# Simplify Fractions Calculator

Use this calculator to easily simplify fractions.

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* * Simplifying fractions

Simplifying fractions is the action of dividing the numerator and denominator (top and bottom) by the highest number that divide each of them exactly. Through simplification, a fraction becomes as simple as possible, for example 10/20 becomes 1/2, and 4/9 becomes 2/3. Similarly, a fraction which is greater than 1 will become a composite, e.g. 13/3 will become 4 1/3.

* * How to simplify fractions?

The naive method is to try to divide (exactly, without remainder) the numerator and denominator by 2,3,5,7,9... (prime numbers) until you can no longer divide both parts by the same number. For example, 24/60 can be divided by 2 to get 12/30, which further be divided by 2 to get 6/15, which can then be divided by 3 to get 2/5. 2/5 can no longer be divided by the same number without remainder.

The more advanced method is to first find the greatest common factor (GCF), also known as the greatest common divisor (GCD), then divide the numerator and denominator by it. The greatest common factor of 24 and 60 is 12, so by dividing 24/12 and 60/12 you get 2/5, exactly as using the first method. Of course, in all cases it is quicker and easier to just use our online simplify fractions calculator above.

* * Practical Examples

Example task #1: You read in a news source that a statistical survey revealed that 20 out of every 100 men in Spain are unemployed. How do you simplify that fraction?

*Solution*: the fraction is 20/100, both can be divided by 2, resulting in 10/50, both of which can further be divided by 2, resulting in 5/25, which cannot be divided by 2 or 3, but can be divided in 5, resulting in 1/5, which can be divided no further. 20/80 simplified is 1/5. You can verify the result using our simplify fractions calculator online.

Example task #2: You have a pizza with 12 slices and you were told that you can eat 4 out of the 12 slices. How can you simplify that fraction?

*Solution*: the fraction is 4/12, both of which are divisible by 2, resulting in 2/6, both of which further divisible by 3, resulting in 1/3. Therefore, you can eat a third of the pizza.

As you can see, having a fraction simlpifier is definitely useful.

#### Cite this calculator & page

If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation:

Georgiev G.Z., *"Simplify Fractions Calculator"*, [online] Available at: https://www.gigacalculator.com/calculators/simplify-fractions-calculator.php URL [Accessed Date: 27 Jan, 2022].

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