Convert \[$2 \frac{1}{5}\$\] Into An Improper Fraction.A. \[$\frac{11}{5}\$\] B. \[$\frac{12}{2}\$\] C. \[$\frac{13}{5}\$\] D. \[$\frac{8}{2}\$\]

What is a Mixed Number?

A mixed number is a combination of a whole number and a proper fraction. It is written in the form of a fraction with a whole number part and a fractional part. For example, $2 \frac{1}{5}$ is a mixed number where 2 is the whole number part and $\frac{1}{5}$ is the fractional part.

Why Convert Mixed Numbers to Improper Fractions?

Converting mixed numbers to improper fractions is an essential skill in mathematics, particularly in algebra and geometry. Improper fractions are easier to work with and can be used to simplify complex calculations. In this article, we will learn how to convert mixed numbers to improper fractions using a step-by-step approach.

Step 1: Multiply the Whole Number by the Denominator

To convert a mixed number to an improper fraction, we need to multiply the whole number part by the denominator of the fractional part. In the case of $2 \frac{1}{5}$, we multiply 2 by 5.

2 × 5 = 10

Step 2: Add the Numerator

Next, we add the numerator of the fractional part to the product obtained in Step 1. In this case, we add 1 to 10.

10 + 1 = 11

Step 3: Write the Improper Fraction

Now that we have the numerator and the denominator, we can write the improper fraction. In this case, the improper fraction is $\frac{11}{5}$.

The Final Answer

Therefore, the mixed number $2 \frac{1}{5}$ can be converted to an improper fraction as $\frac{11}{5}$.

Comparison with Other Options

Let's compare our answer with the other options provided:

• A. $\frac{11}{5}$: This is the correct answer.
• B. $\frac{12}{2}$: This is not the correct answer. The numerator is incorrect.
• C. $\frac{13}{5}$: This is not the correct answer. The numerator is incorrect.
• D. $\frac{8}{2}$: This is not the correct answer. The numerator and denominator are incorrect.

Conclusion

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions about converting mixed numbers to improper fractions.

Q: What is a mixed number?

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

Q: Why convert mixed numbers to improper fractions?

A: Converting mixed numbers to improper fractions is an essential skill in mathematics, particularly in algebra and geometry. Improper fractions are easier to work with and can be used to simplify complex calculations.

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

A: To convert a mixed number to an improper fraction, you need to multiply the whole number part by the denominator of the fractional part and then add the numerator. For example, to convert $2 \frac{1}{5}$ to an improper fraction, you would multiply 2 by 5 and then add 1.

Q: What is the formula for converting a mixed number to an improper fraction?

A: The formula for converting a mixed number to an improper fraction is:

Improper Fraction = (Whole Number × Denominator) + Numerator

Q: How do I know if I have the correct answer?

A: To check if you have the correct answer, you can convert the improper fraction back to a mixed number. If the mixed number is the same as the original mixed number, then you have the correct answer.

Q: Can I use a calculator to convert mixed numbers to improper fractions?

A: Yes, you can use a calculator to convert mixed numbers to improper fractions. However, it is always a good idea to understand the process and be able to do it manually.

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

A: Some common mistakes to avoid when converting mixed numbers to improper fractions include:

• Incorrect multiplication: Make sure to multiply the whole number part by the denominator correctly.
• Incorrect addition: Make sure to add the numerator correctly.
• Incorrect order: Make sure to write the improper fraction in the correct order (numerator/denominator).

Q: Can I convert a mixed number to an improper fraction with a negative whole number?

A: Yes, you can convert a mixed number to an improper fraction with a negative whole number. The process is the same as converting a mixed number with a positive whole number.

Q: Can I convert a mixed number to an improper fraction with a negative numerator?

A: Yes, you can convert a mixed number to an improper fraction with a negative numerator. The process is the same as converting a mixed number with a positive numerator.

Conclusion

Converting mixed numbers to improper fractions is a simple process that involves multiplying the whole number part by the denominator and adding the numerator. By following these steps and avoiding common mistakes, you can convert mixed numbers to improper fractions with ease. In this article, we answered some of the most frequently asked questions about converting mixed numbers to improper fractions.