Simplifying Fractions Calculator

Simplifying fractions at a glance#

A simplifying fractions calculator reduces a fraction to its simplest form, also called lowest terms. Find the greatest common factor (GCF) of the numerator and denominator, then divide both by it. For example, 8/12 has a GCF of 4, so 8/12 = 2/3.

A fraction is in simplest form when the numerator and denominator share no common factor other than 1. So 15/25 reduces by 5 to give 3/5, and 3/5 cannot be reduced any further.

Enter your numerator and denominator in the calculator above for the simplest form, with the GCF and any mixed-number version shown alongside. A whole-number result like 6/3 simplifies to 2, since the denominator divides the numerator exactly.

Proper and improper fractions#

In a proper fraction the numerator is smaller than the denominator, so its value is less than 1, such as 1/3, 2/5, or 7/10. In an improper fraction the numerator is equal to or greater than the denominator, so its value is 1 or more, such as 9/4, 15/8, or 22/7. Both kinds reduce the same way: divide top and bottom by their GCF.

Two more examples#

To simplify 24/36, the GCF of 24 and 36 is 12. Divide both by 12: 24 ÷ 12 = 2 and 36 ÷ 12 = 3, so 24/36 = 2/3. To simplify 50/100, the GCF is 50, so 50 ÷ 50 = 1 and 100 ÷ 50 = 2, giving 1/2.

Converting an improper fraction to a mixed number#

Divide the numerator by the denominator. The whole-number part of the division is the whole number, the remainder becomes the new numerator, and the denominator stays the same. For 17/5, dividing 17 by 5 gives 3 with a remainder of 2, so 17/5 = 3 2/5.

Using prime factorization for the GCF#

For larger numbers, break each part into prime factors and multiply the factors they share. To simplify 210/462, factor 210 as 2 × 3 × 5 × 7 and 462 as 2 × 3 × 7 × 11. The shared factors are 2, 3, and 7, which multiply to 42, the GCF. Dividing both by 42 gives 210 ÷ 42 = 5 and 462 ÷ 42 = 11, so 210/462 = 5/11.

Simplifying fractions FAQ#

How do you simplify 45/60?#

The GCF of 45 and 60 is 15. Divide both by 15: 45 ÷ 15 = 3 and 60 ÷ 15 = 4, so 45/60 = 3/4.

How does the calculator handle improper fractions?#

It reduces the fraction to lowest terms and also shows the mixed-number form. Enter 17/5 and it returns both 17/5 in simplest terms and the mixed number 3 2/5.

What is the fastest way to find the GCF?#

For small numbers, list the factors of each part and pick the largest shared one. For large numbers, use prime factorization and multiply the common prime factors, as in the 210/462 example above.