Calculate The Product:${ 9 \frac{1}{3} \times 2 \frac{1}{4} }$

Introduction

In mathematics, mixed numbers are a combination of a whole number and a fraction. When we need to calculate the product of two 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 find the product of two mixed numbers. In this article, we will learn how to calculate the product of two mixed numbers, specifically $9 \frac{1}{3} \times 2 \frac{1}{4}$.

Understanding Mixed Numbers

A mixed number is a combination of a whole number and a fraction. It is written in the form of $a \frac{b}{c}$, where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator. For example, $3 \frac{2}{5}$ is a mixed number where $3$ is the whole number, $2$ is the numerator, and $5$ is the denominator.

Converting Mixed Numbers to Improper Fractions

To calculate the product of two mixed numbers, we need to convert them into 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 the new numerator over the denominator.

For example, let's convert $9 \frac{1}{3}$ to an improper fraction:

1. Multiply the whole number by the denominator: $9 \times 3 = 27$
2. Add the numerator: $27 + 1 = 28$
3. Write the result as the new numerator over the denominator: $\frac{28}{3}$

Similarly, let's convert $2 \frac{1}{4}$ to an improper fraction:

1. Multiply the whole number by the denominator: $2 \times 4 = 8$
2. Add the numerator: $8 + 1 = 9$
3. Write the result as the new numerator over the denominator: $\frac{9}{4}$

Calculating the Product of Improper Fractions

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

For example, let's calculate the product of $\frac{28}{3}$ and $\frac{9}{4}$:

1. Multiply the numerators: $28 \times 9 = 252$
2. Multiply the denominators: $3 \times 4 = 12$
3. Write the result as the product of the two fractions: $\frac{252}{12}$

Simplifying the Product

The product of the two fractions is $\frac{252}{12}$. However, this fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of $252$ and $12$ is $12$. Therefore, we can simplify the fraction by dividing both the numerator and the denominator by $12$:

$\frac{252}{12} = \frac{252 \div 12}{12 \div 12} = \frac{21}{1}$

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 find the product. In this article, we learned how to calculate the product of two mixed numbers, specifically $9 \frac{1}{3} \times 2 \frac{1}{4}$. We converted the mixed numbers to improper fractions, multiplied the numerators and denominators, and simplified the product. With practice and patience, you can become proficient in calculating the product of mixed numbers.

Example Problems

1. Calculate the product of $5 \frac{2}{3}$ and $3 \frac{1}{2}$.
2. Calculate the product of $2 \frac{3}{4}$ and $4 \frac{2}{3}$.
3. Calculate the product of $6 \frac{1}{2}$ and $2 \frac{1}{3}$.

Tips and Tricks

• When converting mixed numbers to improper fractions, make sure to multiply the whole number by the denominator and add the numerator.
• When multiplying improper fractions, make sure to multiply the numerators and denominators separately.
• When simplifying the product, make sure to divide both the numerator and the denominator by their greatest common divisor (GCD).

Glossary of Terms

• Mixed number: A combination of a whole number and a fraction.
• Improper fraction: A fraction where the numerator is greater than or equal to the denominator.
• Greatest common divisor (GCD): The largest number that divides two or more numbers without leaving a remainder.
  Frequently Asked Questions (FAQs) about Calculating the Product of Mixed Numbers ====================================================================================

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 of $a \frac{b}{c}$, 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 need to multiply the whole number by the denominator and add the numerator. The result is then written as the new numerator over the denominator.

Q: What is an improper fraction?

A: An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, $\frac{5}{2}$ is an improper fraction.

Q: How do I multiply two improper fractions?

A: To multiply two improper fractions, you simply multiply the numerators and multiply the denominators. For example, to multiply $\frac{3}{4}$ and $\frac{5}{6}$, you would multiply the numerators (3 and 5) and multiply the denominators (4 and 6).

Q: How do I simplify a product of fractions?

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

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder.

Q: How do I find the GCD of two numbers?

A: There are several ways to find the GCD of two numbers. One way is to list the factors of each number and find the largest factor they have in common.

Q: Can I use a calculator to find the GCD?

A: Yes, you can use a calculator to find the GCD. Most calculators have a built-in function to find the GCD.

Q: What if I have a mixed number and a fraction? How do I multiply them?

A: To multiply a mixed number and a fraction, you need to convert the mixed number to an improper fraction and then multiply the two fractions.

Q: Can I multiply a mixed number and a fraction in the same way as two fractions?

A: No, you cannot multiply a mixed number and a fraction in the same way as two fractions. You need to convert the mixed number to an improper fraction first.

Q: What if I have a product of fractions and I want to simplify it? How do I do it?

A: To simplify a product of fractions, you need to find the GCD of the numerator and the denominator and divide both by the GCD.

Q: Can I use a calculator to simplify a product of fractions?

A: Yes, you can use a calculator to simplify a product of fractions. Most calculators have a built-in function to simplify fractions.

Q: What if I have a product of mixed numbers and I want to simplify it? How do I do it?

A: To simplify a product of mixed numbers, you need to convert the mixed numbers to improper fractions, multiply the fractions, and then simplify the result.

Q: Can I use a calculator to simplify a product of mixed numbers?

A: Yes, you can use a calculator to simplify a product of mixed numbers. Most calculators have a built-in function to simplify fractions.

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, you can easily find the product. In this article, we answered some frequently asked questions about calculating the product of mixed numbers and provided tips and tricks to help you become proficient in this area.