What Is $4 \times 5 \frac{3}{4}$?

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Understanding the Problem

When dealing with multiplication of mixed numbers, it's essential to understand the concept of converting mixed numbers to improper fractions. 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 the denominator. In this case, we have the mixed number $5 \frac{3}{4}$, and we need to multiply it by 4.

Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, we need to multiply the whole number part by the denominator and then add the numerator. In this case, we have $5 \frac{3}{4}$, which can be converted to an improper fraction as follows:

$$5 \frac{3}{4} = \frac{(5 \times 4) + 3}{4} = \frac{20 + 3}{4} = \frac{23}{4}$$

Multiplying Improper Fractions

Now that we have converted the mixed number to an improper fraction, we can multiply it by 4. To multiply two improper fractions, we simply multiply the numerators and denominators separately.

$$4 \times \frac{23}{4} = \frac{4 \times 23}{4 \times 4} = \frac{92}{16}$$

Simplifying the Result

The result we obtained is an improper fraction. However, we can simplify it by dividing both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 92 and 16 is 4.

$$\frac{92}{16} = \frac{92 \div 4}{16 \div 4} = \frac{23}{4}$$

Final Answer

Therefore, the final answer to the problem $4 \times 5 \frac{3}{4}$ is $\frac{23}{4}$.

Real-World Applications

Multiplication of mixed numbers is an essential concept in mathematics, and it has numerous real-world applications. For example, in architecture, mixed numbers are used to represent measurements of lengths and widths of buildings. In cooking, mixed numbers are used to represent measurements of ingredients. In finance, mixed numbers are used to represent interest rates and investment returns.

Conclusion

In conclusion, multiplying mixed numbers involves converting them to improper fractions and then multiplying the resulting fractions. The result can be simplified by dividing both the numerator and denominator by their greatest common divisor. This concept is essential in mathematics and has numerous real-world applications.

Common Mistakes to Avoid

When multiplying mixed numbers, it's essential to avoid common mistakes such as:

• Not converting the mixed number to an improper fraction
• Not multiplying the numerators and denominators separately
• Not simplifying the result by dividing both the numerator and denominator by their greatest common divisor

Tips and Tricks

Here are some tips and tricks to help you master the concept of multiplying mixed numbers:

• Always convert mixed numbers to improper fractions before multiplying
• Multiply the numerators and denominators separately
• Simplify the result by dividing both the numerator and denominator by their greatest common divisor
• Practice, practice, practice! The more you practice, the more comfortable you'll become with multiplying mixed numbers.

Frequently Asked Questions

Here are some frequently asked questions related to multiplying mixed numbers:

• What is the difference between a mixed number and an improper fraction?
  • 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 the denominator.
• How do I convert a mixed number to an improper fraction?
  • To convert a mixed number to an improper fraction, multiply the whole number part by the denominator and then add the numerator.
• How do I multiply two improper fractions?
  • To multiply two improper fractions, multiply the numerators and denominators separately.

References

Here are some references related to multiplying mixed numbers:

• Math Open Reference
• Khan Academy
• Mathway

Conclusion

Frequently Asked Questions

Here are some frequently asked questions related to multiplying mixed numbers:

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 the denominator.

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 part by the denominator and then add the numerator. For example, to convert $5 \frac{3}{4}$ to an improper fraction, multiply 5 by 4 and add 3 to get $\frac{20 + 3}{4} = \frac{23}{4}$.

Q: How do I multiply two improper fractions?

A: To multiply two improper fractions, multiply the numerators and denominators separately. For example, to multiply $\frac{4}{5}$ and $\frac{3}{4}$, multiply 4 by 3 to get 12 and multiply 5 by 4 to get 20, resulting in $\frac{12}{20}$.

Q: How do I simplify the result of multiplying mixed numbers?

A: To simplify the result of multiplying mixed numbers, divide both the numerator and denominator by their greatest common divisor (GCD). For example, to simplify $\frac{92}{16}$, divide both 92 and 16 by 4 to get $\frac{23}{4}$.

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

A: Some common mistakes to avoid when multiplying mixed numbers include:

• Not converting the mixed number to an improper fraction
• Not multiplying the numerators and denominators separately
• Not simplifying the result by dividing both the numerator and denominator by their greatest common divisor

Q: How do I practice multiplying mixed numbers?

A: To practice multiplying mixed numbers, try the following:

• Start with simple mixed numbers, such as $2 \frac{1}{2}$ and $3 \frac{1}{4}$.
• Multiply the mixed numbers and simplify the result.
• Check your answer by converting the mixed numbers to improper fractions and multiplying them.
• Gradually increase the difficulty of the mixed numbers as you become more comfortable with the concept.

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

A: Multiplying mixed numbers has numerous real-world applications, including:

• Architecture: Mixed numbers are used to represent measurements of lengths and widths of buildings.
• Cooking: Mixed numbers are used to represent measurements of ingredients.
• Finance: Mixed numbers are used to represent interest rates and investment returns.

Q: How do I use technology to help me with multiplying mixed numbers?

A: There are several online tools and resources available to help you with multiplying mixed numbers, including:

• Online calculators, such as Mathway and Wolfram Alpha
• Math software, such as Mathematica and Maple
• Online math resources, such as Khan Academy and Math Open Reference

Q: What are some tips and tricks for mastering the concept of multiplying mixed numbers?

A: Here are some tips and tricks for mastering the concept of multiplying mixed numbers:

• Always convert mixed numbers to improper fractions before multiplying.
• Multiply the numerators and denominators separately.
• Simplify the result by dividing both the numerator and denominator by their greatest common divisor.
• Practice, practice, practice! The more you practice, the more comfortable you'll become with multiplying mixed numbers.

Conclusion

In conclusion, multiplying mixed numbers involves converting them to improper fractions and then multiplying the resulting fractions. The result can be simplified by dividing both the numerator and denominator by their greatest common divisor. This concept is essential in mathematics and has numerous real-world applications. By following the tips and tricks outlined in this article, you can master the concept of multiplying mixed numbers and become more confident in your math skills.