominator) and then multiplying.

Q: Can I multiply a negative fraction by a positive fraction?

A: Yes, you can multiply a negative fraction by a positive fraction. The result will be a negative fraction.

Q: Can I multiply a fraction by a decimal?

A: Yes, you can multiply a fraction by a decimal. To do this, simply convert the decimal to a fraction and then multiply.

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

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

Not simplifying the fraction after multiplying
Not finding the greatest common divisor (GCD) of the numerator and the denominator
Not finding the least common multiple (LCM) of the two denominators
Not inverting the second fraction when dividing

Conclusion

In this article, we addressed some of the most frequently asked questions about multiplying fractions. We hope that this article has provided you with a better understanding of how to multiply fractions and has helped to clarify any confusion you may have had.

Additional Resources

If you are still having trouble with multiplying fractions, we recommend checking out the following resources:

Khan Academy: Multiplying Fractions
Mathway: Multiplying Fractions
IXL: Multiplying Fractions

These resources provide additional practice and examples to help you master the concept of multiplying fractions.