Expressing the Fraction in Lowest Terms

Oct 13, 2025 by talynt.org 135 views

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Introduction

In mathematics, percentages are often used to express a value as a fraction of 100. However, when we need to express a percentage as a fraction in its lowest terms, we must perform a series of steps to simplify the fraction. In this article, we will explore how to express the percentage $\frac{1}{2} \%$ as a fraction in its lowest terms.

Understanding Percentages

A percentage is a way of expressing a value as a fraction of 100. It is denoted by the symbol $\%$ . For example, $25\%$ means 25 out of 100, or $\frac{25}{100}$ . To express a percentage as a fraction, we can simply write it as a fraction with a denominator of 100.

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

To express $\frac{1}{2} \%$ as a fraction, we can start by writing it as a fraction with a denominator of 100. This gives us:

\frac{1}{2} \% = \frac{1}{2} \times \frac{1}{100}

Simplifying the Fraction

To simplify the fraction, we can multiply the numerators and denominators together:

\frac{1}{2} \times \frac{1}{100} = \frac{1 \times 1}{2 \times 100} = \frac{1}{200}

Expressing the Fraction in Lowest Terms

To express the fraction in its lowest terms, we need to find the greatest common divisor (GCD) of the numerator and denominator. The GCD of 1 and 200 is 1, so the fraction $\frac{1}{200}$ is already in its lowest terms.

Conclusion

In conclusion, we have expressed the percentage $\frac{1}{2} \%$ as a fraction in its lowest terms. We started by writing it as a fraction with a denominator of 100, then simplified the fraction by multiplying the numerators and denominators together. Finally, we expressed the fraction in its lowest terms by finding the greatest common divisor of the numerator and denominator.

Example Problems

Problem 1

Express $3\%$ as a fraction in its lowest terms.

Solution

To express $3\%$ as a fraction, we can start by writing it as a fraction with a denominator of 100:

3\% = \frac{3}{100}

We can then simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 1:

\frac{3}{100} = \frac{3}{100}

Since the GCD of 3 and 100 is 1, the fraction $\frac{3}{100}$ is already in its lowest terms.

Problem 2

Express $12\%$ as a fraction in its lowest terms.

Solution

To express $12\%$ as a fraction, we can start by writing it as a fraction with a denominator of 100:

12\% = \frac{12}{100}

We can then simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4:

\frac{12}{100} = \frac{3}{25}

Since the GCD of 3 and 25 is 1, the fraction $\frac{3}{25}$ is already in its lowest terms.

Tips and Tricks

When expressing a percentage as a fraction, make sure to write it as a fraction with a denominator of 100.
To simplify a fraction, multiply the numerators and denominators together.
To express a fraction in its lowest terms, find the greatest common divisor of the numerator and denominator.

Frequently Asked Questions

Q: How do I express a percentage as a fraction?

A: To express a percentage as a fraction, write it as a fraction with a denominator of 100.

Q: How do I simplify a fraction?

A: To simplify a fraction, multiply the numerators and denominators together.

Q: How do I express a fraction in its lowest terms?

A: To express a fraction in its lowest terms, find the greatest common divisor of the numerator and denominator.

Conclusion

In conclusion, expressing a percentage as a fraction in its lowest terms requires a series of steps. We must start by writing the percentage as a fraction with a denominator of 100, then simplify the fraction by multiplying the numerators and denominators together. Finally, we must express the fraction in its lowest terms by finding the greatest common divisor of the numerator and denominator. By following these steps, we can express any percentage as a fraction in its lowest terms.

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Introduction

Expressing percentages as fractions can be a challenging task, especially when it comes to simplifying the fraction and expressing it in its lowest terms. In this article, we will provide a comprehensive Q&A guide to help you understand how to express percentages as fractions and simplify them.

Q&A Guide

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 $\%$ . For example, $25\%$ means 25 out of 100, or $\frac{25}{100}$ .

Q: How do I express a percentage as a fraction?

A: To express a percentage as a fraction, write it as a fraction with a denominator of 100. For example, $25\%$ can be expressed as $\frac{25}{100}$ .

Q: How do I simplify a fraction?

A: To simplify a fraction, multiply the numerators and denominators together. For example, $\frac{25}{100}$ can be simplified to $\frac{1}{4}$ by dividing both the numerator and denominator by 25.

Q: How do I express a fraction in its lowest terms?

A: To express a fraction in its lowest terms, find the greatest common divisor (GCD) of the numerator and denominator. For example, $\frac{1}{4}$ is already in its lowest terms because the GCD of 1 and 4 is 1.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and denominator of a fraction without leaving a remainder. For example, the GCD of 12 and 18 is 6 because 6 is the largest number that divides both 12 and 18 without leaving a remainder.

Q: How do I find the GCD of two numbers?

A: To find the GCD of two numbers, you can use the following steps:

List the factors of each number.
Identify the common factors.
Choose the largest common factor.

For example, to find the GCD of 12 and 18, you can list the factors of each number as follows:

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18

The common factors of 12 and 18 are 1, 2, 3, and 6. The largest common factor is 6, so the GCD of 12 and 18 is 6.

Q: How do I express a mixed number as an improper fraction?

A: To express a mixed number as an improper fraction, follow these steps:

Multiply the whole number by the denominator.
Add the product to the numerator.
Write the result as an improper fraction.

For example, to express the mixed number $2\frac{1}{4}$ as an improper fraction, follow these steps:

Multiply the whole number by the denominator: $2 \times 4 = 8$
Add the product to the numerator: $8 + 1 = 9$
Write the result as an improper fraction: $\frac{9}{4}$

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

A: To convert a decimal to a fraction, follow these steps:

Write the decimal as a fraction with a denominator of 1.
Multiply the numerator and denominator by the same power of 10 as the number of decimal places.
Simplify the fraction.

For example, to convert the decimal 0.5 to a fraction, follow these steps:

Write the decimal as a fraction with a denominator of 1: $\frac{0.5}{1}$
Multiply the numerator and denominator by 10: $\frac{0.5 \times 10}{1 \times 10} = \frac{5}{10}$
Simplify the fraction: $\frac{5}{10} = \frac{1}{2}$

Conclusion

In conclusion, expressing percentages as fractions and simplifying them can be a challenging task, but with the right tools and techniques, it can be done easily. By following the steps outlined in this Q&A guide, you can express any percentage as a fraction in its lowest terms and simplify it with ease.

Tips and Tricks

When expressing a percentage as a fraction, make sure to write it as a fraction with a denominator of 100.
To simplify a fraction, multiply the numerators and denominators together.
To express a fraction in its lowest terms, find the greatest common divisor of the numerator and denominator.
To convert a decimal to a fraction, write it as a fraction with a denominator of 1, multiply the numerator and denominator by the same power of 10 as the number of decimal places, and simplify the fraction.

Frequently Asked Questions

Q: How do I express a percentage as a fraction?

A: To express a percentage as a fraction, write it as a fraction with a denominator of 100.

Q: How do I simplify a fraction?

A: To simplify a fraction, multiply the numerators and denominators together.

Q: How do I express a fraction in its lowest terms?

A: To express a fraction in its lowest terms, find the greatest common divisor of the numerator and denominator.

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

A: To convert a decimal to a fraction, write it as a fraction with a denominator of 1, multiply the numerator and denominator by the same power of 10 as the number of decimal places, and simplify the fraction.

Conclusion

In conclusion, expressing percentages as fractions and simplifying them is an essential skill in mathematics. By following the steps outlined in this Q&A guide, you can express any percentage as a fraction in its lowest terms and simplify it with ease.