Multiply. Write Your Answer As A Fraction, Whole Number, Or Mixed Number.$4 \frac{1}{2} \times \frac{3}{4} =$\square$

Understanding the Problem

In this problem, we are required to multiply two mixed numbers and fractions, $4 \frac{1}{2}$ and $\frac{3}{4}$. To solve this problem, we need to first convert the mixed number $4 \frac{1}{2}$ into an improper fraction.

Converting Mixed Numbers to Improper Fractions

A mixed number is a combination of a whole number and a fraction. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and then add the numerator. The result is then written as the new numerator over the denominator.

In this case, $4 \frac{1}{2}$ can be converted to an improper fraction as follows:

$4 \frac{1}{2} = \frac{(4 \times 2) + 1}{2} = \frac{8 + 1}{2} = \frac{9}{2}$

Multiplying the Fractions

Now that we have converted the mixed number to an improper fraction, we can multiply the two fractions together.

$\frac{9}{2} \times \frac{3}{4} = \frac{9 \times 3}{2 \times 4} = \frac{27}{8}$

Simplifying the Result

The result of the multiplication is $\frac{27}{8}$. However, we can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

The GCD of 27 and 8 is 1, so the fraction $\frac{27}{8}$ is already in its simplest form.

Conclusion

In conclusion, the product of $4 \frac{1}{2}$ and $\frac{3}{4}$ is $\frac{27}{8}$.

Why is this Important?

Multiplying mixed numbers and fractions is an important skill in mathematics, as it allows us to solve a wide range of problems in algebra, geometry, and other areas of mathematics.

Real-World Applications

Multiplying mixed numbers and fractions has many real-world applications, such as calculating the area of a room, the volume of a container, or the cost of a product.

Tips and Tricks

When multiplying mixed numbers and fractions, it is often helpful to convert the mixed number to an improper fraction first. This can make the multiplication process easier and less prone to errors.

Common Mistakes

One common mistake when multiplying mixed numbers and fractions is to forget to convert the mixed number to an improper fraction. This can lead to incorrect results and confusion.

Practice Problems

To practice multiplying mixed numbers and fractions, try the following problems:

• $3 \frac{1}{3} \times \frac{2}{5} = \square$
• $2 \frac{3}{4} \times \frac{5}{6} = \square$
• $1 \frac{1}{2} \times \frac{3}{8} = \square$

Answer Key

• $3 \frac{1}{3} \times \frac{2}{5} = \frac{11}{10}$
• $2 \frac{3}{4} \times \frac{5}{6} = \frac{25}{12}$
• $1 \frac{1}{2} \times \frac{3}{8} = \frac{3}{8}$
  Multiplication of Mixed Numbers and Fractions: Q&A =====================================================

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions about multiplying mixed numbers and fractions.

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 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 then add the numerator. The result is then written as the new numerator over the denominator.

Q: What is the greatest common divisor (GCD) and why is it important?

A: The GCD is the largest number that divides two or more numbers without leaving a remainder. It is important because it helps us simplify fractions by dividing both the numerator and the denominator by their GCD.

Q: How do I multiply mixed numbers and fractions?

A: To multiply mixed numbers and fractions, you first convert the mixed number to an improper fraction. Then, you multiply the two fractions together by multiplying the numerators and denominators separately.

Q: What are some common mistakes to avoid when multiplying mixed numbers and fractions?

A: Some common mistakes to avoid when multiplying mixed numbers and fractions include forgetting to convert the mixed number to an improper fraction, multiplying the whole numbers and fractions separately, and not simplifying the result.

Q: How do I simplify a fraction?

A: To simplify a fraction, you divide both the numerator and the denominator by their greatest common divisor (GCD).

Q: What are some real-world applications of multiplying mixed numbers and fractions?

A: Some real-world applications of multiplying mixed numbers and fractions include calculating the area of a room, the volume of a container, or the cost of a product.

Q: How can I practice multiplying mixed numbers and fractions?

A: You can practice multiplying mixed numbers and fractions by trying the following problems:

• $3 \frac{1}{3} \times \frac{2}{5} = \square$
• $2 \frac{3}{4} \times \frac{5}{6} = \square$
• $1 \frac{1}{2} \times \frac{3}{8} = \square$

Q: What are some tips and tricks for multiplying mixed numbers and fractions?

A: Some tips and tricks for multiplying mixed numbers and fractions include converting the mixed number to an improper fraction first, multiplying the numerators and denominators separately, and simplifying the result.

Q: How can I use technology to help me multiply mixed numbers and fractions?

A: You can use technology such as calculators or online tools to help you multiply mixed numbers and fractions. These tools can help you convert mixed numbers to improper fractions, multiply fractions, and simplify results.

Q: What are some common misconceptions about multiplying mixed numbers and fractions?

A: Some common misconceptions about multiplying mixed numbers and fractions include thinking that you can multiply the whole numbers and fractions separately, or that you don't need to simplify the result.

Q: How can I apply what I've learned about multiplying mixed numbers and fractions to real-world problems?

A: You can apply what you've learned about multiplying mixed numbers and fractions to real-world problems by using the skills and concepts you've learned to solve problems in areas such as algebra, geometry, and other areas of mathematics.

Conclusion

In conclusion, multiplying mixed numbers and fractions is an important skill in mathematics that has many real-world applications. By understanding the concepts and techniques involved in multiplying mixed numbers and fractions, you can solve a wide range of problems in algebra, geometry, and other areas of mathematics.