Convert the mixed numbers to improper fractions

Oct 13, 2025 by miodeya.com 82 views

$Convert the mixed numbers to improper fractions$

Introduction

When dealing with mixed numbers, it's essential to understand how to multiply them. Mixed numbers are a combination of a whole number and a fraction. In this article, we will explore the process of multiplying mixed numbers and determine if the product will be more or less than $$\frac{39}{2}$$.

Understanding Mixed Numbers

Before we dive into the multiplication process, let's understand what mixed numbers are. A mixed number is a combination of a whole number and a fraction. It's written in the form of $$a \frac{b}{c}$$, where $$a$$ is the whole number, $$b$$ is the numerator, and $$c$$ is the denominator.

Multiplying Mixed Numbers

To multiply mixed numbers, we need to follow a specific process. Here are the steps:

Convert the mixed numbers to improper fractions: We need to convert both mixed numbers to improper fractions. To do this, we multiply the whole number by the denominator and add the numerator. The result is the new numerator, and the denominator remains the same.
Multiply the numerators: Once we have the improper fractions, we multiply the numerators together.
Multiply the denominators: We also multiply the denominators together.
Multiply the numerators and denominators: Now, we multiply the results of the numerator and denominator multiplication.
Simplify the result: Finally, we simplify the result by dividing the numerator by the denominator.

Calculating $$1 \frac{2}{3} \times 3 \frac{1}{2}$$

Let's apply the steps above to calculate $$1 \frac{2}{3} \times 3 \frac{1}{2}$$.

Step 1: Convert the mixed numbers to improper fractions

1 \frac{2}{3} = \frac{(1 \times 3) + 2}{3} = \frac{5}{3}

3 \frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{7}{2}

Step 2: Multiply the numerators

5 \times 7 = 35

Step 3: Multiply the denominators

3 \times 2 = 6

Step 4: Multiply the numerators and denominators

\frac{35}{6}

Step 5: Simplify the result

The result is already in its simplest form.

Conclusion

The product of $$1 \frac{2}{3} \times 3 \frac{1}{2}$$ is $$\frac{35}{6}$$. To determine if the product is more or less than $$\frac{39}{2}$$, we need to compare the two fractions.

Comparing the Fractions

To compare the fractions, we need to find a common denominator. The least common multiple (LCM) of 6 and 2 is 6. We can rewrite $$\frac{39}{2}$$ as $$\frac{39 \times 3}{2 \times 3} = \frac{117}{6}$$.

Now, we can compare the two fractions:

\frac{35}{6} < \frac{117}{6}

Therefore, the product of $$1 \frac{2}{3} \times 3 \frac{1}{2}$$ is less than $$\frac{39}{2}$$.

Final Answer

The final answer is $$\frac{35}{6}$$.

Discussion

Multiplying mixed numbers can be a bit challenging, but with the right steps, it's achievable. In this article, we explored the process of multiplying mixed numbers and determined if the product will be more or less than $$\frac{39}{2}$$. We also compared the fractions to determine the final answer.

Conclusion

In conclusion, multiplying mixed numbers requires a specific process, and it's essential to understand how to convert mixed numbers to improper fractions and vice versa. By following the steps outlined in this article, you can calculate the product of mixed numbers and determine if it's more or less than a given fraction.

Q&A: Multiplying Mixed Numbers

In the previous article, we explored the process of multiplying mixed numbers and calculated the product of $$1 \frac{2}{3} \times 3 \frac{1}{2}$$. In this article, we will answer some frequently asked questions about multiplying mixed numbers.

Q: What is the first step in multiplying mixed numbers?

A: The first step in multiplying mixed numbers is to convert the mixed numbers to improper fractions. This involves multiplying the whole number by the denominator and adding the numerator.

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

Q: What is the next step in multiplying mixed numbers?

A: After converting the mixed numbers to improper fractions, you multiply the numerators together and the denominators together.

Q: How do I multiply the numerators and denominators?

A: To multiply the numerators and denominators, you simply multiply the numbers together. For example, if you have $$\frac{5}{3} \times \frac{7}{2}$$, you would multiply 5 and 7 to get 35, and multiply 3 and 2 to get 6.

Q: What is the final step in multiplying mixed numbers?

A: The final step in multiplying mixed numbers is to simplify the result by dividing the numerator by the denominator.

Q: Can I simplify the result before dividing the numerator by the denominator?

A: Yes, you can simplify the result before dividing the numerator by the denominator. In fact, it's often easier to simplify the result before dividing.

Q: How do I compare two fractions?

A: To compare two fractions, you need to find a common denominator. The least common multiple (LCM) of the two denominators is the common denominator. You can then rewrite each fraction with the common denominator and compare the numerators.

Q: What is the least common multiple (LCM) of two numbers?

A: The least common multiple (LCM) of two numbers is the smallest number that both numbers can divide into evenly.

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

A: To find the LCM of two numbers, you can list the multiples of each number and find the smallest number that appears in both lists.

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

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

Q: What is the final answer to the problem $$1 \frac{2}{3} \times 3 \frac{1}{2}$$?

A: The final answer to the problem $$1 \frac{2}{3} \times 3 \frac{1}{2}$$ is $$\frac{35}{6}$$.

Q: Is the product of $$1 \frac{2}{3} \times 3 \frac{1}{2}$$ more or less than $$\frac{39}{2}$$?

A: The product of $$1 \frac{2}{3} \times 3 \frac{1}{2}$$ is less than $$\frac{39}{2}$$.

Conclusion

Final Answer

The final answer is $$\frac{35}{6}$$.

Discussion

Multiplying mixed numbers can be a bit challenging, but with the right steps, it's achievable. In this article, we explored the process of multiplying mixed numbers and answered some frequently asked questions. We also compared the fractions to determine the final answer.

Related Resources

[Mathway: Multiplying Mixed Numbers](https://www.mathway.com/answers/Multiplying_Mixed_Numbers/1.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0