Reducing a Fraction to its Lowest Terms

Oct 13, 2025 by miodeya.com 126 views

Introduction

In mathematics, percentages are often used to express a value as a fraction of 100. However, in many mathematical operations, it's more convenient to work with fractions. In this article, we'll learn how to convert a percentage to a fraction and reduce it to its lowest terms.

What is a Percentage?

A percentage is a way of expressing a value as a fraction of 100. It's denoted by the symbol "%". For example, 25% means 25 out of 100.

Converting 4% to a Fraction

To convert 4% to a fraction, we need to divide 4 by 100 and simplify the result.

Step 1: Divide 4 by 100

4 ÷ 100 = 0.04

Step 2: Convert the Decimal to a Fraction

To convert the decimal 0.04 to a fraction, we can write it as 4/100.

Step 3: Simplify the Fraction

We can simplify the fraction 4/100 by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 4 and 100 is 4.

4 ÷ 4 = 1 100 ÷ 4 = 25

So, the simplified fraction is 1/25.

Reducing a Fraction to its Lowest Terms

A fraction is said to be in its lowest terms if the numerator and the denominator have no common factors other than 1. To reduce a fraction to its lowest terms, we need to find the GCD of the numerator and the denominator and divide both by the GCD.

Example: Reducing 2/6 to its Lowest Terms

To reduce 2/6 to its lowest terms, we need to find the GCD of 2 and 6.

The factors of 2 are 1 and 2. The factors of 6 are 1, 2, 3, and 6.

The greatest common factor of 2 and 6 is 2.

2 ÷ 2 = 1 6 ÷ 2 = 3

So, the reduced fraction is 1/3.

Conclusion

Converting a percentage to a fraction and reducing it to its lowest terms is an essential skill in mathematics. By following the steps outlined in this article, you can convert any percentage to a fraction and reduce it to its lowest terms.

Common Percentages and their Equivalent Fractions

Here are some common percentages and their equivalent fractions:

Percentage	Equivalent Fraction
1%	1/100
5%	5/100 = 1/20
10%	10/100 = 1/10
25%	25/100 = 1/4
50%	50/100 = 1/2

Practice Problems

Convert 8% to a fraction and reduce it to its lowest terms.
Convert 12% to a fraction and reduce it to its lowest terms.
Convert 18% to a fraction and reduce it to its lowest terms.

Answer Key

8% = 8/100 = 2/25
12% = 12/100 = 3/25
18% = 18/100 = 9/50
Frequently Asked Questions: Converting Percentages to Fractions ================================================================

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

A: A percentage is a way of expressing a value as a fraction of 100, while a fraction is a way of expressing a value as a ratio of two numbers.

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

A: To convert a percentage to a fraction, you need to divide the percentage by 100 and simplify the result.

Q: What is the greatest common divisor (GCD) and how do I find it?

A: The GCD is the largest number that divides two numbers without leaving a remainder. To find the GCD, you can list the factors of each number and find the largest common factor.

Q: How do I reduce a fraction to its lowest terms?

A: To reduce a fraction to its lowest terms, you need to find the GCD of the numerator and the denominator and divide both by the GCD.

Q: What are some common percentages and their equivalent fractions?

A: Here are some common percentages and their equivalent fractions:

Percentage	Equivalent Fraction
1%	1/100
5%	5/100 = 1/20
10%	10/100 = 1/10
25%	25/100 = 1/4
50%	50/100 = 1/2

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

A: To convert a decimal to a fraction, you can write it as a ratio of two numbers. For example, 0.5 can be written as 5/10 or 1/2.

Q: What is the difference between a simplified fraction and a reduced fraction?

A: A simplified fraction is a fraction that has been reduced to its lowest terms, while a reduced fraction is a fraction that has been simplified by dividing both the numerator and the denominator by their greatest common divisor.

Q: Can I use a calculator to convert a percentage to a fraction?

A: Yes, you can use a calculator to convert a percentage to a fraction. However, it's always a good idea to double-check your work by simplifying the fraction.

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

A: To convert a mixed number to a fraction, you need to multiply the whole number by the denominator and add the numerator. Then, you can simplify the fraction.

Q: What are some real-world applications of converting percentages to fractions?

A: Converting percentages to fractions is an essential skill in many fields, including finance, engineering, and science. It's used to calculate interest rates, percentages, and proportions.

Q: Can I use a calculator to reduce a fraction to its lowest terms?

A: Yes, you can use a calculator to reduce a fraction to its lowest terms. However, it's always a good idea to double-check your work by simplifying the fraction.

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

A: To convert a fraction to a decimal, you can divide the numerator by the denominator.

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

A: A fraction is a way of expressing a value as a ratio of two numbers, while a proportion is a statement that two ratios are equal.

Q: Can I use a calculator to convert a proportion to a fraction?

A: Yes, you can use a calculator to convert a proportion to a fraction. However, it's always a good idea to double-check your work by simplifying the fraction.