Calculate The Product Of The Following Fractions:$\frac{4}{7} \times \frac{2}{3}$

Introduction

In mathematics, fractions are a fundamental concept that plays a crucial role in various mathematical operations. One of the most common operations involving fractions is multiplication. In this article, we will explore how to calculate the product of fractions, with a focus on the given problem: $\frac{4}{7} \times \frac{2}{3}$.

Understanding Fractions

Before we dive into the calculation, let's briefly review what fractions are. A fraction is a way of expressing a part of a whole as a ratio of two numbers. It consists of a numerator (the top number) and a denominator (the bottom number). For example, in the fraction $\frac{4}{7}$, 4 is the numerator and 7 is the denominator.

Multiplying Fractions

To multiply fractions, we simply multiply the numerators together and the denominators together. This is based on the principle that when we multiply two fractions, we are essentially finding the area of a rectangle with the first fraction's numerator as the length and the second fraction's numerator as the width, and then dividing that area by the product of the two fractions' denominators.

Calculating the Product of $\frac{4}{7} \times \frac{2}{3}$

Now, let's apply this principle to the given problem. To calculate the product of $\frac{4}{7} \times \frac{2}{3}$, we multiply the numerators together and the denominators together:

$\frac{4}{7} \times \frac{2}{3} = \frac{4 \times 2}{7 \times 3}$

Simplifying the Fraction

To simplify the fraction, we can cancel out any common factors between the numerator and the denominator. In this case, the numerator and the denominator have no common factors, so the fraction is already in its simplest form.

The Final Answer

Therefore, the product of $\frac{4}{7} \times \frac{2}{3}$ is:

$\frac{8}{21}$

Why is this Important?

Calculating the product of fractions is an essential skill in mathematics, particularly in algebra and geometry. It is used to solve problems involving area, volume, and other quantities that can be represented as fractions. By mastering this skill, you will be able to tackle a wide range of mathematical problems with confidence.

Real-World Applications

The concept of multiplying fractions has numerous real-world applications. For example, in cooking, you may need to multiply a recipe by a certain fraction to make a larger or smaller batch of food. In construction, you may need to calculate the area of a room or a building by multiplying the length and width of the space by a fraction.

Conclusion

In conclusion, calculating the product of fractions is a fundamental skill in mathematics that requires a clear understanding of fractions and their properties. By following the steps outlined in this article, you can confidently calculate the product of fractions, including the given problem: $\frac{4}{7} \times \frac{2}{3}$. Whether you are a student, a teacher, or simply someone who enjoys mathematics, this skill will serve you well in a wide range of mathematical and real-world applications.

Additional Resources

For further practice and review, we recommend the following resources:

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

Final Thoughts

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 means that if you have two fractions, $\frac{a}{b}$ and $\frac{c}{d}$, the product is $\frac{a \times c}{b \times d}$.

Q: How do I simplify a fraction after multiplying?

A: To simplify a fraction after multiplying, you need to find any common factors between the numerator and the denominator and cancel them out. This will give you the simplest form of the fraction.

Q: What if the numerator and denominator have no common factors?

A: If the numerator and denominator have no common factors, the fraction is already in its simplest form. You don't need to simplify it further.

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. Then, multiply the fractions together using the rule for multiplying fractions.

Q: What if I have a negative fraction?

A: If you have a negative fraction, you can multiply it by a negative number to get a positive fraction. For example, $-\frac{1}{2} \times -3 = \frac{3}{2}$.

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

A: Yes, you can multiply a fraction by a mixed number. To do this, first convert the mixed number to an improper fraction. Then, multiply the fractions together using the rule for multiplying fractions.

Q: How do I multiply a fraction by a fraction with a variable?

A: To multiply a fraction by a fraction with a variable, simply multiply the numerators together and the denominators together. This will give you a new fraction with the variable.

Q: What if I have a fraction with a variable in the denominator?

A: If you have a fraction with a variable in the denominator, you can multiply both the numerator and the denominator by the variable to get rid of it.

Q: Can I use a calculator to multiply fractions?

A: Yes, you can use a calculator to multiply fractions. Simply enter the fractions into the calculator and multiply them together.

Q: How do I check my work when multiplying fractions?

A: To check your work when multiplying fractions, simply multiply the fractions together again and see if you get the same answer. If you don't get the same answer, go back and recheck your work.

Conclusion

Calculating the product of fractions is a fundamental skill in mathematics that requires a clear understanding of fractions and their properties. By following the steps outlined in this article and practicing with different types of fractions, you can become proficient in multiplying fractions and tackle a wide range of mathematical problems with confidence.

Additional Resources

For further practice and review, we recommend the following resources:

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

Final Thoughts

Multiplying fractions is a skill that requires patience, practice, and persistence. By mastering this skill, you will be able to tackle a wide range of mathematical problems with confidence and accuracy. Remember to always simplify your fractions and check your work to ensure that you are getting the correct answer. Happy calculating!