Choose The Improper Fraction Equivalent To The Mixed Number Below.${ 3 \frac{3}{7} }$A. { \frac{23}{7}$}$B. { \frac{24}{7}$}$C. { \frac{22}{7}$}$D. { \frac{25}{7}$}$

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Understanding Mixed Numbers and Improper Fractions

In mathematics, mixed numbers and improper fractions are two ways to express a number that is greater than 1. A mixed number consists of a whole number part and a fractional part, while an improper fraction is a single fraction with a numerator greater than the denominator. In this article, we will focus on converting mixed numbers to improper fractions, and we will use the given problem as an example.

What is a Mixed Number?

A mixed number is a combination of a whole number and a fraction. It is written in the form of:

abc{ a \frac{b}{c} }

where:

  • a{ a } is the whole number part
  • b{ b } is the numerator of the fractional part
  • c{ c } is the denominator of the fractional part

What is an Improper Fraction?

An improper fraction is a single fraction with a numerator greater than the denominator. It is written in the form of:

ab{ \frac{a}{b} }

where:

  • a{ a } is the numerator
  • b{ b } is the denominator

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. The result is the new numerator, and the denominator remains the same.

Step-by-Step Procedure

Here are the steps to convert a mixed number to an improper fraction:

  1. Multiply the whole number part by the denominator.
  2. Add the numerator to the result.
  3. Write the result as the new numerator over the denominator.

Example Problem

Let's use the given problem as an example:

337{ 3 \frac{3}{7} }

We need to convert this mixed number to an improper fraction.

Step 1: Multiply the Whole Number Part by the Denominator

Multiply 3 by 7:

3×7=21{ 3 \times 7 = 21 }

Step 2: Add the Numerator

Add 3 to the result:

21+3=24{ 21 + 3 = 24 }

Step 3: Write the Result as the New Numerator Over the Denominator

The new numerator is 24, and the denominator remains 7. Therefore, the improper fraction equivalent to the mixed number is:

247{ \frac{24}{7} }

Answer

The improper fraction equivalent to the mixed number is:

247{ \frac{24}{7} }

This is option B.

Conclusion

In this article, we learned how to convert mixed numbers to improper fractions. We used the given problem as an example and followed the step-by-step procedure to arrive at the correct answer. We also discussed the difference between mixed numbers and improper fractions and provided a clear explanation of the conversion process.

Common Mistakes to Avoid

When converting mixed numbers to improper fractions, it's essential to avoid common mistakes. Here are some tips to help you avoid errors:

  • Make sure to multiply the whole number part by the denominator correctly.
  • Add the numerator to the result correctly.
  • Write the result as the new numerator over the denominator correctly.

Practice Problems

To practice converting mixed numbers to improper fractions, try the following problems:

  1. Convert the mixed number 258{ 2 \frac{5}{8} } to an improper fraction.
  2. Convert the mixed number 423{ 4 \frac{2}{3} } to an improper fraction.
  3. Convert the mixed number 179{ 1 \frac{7}{9} } to an improper fraction.

Answer Key

  1. 198{ \frac{19}{8} }
  2. 143{ \frac{14}{3} }
  3. 169{ \frac{16}{9} }

Conclusion

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 single fraction with a numerator 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 add the numerator. The result is the new numerator, and the denominator remains the same.

Q: What is the step-by-step procedure for converting a mixed number to an improper fraction?

A: Here are the steps to convert a mixed number to an improper fraction:

  1. Multiply the whole number part by the denominator.
  2. Add the numerator to the result.
  3. Write the result as the new numerator over the denominator.

Q: Can you provide an example of converting a mixed number to an improper fraction?

A: Let's use the mixed number 337{ 3 \frac{3}{7} } as an example. To convert this mixed number to an improper fraction, we multiply the whole number part by the denominator:

3×7=21{ 3 \times 7 = 21 }

Then, we add the numerator:

21+3=24{ 21 + 3 = 24 }

Finally, we write the result as the new numerator over the denominator:

247{ \frac{24}{7} }

Q: What are some common mistakes to avoid when converting mixed numbers to improper fractions?

A: Here are some common mistakes to avoid:

  • Make sure to multiply the whole number part by the denominator correctly.
  • Add the numerator to the result correctly.
  • Write the result as the new numerator over the denominator correctly.

Q: How can I practice converting mixed numbers to improper fractions?

A: You can practice converting mixed numbers to improper fractions by trying the following problems:

  1. Convert the mixed number 258{ 2 \frac{5}{8} } to an improper fraction.
  2. Convert the mixed number 423{ 4 \frac{2}{3} } to an improper fraction.
  3. Convert the mixed number 179{ 1 \frac{7}{9} } to an improper fraction.

Q: What are the answers to the practice problems?

A: Here are the answers to the practice problems:

  1. 198{ \frac{19}{8} }
  2. 143{ \frac{14}{3} }
  3. 169{ \frac{16}{9} }

Q: Why is it important to convert mixed numbers to improper fractions?

A: Converting mixed numbers to improper fractions is important because it allows us to perform arithmetic operations more easily. For example, we can add and subtract improper fractions more easily than mixed numbers.

Q: Can you provide any additional tips for converting mixed numbers to improper fractions?

A: Here are some additional tips:

  • Make sure to read the problem carefully and understand what is being asked.
  • Use a step-by-step approach to convert the mixed number to an improper fraction.
  • Check your work to ensure that the answer is correct.

Conclusion

In conclusion, converting mixed numbers to improper fractions is a straightforward process that requires attention to detail. By following the step-by-step procedure and avoiding common mistakes, you can accurately convert mixed numbers to improper fractions. Practice problems are provided to help you reinforce your understanding of the concept.