Multiply. Write The Answer In Simplest Form. 3 8 ⋅ 2 3 = □ \frac{3}{8} \cdot \frac{2}{3} = \square 8 3 ​ ⋅ 3 2 ​ = □

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Introduction

When it comes to multiplying fractions, it's essential to understand the concept of simplifying the resulting product. In this article, we will delve into the world of fraction multiplication and explore the step-by-step process of simplifying the product of two fractions, specifically $\frac{3}{8} \cdot \frac{2}{3}$.

Understanding Fraction Multiplication

To multiply fractions, we need to multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom). This is a fundamental concept in mathematics, and it's essential to grasp it to simplify complex fraction products.

The Formula for Multiplying Fractions

The formula for multiplying fractions is as follows:

$\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}$

Where:

• $a$ and $c$ are the numerators
• $b$ and $d$ are the denominators

Applying the Formula to $\frac{3}{8} \cdot \frac{2}{3}$

Now that we have a solid understanding of the formula, let's apply it to the given problem:

$\frac{3}{8} \cdot \frac{2}{3} = \frac{3 \cdot 2}{8 \cdot 3}$

Simplifying the Product

To simplify the product, we need to find the greatest common divisor (GCD) of the numerator and the denominator. In this case, the GCD of 6 and 24 is 6.

Simplifying the Numerator

The numerator is 6, which is already simplified.

Simplifying the Denominator

The denominator is 24, which can be simplified by dividing it by the GCD (6).

$24 \div 6 = 4$

So, the simplified denominator is 4.

The Final Answer

Now that we have simplified the numerator and the denominator, we can write the final answer:

$\frac{3}{8} \cdot \frac{2}{3} = \frac{6}{4}$

Further Simplification

We can further simplify the fraction by dividing both the numerator and the denominator by their GCD, which is 2.

$\frac{6}{4} \div 2 = \frac{3}{2}$

Conclusion

In conclusion, multiplying fractions involves multiplying the numerators and denominators and then simplifying the resulting product. By following the step-by-step process outlined in this article, we can simplify complex fraction products, such as $\frac{3}{8} \cdot \frac{2}{3}$, and arrive at the final answer.

Frequently Asked Questions

• What is the formula for multiplying fractions? The formula for multiplying fractions is $\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}$.
• How do I simplify a fraction product? To simplify a fraction product, find the GCD of the numerator and the denominator and divide both numbers by the GCD.
• What is the final answer to $\frac{3}{8} \cdot \frac{2}{3}$? The final answer to $\frac{3}{8} \cdot \frac{2}{3}$ is $\frac{3}{2}$.

Additional Resources

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

Final Thoughts

Multiplying fractions is a fundamental concept in mathematics, and it's essential to understand the step-by-step process of simplifying the resulting product. By following the formula and simplifying the numerator and denominator, we can arrive at the final answer and solve complex fraction problems with ease.

Introduction

In our previous article, we explored the concept of multiplying fractions and simplifying the resulting product. However, we understand that sometimes, it's not enough to just provide a step-by-step guide. That's why we've put together this Q&A article, where we'll answer some of the most frequently asked questions about multiplying fractions.

Q&A: Multiplying Fractions

Q: What is the formula for multiplying fractions?

A: The formula for multiplying fractions is $\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}$.

Q: How do I simplify a fraction product?

A: To simplify a fraction product, find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.

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

A: The final answer to $\frac{3}{8} \cdot \frac{2}{3}$ is $\frac{3}{2}$.

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: How do I multiply a fraction by a decimal?

A: To multiply a fraction by a decimal, first convert the decimal to a fraction and then multiply the fractions.

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

A: Multiplying fractions involves multiplying the numerators and denominators, while adding fractions involves finding a common denominator and adding the numerators.

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

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

Q: How do I simplify a fraction product with a zero in the numerator or denominator?

A: If the numerator or denominator is zero, the fraction product is undefined. However, if the numerator is zero and the denominator is non-zero, the fraction product is zero.

Q: Can I multiply a fraction by a fraction with a different sign?

A: Yes, you can multiply a fraction by a fraction with a different sign. To do this, simply multiply the numerators and denominators as usual.

Real-World Applications of Multiplying Fractions

Multiplying fractions has many real-world applications, including:

• Calculating the area of a rectangle
• Finding the volume of a rectangular prism
• Determining the cost of a product
• Calculating the probability of an event

Conclusion

In conclusion, multiplying fractions is a fundamental concept in mathematics that has many real-world applications. By understanding the formula and simplifying the resulting product, we can solve complex fraction problems with ease. We hope this Q&A article has provided you with a better understanding of multiplying fractions and has helped you to become more confident in your math skills.

Frequently Asked Questions

• What is the formula for multiplying fractions?
• How do I simplify a fraction product?
• What is the final answer to $\frac{3}{8} \cdot \frac{2}{3}$?
• Can I multiply a fraction by a whole number?
• How do I multiply a fraction by a decimal?

Additional Resources

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

Final Thoughts

Multiplying fractions is a fundamental concept in mathematics that has many real-world applications. By understanding the formula and simplifying the resulting product, we can solve complex fraction problems with ease. We hope this Q&A article has provided you with a better understanding of multiplying fractions and has helped you to become more confident in your math skills.