Calculate The Product: 2 1 2 × 3 4 5 = 2 \frac{1}{2} \times 3 \frac{4}{5} = 2 2 1 ​ × 3 5 4 ​ =

Calculate the Product: $2 \frac{1}{2} \times 3 \frac{4}{5}$

In mathematics, multiplication of fractions and mixed numbers is a fundamental operation that requires a clear understanding of the concept. A mixed number is a combination of a whole number and a fraction, while a fraction represents a part of a whole. In this article, we will explore the process of calculating the product of two mixed numbers, $2 \frac{1}{2} \times 3 \frac{4}{5}$.

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, $2 \frac{1}{2}$ is a mixed number where $2$ is the whole number, $1$ is the numerator, and $2$ is the denominator.

Converting Mixed Numbers to Improper Fractions

To multiply mixed numbers, it is often easier 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 product as the numerator and the original denominator as the denominator.

For example, to convert $2 \frac{1}{2}$ to an improper fraction, we multiply $2$ by $2$ and add $1$, resulting in $\frac{5}{2}$. Similarly, to convert $3 \frac{4}{5}$ to an improper fraction, we multiply $3$ by $5$ and add $4$, resulting in $\frac{19}{5}$.

Multiplying Improper Fractions

Now that we have converted the mixed numbers to improper fractions, we can multiply them together. To multiply two improper fractions, we multiply the numerators together and multiply the denominators together. The result is then written as a fraction with the product of the numerators as the numerator and the product of the denominators as the denominator.

For example, to multiply $\frac{5}{2}$ and $\frac{19}{5}$, we multiply $5$ and $19$ to get $95$, and multiply $2$ and $5$ to get $10$. The result is $\frac{95}{10}$.

Simplifying the Result

The result of the multiplication, $\frac{95}{10}$, can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of $95$ and $10$ is $5$, so we divide both the numerator and the denominator by $5$ to get $\frac{19}{2}$.

In conclusion, calculating the product of two mixed numbers, $2 \frac{1}{2} \times 3 \frac{4}{5}$, requires converting the mixed numbers to improper fractions, multiplying the improper fractions together, and simplifying the result. By following these steps, we can accurately calculate the product of two mixed numbers.

• $2 \frac{1}{3} \times 4 \frac{2}{5} = ?$
• $3 \frac{1}{4} \times 2 \frac{3}{5} = ?$
• $1 \frac{1}{2} \times 3 \frac{4}{7} = ?$

$2 \frac{1}{3} \times 4 \frac{2}{5}$

1. Convert the mixed numbers to improper fractions: $\frac{7}{3}$ and $\frac{22}{5}$.
2. Multiply the improper fractions together: $\frac{7}{3} \times \frac{22}{5} = \frac{154}{15}$.
3. Simplify the result: $\frac{154}{15}$ cannot be simplified further.

$3 \frac{1}{4} \times 2 \frac{3}{5}$

1. Convert the mixed numbers to improper fractions: $\frac{13}{4}$ and $\frac{13}{5}$.
2. Multiply the improper fractions together: $\frac{13}{4} \times \frac{13}{5} = \frac{169}{20}$.
3. Simplify the result: $\frac{169}{20}$ cannot be simplified further.

$1 \frac{1}{2} \times 3 \frac{4}{7}$

1. Convert the mixed numbers to improper fractions: $\frac{3}{2}$ and $\frac{25}{7}$.
2. Multiply the improper fractions together: $\frac{3}{2} \times \frac{25}{7} = \frac{75}{14}$.
3. Simplify the result: $\frac{75}{14}$ cannot be simplified further.

Frequently Asked Questions

Q: What is the product of $2 \frac{1}{2} \times 3 \frac{4}{5}$?

A: The product of $2 \frac{1}{2} \times 3 \frac{4}{5}$ is $\frac{19}{2}$.

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

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

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Q: How do I multiply two improper fractions together?

A: To multiply two improper fractions together, multiply the numerators together and multiply the denominators together. The result is then written as a fraction with the product of the numerators as the numerator and the product of the denominators as the denominator.

Q: Can I simplify the result of multiplying two improper fractions?

A: Yes, you can simplify the result of multiplying two improper fractions by dividing both the numerator and the denominator by their greatest common divisor (GCD).

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

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

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

A: To find the GCD of two numbers, list the factors of each number and find the largest factor that they have in common.

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

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

Q: What is the product of $4 \frac{2}{3} \times 2 \frac{1}{5}$?

A: To find the product of $4 \frac{2}{3} \times 2 \frac{1}{5}$, first convert the mixed numbers to improper fractions: $\frac{14}{3}$ and $\frac{11}{5}$. Then multiply the improper fractions together: $\frac{14}{3} \times \frac{11}{5} = \frac{154}{15}$. The result cannot be simplified further.

Q: What is the product of $3 \frac{4}{7} \times 2 \frac{3}{5}$?

A: To find the product of $3 \frac{4}{7} \times 2 \frac{3}{5}$, first convert the mixed numbers to improper fractions: $\frac{25}{7}$ and $\frac{13}{5}$. Then multiply the improper fractions together: $\frac{25}{7} \times \frac{13}{5} = \frac{325}{35}$. The result can be simplified by dividing both the numerator and the denominator by their GCD, which is 5. The simplified result is $\frac{65}{7}$.

Q: What is the product of $1 \frac{1}{2} \times 3 \frac{4}{7}$?

A: To find the product of $1 \frac{1}{2} \times 3 \frac{4}{7}$, first convert the mixed numbers to improper fractions: $\frac{3}{2}$ and $\frac{25}{7}$. Then multiply the improper fractions together: $\frac{3}{2} \times \frac{25}{7} = \frac{75}{14}$. The result cannot be simplified further.

The final answer is $\boxed{\frac{19}{2}}$.