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Converting a percent to a fraction is a straightforward process once you understand the basic idea behind it.
Percent literally means 'per hundred'. This means you can convert any percent to a fraction by simply writing the given number over 100.
For example, if you have 140%, it can be written as \( \frac{140}{100} \). This is your starting fraction.
This step is crucial as it forms the foundation for further simplification. Remember, every percentage value can be represented in this way, making it easier to work with in different mathematical problems.

Simplifying fractions means making the fraction as simple as possible by ensuring the numerator (the top number) and the denominator (the bottom number) share no common factors other than 1.
In our example, the fraction \( \frac{140}{100} \) needs to be simplified. We do this by dividing both the numerator and the denominator by the same number.
The trickiest part can often be figuring out which number to divide by. This number is called the Greatest Common Divisor (GCD).
Once you find the GCD, divide both the numerator and the denominator by this number.
For instance, the GCD of 140 and 100 is 20. So, we divide both 140 and 100 by 20, giving us \( \frac{140 / 20}{100 / 20} = \frac{7}{5} \). This is the fraction in its simplest form.

The Greatest Common Divisor (GCD) is the largest number that can exactly divide both the numerator and the denominator of a fraction.
Finding the GCD is crucial for simplifying fractions, as it helps us reduce the fraction to its lowest terms without changing its value.
One useful method to find the GCD is listing out the factors of both numbers and identifying the largest one they both share.
For example, the factors of 140 are: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, and 140.
The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, and 100.
The highest number common to both lists is 20, hence the GCD of 140 and 100 is 20.
Using this GCD, we divide the numerator and the denominator of the fraction to simplify it. This process ensures our fraction is presented in the simplest form possible.