Padma Has Tried To Work Out $12 \div 1 \frac{1}{3}$.a) Write A Sentence Explaining The Mistake That Padma Has Made.b) Work Out The Correct Answer.$[ \begin{aligned} 12 \div 1 \frac{1}{3} &= 12 \div \frac{4}{3} \ &= 12 \times

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Understanding and Solving Mixed Fractions in Division

When it comes to solving mathematical problems, it's essential to understand the concept of mixed fractions and how to handle them in different operations. In this article, we will explore the mistake made by Padma in her attempt to work out the division problem involving a mixed fraction and provide the correct solution.

The Mistake Made by Padma

Padma's mistake lies in not converting the mixed fraction to an improper fraction before performing the division operation. A mixed fraction is a combination of a whole number and a proper fraction, denoted as a b/c, where a is the whole number and b/c is the proper fraction. In this case, the mixed fraction 1 1/3 can be converted to an improper fraction by multiplying the whole number by the denominator and then adding the numerator. This results in 4/3.

Converting Mixed Fractions to Improper Fractions

To convert a mixed fraction to an improper fraction, we follow these steps:

  1. Multiply the whole number by the denominator.
  2. Add the numerator to the result.
  3. Write the result as an improper fraction.

Using this method, we can convert the mixed fraction 1 1/3 to an improper fraction as follows:

1 1/3 = (1 × 3) + 1 = 4/3

The Correct Solution

Now that we have converted the mixed fraction to an improper fraction, we can proceed with the division operation.

12 ÷ 1 1/3 = 12 ÷ 4/3

To divide by a fraction, we can multiply by its reciprocal. The reciprocal of 4/3 is 3/4.

12 ÷ 4/3 = 12 × 3/4

To multiply a whole number by a fraction, we multiply the whole number by the numerator and keep the denominator the same.

12 × 3/4 = (12 × 3)/4 = 36/4

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 36 and 4 is 4.

36/4 = 9

Therefore, the correct solution to the division problem is 9.

Conclusion

In conclusion, Padma's mistake was not converting the mixed fraction to an improper fraction before performing the division operation. By following the steps outlined in this article, we can convert mixed fractions to improper fractions and perform division operations with ease. Remember to always convert mixed fractions to improper fractions before performing operations involving fractions.

Common Mistakes to Avoid

When working with mixed fractions, it's essential to avoid the following common mistakes:

  • Not converting mixed fractions to improper fractions before performing operations.
  • Not simplifying fractions after performing operations.
  • Not checking for common factors between the numerator and the denominator.

By being aware of these common mistakes, we can ensure that our calculations are accurate and reliable.

Real-World Applications

Mixed fractions are used extensively in real-world applications, such as:

  • Cooking: Recipes often involve mixed fractions, such as 1 1/2 cups of flour.
  • Building: Architects use mixed fractions to specify measurements, such as 2 3/4 inches.
  • Science: Scientists use mixed fractions to represent measurements, such as 3 1/2 liters.

In conclusion, mixed fractions are an essential concept in mathematics, and understanding how to work with them is crucial for solving problems in various fields.

Practice Problems

To reinforce your understanding of mixed fractions, try solving the following practice problems:

  1. Convert the mixed fraction 2 1/4 to an improper fraction.
  2. Perform the division operation 18 ÷ 3 1/2.
  3. Convert the improper fraction 5/6 to a mixed fraction.

By practicing these problems, you will become more confident in your ability to work with mixed fractions and perform operations involving fractions.

Conclusion

In this article, we explored the concept of mixed fractions and how to convert them to improper fractions. We also discussed the common mistakes to avoid when working with mixed fractions and provided real-world applications of mixed fractions. By following the steps outlined in this article, you will become proficient in working with mixed fractions and performing operations involving fractions.
Mixed Fractions Q&A

In this article, we will address some of the most frequently asked questions about mixed fractions, providing clear and concise answers to help you better understand this essential concept in mathematics.

Q: What is a mixed fraction?

A: A mixed fraction is a combination of a whole number and a proper fraction, denoted as a b/c, where a is the whole number and b/c is the proper fraction.

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

A: To convert a mixed fraction to an improper fraction, follow these steps:

  1. Multiply the whole number by the denominator.
  2. Add the numerator to the result.
  3. Write the result as an improper fraction.

For example, to convert the mixed fraction 1 1/3 to an improper fraction, we would:

1 1/3 = (1 × 3) + 1 = 4/3

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

A: To convert an improper fraction to a mixed fraction, follow these steps:

  1. Divide the numerator by the denominator.
  2. Write the result as a whole number and a remainder.
  3. The remainder becomes the new numerator, and the denominator remains the same.

For example, to convert the improper fraction 4/3 to a mixed fraction, we would:

4/3 = 1 1/3

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

A: A mixed fraction is a combination of a whole number and a proper fraction, while an improper fraction is a single fraction with a numerator greater than the denominator.

Q: Can I add or subtract mixed fractions?

A: Yes, you can add or subtract mixed fractions by first converting them to improper fractions, performing the operation, and then converting the result back to a mixed fraction.

Q: Can I multiply or divide mixed fractions?

A: Yes, you can multiply or divide mixed fractions by first converting them to improper fractions, performing the operation, and then converting the result back to a mixed fraction.

Q: What are some common mistakes to avoid when working with mixed fractions?

A: Some common mistakes to avoid when working with mixed fractions include:

  • Not converting mixed fractions to improper fractions before performing operations.
  • Not simplifying fractions after performing operations.
  • Not checking for common factors between the numerator and the denominator.

Q: How do I simplify a mixed fraction?

A: To simplify a mixed fraction, follow these steps:

  1. Convert the mixed fraction to an improper fraction.
  2. Simplify the improper fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
  3. Convert the simplified improper fraction back to a mixed fraction.

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

A: Mixed fractions are used extensively in real-world applications, such as:

  • Cooking: Recipes often involve mixed fractions, such as 1 1/2 cups of flour.
  • Building: Architects use mixed fractions to specify measurements, such as 2 3/4 inches.
  • Science: Scientists use mixed fractions to represent measurements, such as 3 1/2 liters.

Q: How do I practice working with mixed fractions?

A: To practice working with mixed fractions, try solving the following problems:

  1. Convert the mixed fraction 2 1/4 to an improper fraction.
  2. Perform the division operation 18 ÷ 3 1/2.
  3. Convert the improper fraction 5/6 to a mixed fraction.

By practicing these problems, you will become more confident in your ability to work with mixed fractions and perform operations involving fractions.

Conclusion

In this article, we addressed some of the most frequently asked questions about mixed fractions, providing clear and concise answers to help you better understand this essential concept in mathematics. By following the steps outlined in this article, you will become proficient in working with mixed fractions and performing operations involving fractions.