Write 5.2 As A Fraction Or Mixed Number.A. \[$\frac{52}{10}\$\]B. \[$5 \frac{2}{10}\$\]C. \[$\frac{52}{100}\$\]D. \[$5 \frac{2}{100}\$\]

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Introduction

In mathematics, decimals and fractions are two ways to represent numbers. While decimals are often used in everyday calculations, fractions are a more fundamental way to express numbers as a ratio of two integers. In this article, we will explore how to write decimals as fractions or mixed numbers, with a focus on the decimal 5.2.

What is a Decimal?

A decimal is a way to represent a number using a point (.) as a separator between the whole number part and the fractional part. For example, the decimal 5.2 can be read as "five and two tenths." Decimals are often used in calculations involving money, measurements, and percentages.

Writing Decimals as Fractions

To write a decimal as a fraction, we need to convert the decimal into a ratio of two integers. This can be done by considering the decimal as a fraction with a denominator of 10, 100, 1000, and so on. For example, the decimal 5.2 can be written as a fraction with a denominator of 10:

5210\frac{52}{10}

This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2. This gives us:

265\frac{26}{5}

However, this is not the only way to write the decimal 5.2 as a fraction. We can also consider the decimal as a fraction with a denominator of 100:

520100\frac{520}{100}

This fraction can be simplified by dividing both the numerator and the denominator by their GCD, which is 20. This gives us:

265\frac{26}{5}

As we can see, the fraction 265\frac{26}{5} is equivalent to both 5210\frac{52}{10} and 520100\frac{520}{100}. This is because the decimal 5.2 can be represented as a fraction with a denominator of 10 or 100, and both fractions are equivalent.

Writing Decimals as Mixed Numbers

A mixed number is a way to represent a number as a combination of a whole number and a fraction. For example, the mixed number 52105 \frac{2}{10} can be read as "five and two tenths." To write a decimal as a mixed number, we need to separate the whole number part from the fractional part.

For example, the decimal 5.2 can be written as a mixed number as follows:

52105 \frac{2}{10}

This mixed number can be simplified by dividing the numerator of the fraction by the denominator, which gives us:

5155 \frac{1}{5}

However, this is not the only way to write the decimal 5.2 as a mixed number. We can also consider the decimal as a mixed number with a denominator of 100:

5201005 \frac{20}{100}

This mixed number can be simplified by dividing the numerator of the fraction by the denominator, which gives us:

5155 \frac{1}{5}

As we can see, the mixed number 5155 \frac{1}{5} is equivalent to both 52105 \frac{2}{10} and 5201005 \frac{20}{100}. This is because the decimal 5.2 can be represented as a mixed number with a denominator of 10 or 100, and both mixed numbers are equivalent.

Conclusion

In conclusion, the decimal 5.2 can be written as a fraction or a mixed number. The fraction 5210\frac{52}{10} is equivalent to the mixed number 52105 \frac{2}{10}, and both are equivalent to the fraction 265\frac{26}{5}. Similarly, the mixed number 52105 \frac{2}{10} is equivalent to the mixed number 5201005 \frac{20}{100}, and both are equivalent to the fraction 265\frac{26}{5}.

Answer

Based on the above discussion, the correct answer is:

  • A. 5210\frac{52}{10}
  • B. 52105 \frac{2}{10}
  • C. 52100\frac{52}{100}
  • D. 521005 \frac{2}{100}

All of these options are correct, as they represent the decimal 5.2 as a fraction or a mixed number. However, the most simplified and correct answer is:

  • A. 5210\frac{52}{10}

Introduction

In our previous article, we explored how to write decimals as fractions or mixed numbers, with a focus on the decimal 5.2. In this article, we will answer some frequently asked questions (FAQs) related to writing decimals as fractions or mixed numbers.

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

A: A fraction is a way to represent a number as a ratio of two integers, while a mixed number is a way to represent a number as a combination of a whole number and a fraction.

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

A: To convert a decimal to a fraction, you can consider the decimal as a fraction with a denominator of 10, 100, 1000, and so on. For example, the decimal 5.2 can be written as a fraction with a denominator of 10:

5210\frac{52}{10}

Q: How do I simplify a fraction?

A: To simplify a fraction, you can divide both the numerator and the denominator by their greatest common divisor (GCD). For example, the fraction 5210\frac{52}{10} can be simplified by dividing both the numerator and the denominator by their GCD, which is 2. This gives us:

265\frac{26}{5}

Q: How do I convert a decimal to a mixed number?

A: To convert a decimal to a mixed number, you can separate the whole number part from the fractional part. For example, the decimal 5.2 can be written as a mixed number as follows:

52105 \frac{2}{10}

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

A: A decimal is a way to represent a number using a point (.) as a separator between the whole number part and the fractional part, while a fraction is a way to represent a number as a ratio of two integers.

Q: Can a decimal be written as a fraction with a denominator of 100?

A: Yes, a decimal can be written as a fraction with a denominator of 100. For example, the decimal 5.2 can be written as a fraction with a denominator of 100:

520100\frac{520}{100}

Q: Can a decimal be written as a mixed number with a denominator of 100?

A: Yes, a decimal can be written as a mixed number with a denominator of 100. For example, the decimal 5.2 can be written as a mixed number with a denominator of 100:

5201005 \frac{20}{100}

Q: How do I determine the denominator of a fraction or mixed number?

A: The denominator of a fraction or mixed number is the number that is being divided into the numerator. For example, in the fraction 5210\frac{52}{10}, the denominator is 10.

Q: Can a fraction or mixed number be simplified further?

A: Yes, a fraction or mixed number can be simplified further by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Conclusion

In conclusion, writing decimals as fractions or mixed numbers is an important concept in mathematics. By understanding how to convert decimals to fractions or mixed numbers, you can simplify calculations and solve problems more easily. We hope that this Q&A article has helped to clarify any questions you may have had about writing decimals as fractions or mixed numbers.

Common Mistakes to Avoid

  • Not considering the denominator: When converting a decimal to a fraction, make sure to consider the denominator of the fraction.
  • Not simplifying the fraction: When simplifying a fraction, make sure to divide both the numerator and the denominator by their greatest common divisor (GCD).
  • Not separating the whole number part from the fractional part: When converting a decimal to a mixed number, make sure to separate the whole number part from the fractional part.

Practice Problems

  • Convert the decimal 3.5 to a fraction.
  • Convert the decimal 2.8 to a mixed number.
  • Simplify the fraction 248\frac{24}{8}.
  • Convert the fraction 3612\frac{36}{12} to a decimal.

Answer Key

  • 3.5 = 3510\frac{35}{10}
  • 2.8 = 28102 \frac{8}{10}
  • 248=3\frac{24}{8} = 3
  • 3612=3\frac{36}{12} = 3

We hope that this Q&A article has helped to clarify any questions you may have had about writing decimals as fractions or mixed numbers. If you have any further questions, please don't hesitate to ask.