Calculate The Following Expression:${ \frac{4}{7} \times \frac{2}{3} = }$

Understanding the Basics of Multiplying Fractions

When it comes to multiplying fractions, it's essential to understand the basics of how they work. A fraction is a way of expressing a part of a whole, and it consists of two parts: the numerator (the top number) and the denominator (the bottom number). To multiply fractions, we simply multiply the numerators together and the denominators together.

The Expression to be Calculated

The expression we need to calculate is: $\frac{4}{7} \times \frac{2}{3}$

Step 1: Multiply the Numerators

To multiply the numerators, we simply multiply the top numbers together. In this case, the numerators are 4 and 2. So, we multiply 4 and 2 together to get: $4 \times 2 = 8$

Step 2: Multiply the Denominators

To multiply the denominators, we simply multiply the bottom numbers together. In this case, the denominators are 7 and 3. So, we multiply 7 and 3 together to get: $7 \times 3 = 21$

Step 3: Write the Result as a Fraction

Now that we have the product of the numerators and the product of the denominators, we can write the result as a fraction. The numerator is 8, and the denominator is 21. So, the result is: $\frac{8}{21}$

Simplifying the Fraction (Optional)

If we want to simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 8 and 21 is 1, so the fraction cannot be simplified further.

Conclusion

In conclusion, to calculate the expression $\frac{4}{7} \times \frac{2}{3}$, we simply multiply the numerators together and the denominators together, and then write the result as a fraction. The result is $\frac{8}{21}$.

Real-World Applications of Multiplying Fractions

Multiplying fractions has many real-world applications, such as:

• Cooking: When a recipe calls for a certain amount of an ingredient, and you need to multiply it by a certain factor, you can use multiplying fractions to get the correct amount.
• Building: When building a structure, you may need to multiply the dimensions of a room or a wall by a certain factor to get the correct size.
• Science: In science, multiplying fractions is often used to calculate the concentration of a solution or the volume of a container.

Tips and Tricks for Multiplying Fractions

Here are some tips and tricks for multiplying fractions:

• Use a calculator: If you're having trouble multiplying fractions by hand, you can use a calculator to get the result.
• Simplify the fraction: If you can simplify the fraction, do so to make it easier to work with.
• Use a diagram: If you're having trouble visualizing the problem, use a diagram to help you understand it.

Common Mistakes to Avoid

Here are some common mistakes to avoid when multiplying fractions:

• Forgetting to multiply the denominators: Make sure to multiply the denominators together, just like you multiply the numerators.
• Not simplifying the fraction: If you can simplify the fraction, do so to make it easier to work with.
• Not using a calculator: If you're having trouble multiplying fractions by hand, use a calculator to get the result.

Conclusion

In conclusion, multiplying fractions is a simple process that involves multiplying the numerators together and the denominators together, and then writing the result as a fraction. With practice and patience, you can become proficient in multiplying fractions and apply it to real-world problems.

Understanding the Basics of Multiplying Fractions

Multiplying fractions is a fundamental concept in mathematics that can be used to solve a wide range of problems. However, it can be a bit tricky to understand and apply, especially for those who are new to fractions. In this article, we will provide a Q&A guide to help you understand and apply multiplying fractions.

Q: What is a fraction?

A: A fraction is a way of expressing a part of a whole. It consists of two parts: the numerator (the top number) and the denominator (the bottom number). For example, the fraction 1/2 represents one half of a whole.

Q: How do I multiply fractions?

A: To multiply fractions, you simply multiply the numerators together and the denominators together. For example, to multiply 1/2 and 3/4, you would multiply the numerators (1 and 3) together to get 3, and the denominators (2 and 4) together to get 8. The result is 3/8.

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

A: Multiplying fractions involves multiplying the numerators and denominators together, while adding fractions involves adding the numerators together and keeping the same denominator. For example, to add 1/2 and 1/4, you would add the numerators (1 and 1) together to get 2, and keep the same denominator (2). The result is 2/2, which simplifies to 1.

Q: Can I simplify a fraction after multiplying it?

A: Yes, you can simplify a fraction after multiplying it. To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator, and then divide both numbers by the GCD. For example, to simplify 6/8, you would find the GCD of 6 and 8, which is 2, and then divide both numbers by 2 to get 3/4.

Q: How do I handle zero in a fraction?

A: When multiplying fractions, if either the numerator or denominator is zero, the result is zero. For example, to multiply 1/2 and 0/4, the result is 0.

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

A: Yes, you can multiply a fraction by a whole number. To do this, you simply multiply the numerator by the whole number, and keep the same denominator. For example, to multiply 1/2 by 3, you would multiply the numerator (1) by 3 to get 3, and keep the same denominator (2). The result is 3/2.

Q: How do I handle negative numbers in fractions?

A: When multiplying fractions, if either the numerator or denominator is negative, the result is negative. For example, to multiply -1/2 and 3/4, the result is -3/8.

Q: Can I multiply a fraction by a decimal?

A: Yes, you can multiply a fraction by a decimal. To do this, you simply convert the decimal to a fraction, and then multiply the fractions together. For example, to multiply 1/2 by 0.5, you would convert 0.5 to a fraction (1/2), and then multiply the fractions together to get 1/4.

Q: How do I handle mixed numbers in fractions?

A: When multiplying fractions, if either the numerator or denominator is a mixed number, you need to convert the mixed number to an improper fraction before multiplying. For example, to multiply 1 1/2 and 3/4, you would convert 1 1/2 to an improper fraction (3/2), and then multiply the fractions together to get 9/8.

Conclusion

In conclusion, multiplying fractions is a fundamental concept in mathematics that can be used to solve a wide range of problems. By understanding the basics of multiplying fractions and applying the tips and tricks outlined in this article, you can become proficient in multiplying fractions and apply it to real-world problems.