Sarah Correctly Converted 3.72 Into A Fraction. Is Her Fraction Proper Or Improper? Explain Your Reasoning.Sarah's Fraction Is ____.

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In mathematics, fractions are a way to represent a part of a whole. A fraction consists of two numbers: a numerator and a denominator. The numerator represents the number of equal parts being considered, while the denominator represents the total number of parts the whole is divided into.

What are Proper and Improper Fractions?

A proper fraction is a fraction where the numerator is less than the denominator. For example, 1/2, 3/4, and 2/3 are all proper fractions. On the other hand, an improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, 5/2, 7/4, and 3/2 are all improper fractions.

Converting Decimals to Fractions

Converting decimals to fractions can be a bit tricky, but it's a crucial skill to master in mathematics. When converting a decimal to a fraction, we need to determine whether the resulting fraction is proper or improper.

Sarah's Fraction

Sarah correctly converted 3.72 into a fraction. To do this, we need to convert the decimal 3.72 into a fraction. We can do this by writing 3.72 as 3 + 0.72. Then, we can convert 0.72 into a fraction by writing it as 72/100. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4. This gives us 18/25.

Is Sarah's Fraction Proper or Improper?

Now that we have Sarah's fraction, we can determine whether it's proper or improper. Since the numerator (18) is less than the denominator (25), Sarah's fraction is a proper fraction.

Conclusion

In conclusion, Sarah correctly converted 3.72 into a fraction, which is 18/25. Since the numerator is less than the denominator, Sarah's fraction is a proper fraction.

Key Takeaways

  • A proper fraction is a fraction where the numerator is less than the denominator.
  • An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
  • Converting decimals to fractions can be a bit tricky, but it's a crucial skill to master in mathematics.
  • Sarah's fraction, 18/25, is a proper fraction since the numerator is less than the denominator.

Practice Problems

  • Convert the decimal 2.5 into a fraction. Is the resulting fraction proper or improper?
  • Convert the decimal 4.8 into a fraction. Is the resulting fraction proper or improper?
  • Convert the decimal 1.25 into a fraction. Is the resulting fraction proper or improper?

Answer Key

  • 2.5 = 5/2 (improper fraction)
  • 4.8 = 48/10 = 24/5 (improper fraction)
  • 1.25 = 5/4 (improper fraction)
    Frequently Asked Questions (FAQs) about Proper and Improper Fractions ====================================================================

In our previous article, we discussed the concept of proper and improper fractions, and how to convert decimals to fractions. In this article, we'll answer some frequently asked questions (FAQs) about proper and improper fractions.

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

A: A proper fraction is a fraction where the numerator is less than the denominator. For example, 1/2, 3/4, and 2/3 are all proper fractions. On the other hand, an improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, 5/2, 7/4, and 3/2 are all improper fractions.

Q: How do I convert a decimal to a fraction?

A: To convert a decimal to a fraction, you can follow these steps:

  1. Write the decimal as a fraction by writing it as a numerator over a denominator of 1.
  2. Multiply the numerator and denominator by a power of 10 to get rid of the decimal.
  3. Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor.

For example, to convert 3.72 to a fraction, you can follow these steps:

  1. Write 3.72 as 3 + 0.72.
  2. Write 0.72 as 72/100.
  3. Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4. This gives us 18/25.

Q: How do I determine if a fraction is proper or improper?

A: To determine if a fraction is proper or improper, you can follow these steps:

  1. Compare the numerator and denominator.
  2. If the numerator is less than the denominator, the fraction is proper.
  3. If the numerator is greater than or equal to the denominator, the fraction is improper.

For example, to determine if 18/25 is proper or improper, you can follow these steps:

  1. Compare the numerator (18) and denominator (25).
  2. Since the numerator is less than the denominator, the fraction is proper.

Q: Can a fraction be both proper and improper at the same time?

A: No, a fraction cannot be both proper and improper at the same time. A fraction is either proper or improper, but not both.

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

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

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

For example, to convert 2 3/4 to an improper fraction, you can follow these steps:

  1. Multiply the whole number (2) by the denominator (4). This gives us 8.
  2. Add the numerator (3) to the product. This gives us 11.
  3. Write the result as an improper fraction. This gives us 11/4.

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

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

  1. Divide the numerator by the denominator.
  2. Write the result as a mixed number.

For example, to convert 11/4 to a mixed number, you can follow these steps:

  1. Divide the numerator (11) by the denominator (4). This gives us 2 with a remainder of 3.
  2. Write the result as a mixed number. This gives us 2 3/4.

Conclusion

In conclusion, we've answered some frequently asked questions (FAQs) about proper and improper fractions. We've discussed how to convert decimals to fractions, how to determine if a fraction is proper or improper, and how to convert mixed numbers to improper fractions and vice versa. We hope this article has been helpful in clarifying any confusion you may have had about proper and improper fractions.