Express $71 \frac{1}{2} %$ As A Fraction In Its Simplest Form.(a) 80 100 \frac{80}{100} 100 80 ​ (b) 143 200 \frac{143}{200} 200 143 ​ (c) 143 100 \frac{143}{100} 100 143 ​ (d) 71 2 \frac{71}{2} 2 71 ​ (e) 13 20 \frac{13}{20} 20 13 ​

Understanding the Problem

Expressing a percentage as a fraction in its simplest form is a fundamental concept in mathematics. It involves converting a percentage value into a fraction and then simplifying it to its lowest terms. In this article, we will explore how to express the percentage $71 \frac{1}{2} \%$ as a fraction in its simplest form.

What is a Percentage?

A percentage is a way of expressing a value as a fraction of 100. It is denoted by the symbol $\%$ and is calculated by dividing the value by 100 and multiplying by 100. For example, $25\%$ is equal to $\frac{25}{100}$.

Converting a Percentage to a Fraction

To convert a percentage to a fraction, we can simply write it as a fraction with 100 as the denominator. For example, $25\%$ can be written as $\frac{25}{100}$. However, this fraction may not be in its simplest form.

Simplifying a Fraction

To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder. Once we have found the GCD, we can divide both the numerator and the denominator by the GCD to simplify the fraction.

Expressing $71 \frac{1}{2} \%$ as a Fraction

To express $71 \frac{1}{2} \%$ as a fraction, we can start by converting the mixed number to an improper fraction. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. To convert a mixed number to an improper fraction, we can multiply the whole number part by the denominator and add the numerator. Then, we can write the result as a fraction with the denominator.

$71 \frac{1}{2} \% = \frac{(71 \times 2) + 1}{2} \% = \frac{143}{2} \%$

Now, we can convert this fraction to a percentage by dividing the numerator by 100 and multiplying by 100.

$\frac{143}{2} \% = \frac{143}{2} \times \frac{100}{100} \% = \frac{14300}{200} \%$

However, this fraction is not in its simplest form. To simplify it, we need to find the GCD of the numerator and the denominator.

Finding the GCD

The GCD of 14300 and 200 is 100. Therefore, we can divide both the numerator and the denominator by 100 to simplify the fraction.

$\frac{14300}{200} \% = \frac{14300 \div 100}{200 \div 100} \% = \frac{143}{2} \%$

However, we can simplify it further by dividing both the numerator and the denominator by their GCD, which is 1.

$\frac{143}{2} \% = \frac{143}{2} \%$

Therefore, the simplest form of the fraction is $\frac{143}{2}$.

Conclusion

In this article, we have learned how to express a percentage as a fraction in its simplest form. We have also seen how to convert a mixed number to an improper fraction and simplify a fraction by finding the GCD of the numerator and the denominator. By following these steps, we can express any percentage as a fraction in its simplest form.

Answer

Understanding the Problem

Expressing a percentage as a fraction in its simplest form is a fundamental concept in mathematics. It involves converting a percentage value into a fraction and then simplifying it to its lowest terms. In this article, we will explore how to express the percentage $71 \frac{1}{2} \%$ as a fraction in its simplest form.

Q&A

Q: What is a percentage?

A: A percentage is a way of expressing a value as a fraction of 100. It is denoted by the symbol $\%$ and is calculated by dividing the value by 100 and multiplying by 100.

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

A: To convert a percentage to a fraction, we can simply write it as a fraction with 100 as the denominator. For example, $25\%$ can be written as $\frac{25}{100}$.

Q: What is an improper fraction?

A: An improper fraction is a fraction where the numerator is greater than or equal to the denominator. To convert a mixed number to an improper fraction, we can multiply the whole number part by the denominator and add the numerator. Then, we can write the result as a fraction with the denominator.

Q: How do I simplify a fraction?

A: To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder. Once we have found the GCD, we can divide both the numerator and the denominator by the GCD to simplify the fraction.

Q: How do I express $71 \frac{1}{2} \%$ as a fraction?

A: To express $71 \frac{1}{2} \%$ as a fraction, we can start by converting the mixed number to an improper fraction. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. To convert a mixed number to an improper fraction, we can multiply the whole number part by the denominator and add the numerator. Then, we can write the result as a fraction with the denominator.

$71 \frac{1}{2} \% = \frac{(71 \times 2) + 1}{2} \% = \frac{143}{2} \%$

Now, we can convert this fraction to a percentage by dividing the numerator by 100 and multiplying by 100.

$\frac{143}{2} \% = \frac{143}{2} \times \frac{100}{100} \% = \frac{14300}{200} \%$

However, this fraction is not in its simplest form. To simplify it, we need to find the GCD of the numerator and the denominator.

Q: What is the GCD of 14300 and 200?

A: The GCD of 14300 and 200 is 100. Therefore, we can divide both the numerator and the denominator by 100 to simplify the fraction.

$\frac{14300}{200} \% = \frac{14300 \div 100}{200 \div 100} \% = \frac{143}{2} \%$

However, we can simplify it further by dividing both the numerator and the denominator by their GCD, which is 1.

$\frac{143}{2} \% = \frac{143}{2} \%$

Therefore, the simplest form of the fraction is $\frac{143}{2}$.

Q: What is the correct answer?

A: The correct answer is (b) $\frac{143}{200}$