Lowest terms, the common factor that got you there, and the decimal and percentage it equals
Simplifying a fraction means dividing the top and the bottom by the same number until nothing divides them both. This tool does that, but it also shows the factor it used and the prime factors of each number — because seeing where the common factor comes from is what lets you do the next one without a tool.
A fraction is a division waiting to happen, and dividing the top and the bottom by the same number does not change the result. 18/24 divided by 6 top and bottom is 3/4, and both are 0.75.
The number you divide by is the greatest common divisor — the biggest number that goes into both. Finding it is the whole job. Once you have divided by it, nothing is left to cancel and the fraction is in lowest terms.
You do not have to find it in one go. Halving 18/24 gives 9/12, halving again is not possible, but dividing by 3 gives 3/4. Several small steps land in the same place as one big one.
If both numbers are even, 2 goes into both. If both end in 0 or 5, 5 does. If the digits of each add to a multiple of 3, then 3 does — 18 gives 1 + 8 = 9 and 24 gives 2 + 4 = 6, so both divide by 3.
Those three checks catch most school fractions in a second. For anything stubborn, break both numbers into prime factors and see what they share: 18 is 2 × 3 × 3 and 24 is 2 × 2 × 2 × 3, and the shared part is 2 × 3 = 6.
This is where the times tables earn their keep. Spotting that 21 is 3 × 7 is what makes 7/21 collapse instantly instead of slowly.
3/4, 0.75 and 75% are three ways of writing one value. Converting is always the same move: divide the top by the bottom to get the decimal, then multiply by 100 for the percentage.
Some fractions give a decimal that never ends. 1/3 is 0.333…, because 3 does not divide neatly into a power of ten. A fraction terminates as a decimal only when its denominator, in lowest terms, is built from nothing but 2s and 5s.
That is a useful check: if a fraction simplifies to something over 8, 20 or 25, it will terminate. Over 3, 6, 7 or 9, it will repeat.
Because unsimplified fractions make every later step harder. Adding 18/24 to 5/8 means finding a common denominator for 24 and 8; adding 3/4 to 5/8 is a much smaller problem.
It also makes answers comparable. Two answers written as 6/8 and 3/4 look different and are not, which is exactly the kind of thing that gets marked wrong or argued about.
Divide the numerator and the denominator by the same number until no number greater than 1 divides both. 18/24 divides by 6 to give 3/4.
A fraction is in lowest terms when the only number that divides both the top and the bottom is 1. 3/4 is in lowest terms; 6/8 is not.
Break both numbers into prime factors and multiply the ones they share. For 18 (2 × 3 × 3) and 24 (2 × 2 × 2 × 3), the shared factors are 2 and 3, so the divisor is 6.
Divide the top by the bottom to get a decimal, then multiply by 100. 3 ÷ 4 = 0.75, so 3/4 is 75%.
Any fraction whose denominator in lowest terms has a prime factor other than 2 or 5. 1/3 and 1/7 repeat; 1/8 and 3/20 do not.