Calculate The Product: $\[ 8 \times 3 \frac{7}{9} = \square \\]

Introduction

In mathematics, mixed numbers are a combination of a whole number and a fraction. When we need to calculate the product of mixed numbers, it can be a bit challenging. However, with a clear understanding of the concept and a step-by-step approach, we can easily calculate the product of mixed numbers. In this article, we will discuss how to calculate the product of mixed numbers, with a focus on the given problem: $8 \times 3 \frac{7}{9} = \square$.

Understanding Mixed Numbers

A mixed number is a combination of a whole number and a fraction. It is written in the form $a \frac{b}{c}$, where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator. For example, $3 \frac{7}{9}$ is a mixed number where $3$ is the whole number, $7$ is the numerator, and $9$ is the denominator.

Converting Mixed Numbers to Improper Fractions

To calculate the product of mixed numbers, we need to convert them to improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator. The result is then written as a fraction with the denominator as the new denominator.

For example, let's convert the mixed number $3 \frac{7}{9}$ to an improper fraction:

$3 \frac{7}{9} = \frac{(3 \times 9) + 7}{9} = \frac{27 + 7}{9} = \frac{34}{9}$

Calculating the Product of Mixed Numbers

Now that we have converted the mixed numbers to improper fractions, we can calculate their product. To calculate the product of two fractions, we multiply the numerators and multiply the denominators.

For example, let's calculate the product of $8$ and $3 \frac{7}{9}$:

$8 \times 3 \frac{7}{9} = 8 \times \frac{34}{9} = \frac{(8 \times 34)}{9} = \frac{272}{9}$

Simplifying the Result

The result we obtained is an improper fraction. However, we can simplify it by dividing the numerator by the denominator.

$\frac{272}{9} = 30 \frac{2}{9}$

Conclusion

Calculating the product of mixed numbers can be a bit challenging, but with a clear understanding of the concept and a step-by-step approach, we can easily calculate the product of mixed numbers. In this article, we discussed how to calculate the product of mixed numbers, with a focus on the given problem: $8 \times 3 \frac{7}{9} = \square$. We converted the mixed numbers to improper fractions, calculated their product, and simplified the result.

Example Problems

Here are a few example problems to help you practice calculating the product of mixed numbers:

• $4 \times 2 \frac{3}{5} = \square$
• $6 \times 3 \frac{2}{7} = \square$
• $9 \times 1 \frac{4}{9} = \square$

Tips and Tricks

Here are a few tips and tricks to help you calculate the product of mixed numbers:

• Always convert mixed numbers to improper fractions before calculating their product.
• Multiply the numerators and multiply the denominators when calculating the product of two fractions.
• Simplify the result by dividing the numerator by the denominator.

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. It is written in the form $a \frac{b}{c}$, where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you multiply the whole number by the denominator and add the numerator. The result is then written as a fraction with the denominator as the new denominator.

For example, let's convert the mixed number $3 \frac{7}{9}$ to an improper fraction:

$3 \frac{7}{9} = \frac{(3 \times 9) + 7}{9} = \frac{27 + 7}{9} = \frac{34}{9}$

Q: How do I calculate the product of mixed numbers?

A: To calculate the product of mixed numbers, you need to convert them to improper fractions, multiply the numerators, multiply the denominators, and simplify the result.

For example, let's calculate the product of $8$ and $3 \frac{7}{9}$:

$8 \times 3 \frac{7}{9} = 8 \times \frac{34}{9} = \frac{(8 \times 34)}{9} = \frac{272}{9}$

Q: Can I simplify the result of the product of mixed numbers?

A: Yes, you can simplify the result of the product of mixed numbers by dividing the numerator by the denominator.

For example, let's simplify the result of the product of $8$ and $3 \frac{7}{9}$:

$\frac{272}{9} = 30 \frac{2}{9}$

Q: What are some common mistakes to avoid when calculating the product of mixed numbers?

A: Some common mistakes to avoid when calculating the product of mixed numbers include:

• Not converting mixed numbers to improper fractions before calculating their product
• Not multiplying the numerators and denominators correctly
• Not simplifying the result correctly

Q: How can I practice calculating the product of mixed numbers?

A: You can practice calculating the product of mixed numbers by working through example problems, such as:

• $4 \times 2 \frac{3}{5} = \square$
• $6 \times 3 \frac{2}{7} = \square$
• $9 \times 1 \frac{4}{9} = \square$

Q: What are some real-world applications of calculating the product of mixed numbers?

A: Calculating the product of mixed numbers has many real-world applications, such as:

• Cooking: When a recipe calls for a mixed number of ingredients, you need to calculate the product of the mixed numbers to get the correct amount.
• Building: When building a structure, you need to calculate the product of mixed numbers to get the correct amount of materials.
• Finance: When calculating interest rates or investments, you need to calculate the product of mixed numbers to get the correct amount.

By following these tips and practicing calculating the product of mixed numbers, you can become more confident in your math skills and apply them to real-world situations.