Simplify Fractions Calculator

1. Simplifying fractions
2. How to simplify fractions
3. Practical examples of fraction simplification

    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 in its simplest form. The above are examples of fraction simplification of proper fractions in which the numerator is smaller than the denominator.

In simplification of improper fractions they will be converted to a mixed number. An improper fraction is defined as one in which the numerator is greater than the denominator. Therefore, any fraction greater than 1 passed to this simplify fractions calculator will be converted to a mixed number with a whole and a fractional part. For example, 13/3 will become 4⅓ with 4 being the whole part and ⅓ the fractional.

    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 can be further 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 fraction simplification calculator above.

    Practical examples of fraction simplification

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 20/100 is proper since 20 < 100. Both the numerator and denominator can be divided by 2, resulting in 10/50 after the first simplification. Both of these can further be divided by 2, resulting in 5/25, which cannot be divided by 2 or 3, but can be divided by the next prime number - 5. The result of this division is 1/5 which can be divided no further. Therefore 20/80 simplified is 1/5. You can verify the result using our simplifying 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. Reducing the fraction results in 2/6, whose numerator and denominator are both further divisible by 3, resulting in 1/3. The reduced fraction of 4/12 is 1/3, therefore you can eat a third of the pizza.

Example task #3: Convert the improper fraction 10/4 to a mixed number.

Solution: Both the numerator and denominator are divisible by two, resulting in 5/2. Both of these are primes so the fraction cannot be reduced further. To convert to a mixed number, divide 5 by 2 to get 2 with a remainder of 1. This is written as the mixed number 2½ (two and a half).

As you can see, having a fraction simplifier is definitely useful in reducing fractions to their simplest form.