Which Statement Is True?${ \begin{array}{|l|l|} \hline \frac{4}{5}=0.08 & 4 \frac{2}{5}=4.4 % \ \hline \frac{9}{4}=0.4 & \frac{9}{4}=225 % \ \hline \end{array} }$

Mathematics is a vast and fascinating field that encompasses various branches, including algebra, geometry, calculus, and more. In this article, we will delve into a specific aspect of mathematics, focusing on the comparison of fractions and percentages. We will examine a table containing two statements, each comparing fractions to percentages. Our goal is to determine which statement is true.

Understanding the Table

The table below presents two statements, each consisting of a fraction and a percentage.

Fraction	Percentage
$\frac{4}{5}=0.08$	$4 \frac{2}{5}=4.4 \%$
$\frac{9}{4}=0.4$	$\frac{9}{4}=225 \%$

Analyzing the Statements

To determine which statement is true, we need to carefully analyze each statement.

Statement 1: $\frac{4}{5}=0.08$

To evaluate this statement, we need to convert the fraction $\frac{4}{5}$ to a decimal. We can do this by dividing the numerator (4) by the denominator (5).

$\frac{4}{5} = 0.8$

As we can see, the decimal equivalent of $\frac{4}{5}$ is 0.8, not 0.08. Therefore, the first statement is false.

Statement 2: $4 \frac{2}{5}=4.4 \%$

To evaluate this statement, we need to convert the mixed number $4 \frac{2}{5}$ to a decimal. We can do this by converting the fraction $\frac{2}{5}$ to a decimal and adding it to the whole number 4.

$\frac{2}{5} = 0.4$

Adding this to the whole number 4, we get:

$4 + 0.4 = 4.4$

However, the statement claims that $4 \frac{2}{5}$ is equal to 4.4%, not 4.4. To convert 4.4 to a percentage, we need to multiply it by 100.

$4.4 \times 100 = 440 \%$

As we can see, the decimal equivalent of $4 \frac{2}{5}$ is 4.4, not 4.4%. Therefore, the second statement is also false.

Statement 3: $\frac{9}{4}=0.4$

To evaluate this statement, we need to convert the fraction $\frac{9}{4}$ to a decimal. We can do this by dividing the numerator (9) by the denominator (4).

$\frac{9}{4} = 2.25$

As we can see, the decimal equivalent of $\frac{9}{4}$ is 2.25, not 0.4. Therefore, the third statement is false.

Statement 4: $\frac{9}{4}=225 \%$

To evaluate this statement, we need to convert the fraction $\frac{9}{4}$ to a percentage. We can do this by multiplying the decimal equivalent of $\frac{9}{4}$ by 100.

$2.25 \times 100 = 225 \%$

As we can see, the decimal equivalent of $\frac{9}{4}$ is indeed 2.25, which is equivalent to 225%. Therefore, the fourth statement is true.

Conclusion

In conclusion, after carefully analyzing each statement, we found that only one statement is true. The statement $\frac{9}{4}=225 \%$ is the only true statement in the table. This highlights the importance of carefully converting fractions to decimals and percentages to ensure accuracy in mathematical calculations.

Final Thoughts

Mathematics is a field that requires precision and attention to detail. In this article, we demonstrated the importance of carefully analyzing mathematical statements to determine their truth. By doing so, we can avoid errors and ensure that our calculations are accurate. Whether you are a student, a teacher, or simply someone who enjoys mathematics, this article provides valuable insights into the world of mathematics.

References

• [1] Khan Academy. (n.d.). Fractions and Decimals. Retrieved from https://www.khanacademy.org/math/fractions-and-decimals
• [2] Math Open Reference. (n.d.). Fractions and Decimals. Retrieved from https://www.mathopenref.com/fractionsanddecimals.html

Additional Resources

• [1] Khan Academy. (n.d.). Percentages. Retrieved from https://www.khanacademy.org/math/percentages
• [2] Math Is Fun. (n.d.). Fractions and Decimals. Retrieved from https://www.mathisfun.com/fractions-and-decimals.html
  Frequently Asked Questions (FAQs) =====================================

Mathematics is a vast and fascinating field that encompasses various branches, including algebra, geometry, calculus, and more. In this article, we will delve into a specific aspect of mathematics, focusing on the comparison of fractions and percentages. We will examine a table containing two statements, each comparing fractions to percentages. Our goal is to determine which statement is true.

Q&A Session

Q: What is the difference between a fraction and a percentage?

A: A fraction is a way of expressing a part of a whole, while a percentage is a way of expressing a part of a whole as a proportion of 100.

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

A: To convert a fraction to a decimal, you can divide the numerator (the top number) by the denominator (the bottom number).

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

A: To convert a decimal to a fraction, you can express the decimal as a fraction by writing it as a ratio of the decimal to 1.

Q: What is the relationship between fractions and percentages?

A: Fractions and percentages are related in that they both express a part of a whole. However, fractions express a part of a whole as a ratio, while percentages express a part of a whole as a proportion of 100.

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

A: To convert a fraction to a percentage, you can multiply the fraction by 100.

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

A: To convert a percentage to a fraction, you can express the percentage as a fraction by writing it as a ratio of the percentage to 100.

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 fraction where the numerator is 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, you can multiply the whole number by the denominator and add the numerator, then write the result as a fraction.

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

A: To convert an improper fraction to a mixed number, you can divide the numerator by the denominator and write the result as a whole number and a fraction.

Q: What is the relationship between fractions and decimals?

A: Fractions and decimals are related in that they both express a part of a whole. However, fractions express a part of a whole as a ratio, while decimals express a part of a whole as a decimal value.

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

A: To convert a fraction to a decimal, you can divide the numerator (the top number) by the denominator (the bottom number).

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

A: To convert a decimal to a fraction, you can express the decimal as a fraction by writing it as a ratio of the decimal to 1.

Conclusion

In conclusion, we have answered some of the most frequently asked questions about fractions and percentages. We have discussed the relationship between fractions and percentages, how to convert fractions to decimals and percentages, and how to convert decimals to fractions. We have also discussed the difference between mixed numbers and improper fractions, and how to convert between them.

Final Thoughts

Mathematics is a field that requires precision and attention to detail. In this article, we have demonstrated the importance of carefully analyzing mathematical statements to determine their truth. By doing so, we can avoid errors and ensure that our calculations are accurate. Whether you are a student, a teacher, or simply someone who enjoys mathematics, this article provides valuable insights into the world of mathematics.

References

• [1] Khan Academy. (n.d.). Fractions and Decimals. Retrieved from https://www.khanacademy.org/math/fractions-and-decimals
• [2] Math Open Reference. (n.d.). Fractions and Decimals. Retrieved from https://www.mathopenref.com/fractionsanddecimals.html

Additional Resources

• [1] Khan Academy. (n.d.). Percentages. Retrieved from https://www.khanacademy.org/math/percentages
• [2] Math Is Fun. (n.d.). Fractions and Decimals. Retrieved from https://www.mathisfun.com/fractions-and-decimals.html