What Is $4 \times 5 \frac{9}{10}$?- Mixed Number- Fraction- Whole Number\[$\square\$\]

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What is $4 \times 5 \frac{9}{10}$?- Mixed number- Fraction- Whole number

Understanding the Problem

When dealing with multiplication involving mixed numbers, fractions, and whole numbers, it's essential to understand the concept of mixed numbers and how to convert them into improper fractions. A mixed number is a combination of a whole number and a proper fraction. In this case, we have a mixed number, 59105 \frac{9}{10}, which can be converted into an improper fraction.

Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and then add the numerator. The result becomes the new numerator, while the denominator remains the same. In this case, we have:

5910=(5×10)+910=50+910=59105 \frac{9}{10} = \frac{(5 \times 10) + 9}{10} = \frac{50 + 9}{10} = \frac{59}{10}

Multiplying Fractions

Now that we have the mixed number converted into an improper fraction, we can proceed with the multiplication. When multiplying fractions, we multiply the numerators together and the denominators together. In this case, we have:

4×5910=4×5910=236104 \times \frac{59}{10} = \frac{4 \times 59}{10} = \frac{236}{10}

Simplifying the Result

The result of the multiplication is an improper fraction. To simplify it, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 236 and 10 is 2. Dividing both the numerator and the denominator by 2, we get:

23610=1185\frac{236}{10} = \frac{118}{5}

Converting the Result to a Mixed Number

To convert the improper fraction back into a mixed number, we divide the numerator by the denominator and keep the remainder as the new numerator. The result becomes the new whole number. In this case, we have:

1185=2335\frac{118}{5} = 23 \frac{3}{5}

Conclusion

In conclusion, when dealing with multiplication involving mixed numbers, fractions, and whole numbers, it's essential to understand the concept of mixed numbers and how to convert them into improper fractions. By following the steps outlined above, we can simplify the result and convert it back into a mixed number.

Key Takeaways

  • Mixed numbers can be converted into improper fractions by multiplying the whole number by the denominator and adding the numerator.
  • When multiplying fractions, we multiply the numerators together and the denominators together.
  • The result of the multiplication can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD).
  • The result can be converted back into a mixed number by dividing the numerator by the denominator and keeping the remainder as the new numerator.

Real-World Applications

Understanding how to multiply mixed numbers, fractions, and whole numbers is essential in various real-world applications, such as:

  • Cooking: When a recipe requires a certain amount of ingredients, it's essential to understand how to multiply mixed numbers and fractions to get the correct amount.
  • Building: When building a structure, it's essential to understand how to multiply mixed numbers and fractions to get the correct measurements.
  • Finance: When dealing with financial transactions, it's essential to understand how to multiply mixed numbers and fractions to get the correct amounts.

Common Mistakes

When dealing with multiplication involving mixed numbers, fractions, and whole numbers, some common mistakes to avoid include:

  • Not converting the mixed number into an improper fraction before multiplying.
  • Not simplifying the result after multiplication.
  • Not converting the result back into a mixed number after simplification.

Tips and Tricks

To make multiplication involving mixed numbers, fractions, and whole numbers easier, here are some tips and tricks:

  • Use a calculator to simplify the result after multiplication.
  • Use a chart or table to keep track of the numerators and denominators.
  • Practice, practice, practice to become more comfortable with multiplication involving mixed numbers, fractions, and whole numbers.

Conclusion

In conclusion, understanding how to multiply mixed numbers, fractions, and whole numbers is essential in various real-world applications. By following the steps outlined above and avoiding common mistakes, we can simplify the result and convert it back into a mixed number. With practice and patience, we can become more comfortable with multiplication involving mixed numbers, fractions, and whole numbers.
Frequently Asked Questions (FAQs) - Multiplication Involving Mixed Numbers, Fractions, and Whole 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 proper 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, multiply the whole number by the denominator and add the numerator. The result becomes the new numerator, while the denominator remains the same.

Q: What is the rule for multiplying fractions?

A: When multiplying fractions, multiply the numerators together and the denominators together.

Q: How do I simplify the result after multiplication?

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

Q: Can I convert the result back into a mixed number after simplification?

A: Yes, you can convert the result back into a mixed number by dividing the numerator by the denominator and keeping the remainder as the new numerator.

Q: What are some common mistakes to avoid when dealing with multiplication involving mixed numbers, fractions, and whole numbers?

A: Some common mistakes to avoid include not converting the mixed number into an improper fraction before multiplying, not simplifying the result after multiplication, and not converting the result back into a mixed number after simplification.

Q: How can I make multiplication involving mixed numbers, fractions, and whole numbers easier?

A: You can use a calculator to simplify the result after multiplication, use a chart or table to keep track of the numerators and denominators, and practice, practice, practice to become more comfortable with multiplication involving mixed numbers, fractions, and whole numbers.

Q: What are some real-world applications of multiplication involving mixed numbers, fractions, and whole numbers?

A: Some real-world applications include cooking, building, and finance. In cooking, you may need to multiply mixed numbers and fractions to get the correct amount of ingredients. In building, you may need to multiply mixed numbers and fractions to get the correct measurements. In finance, you may need to multiply mixed numbers and fractions to get the correct amounts.

Q: Can I use a calculator to simplify the result after multiplication?

A: Yes, you can use a calculator to simplify the result after multiplication. However, it's still essential to understand the concept of multiplication involving mixed numbers, fractions, and whole numbers to avoid common mistakes.

Q: How can I practice multiplication involving mixed numbers, fractions, and whole numbers?

A: You can practice multiplication involving mixed numbers, fractions, and whole numbers by using online resources, such as worksheets and practice problems, or by working with a tutor or teacher.

Q: What are some tips for converting mixed numbers to improper fractions?

A: Some tips for converting mixed numbers to improper fractions include multiplying the whole number by the denominator and adding the numerator, and using a chart or table to keep track of the numerators and denominators.

Q: Can I use a chart or table to keep track of the numerators and denominators?

A: Yes, you can use a chart or table to keep track of the numerators and denominators. This can help you to avoid common mistakes and make multiplication involving mixed numbers, fractions, and whole numbers easier.

Q: How can I use multiplication involving mixed numbers, fractions, and whole numbers in real-world applications?

A: You can use multiplication involving mixed numbers, fractions, and whole numbers in real-world applications by applying the concepts to cooking, building, and finance. For example, you may need to multiply mixed numbers and fractions to get the correct amount of ingredients in a recipe, or to get the correct measurements for a building project.

Q: What are some common misconceptions about multiplication involving mixed numbers, fractions, and whole numbers?

A: Some common misconceptions about multiplication involving mixed numbers, fractions, and whole numbers include thinking that you can simply multiply the whole number by the fraction, or that you can ignore the denominator when multiplying fractions. It's essential to understand the concept of multiplication involving mixed numbers, fractions, and whole numbers to avoid these common misconceptions.