Simplifying Fractions

Divide top and bottom by the GCF

List the factors of the numerator and the factors of the denominator, and find the largest one they share. Then divide both the top and the bottom by it. Dividing both parts by the same number keeps the fraction's value unchanged, because you're really dividing by $1$ in disguise: $\dfrac{6}{6} = 1$.

For $\dfrac{12}{20}$: the factors of $12$ are $1, 2, 3, 4, 6, 12$ and the factors of $20$ are $1, 2, 4, 5, 10, 20$. The greatest shared factor is $4$, so $\dfrac{12}{20} = \dfrac{3}{5}$.

How to know you're finished

A fraction is in simplest form when the GCF of its numerator and denominator is $1$ — the top and bottom share no factor bigger than $1$. $\dfrac{3}{5}$ is finished because nothing divides both $3$ and $5$. $\dfrac{6}{10}$ is not, because $2$ still divides both.

Quick checks: if the top and bottom are both even, you're not done. If one divides evenly into the other, like $\dfrac{4}{12}$, you're not done. If the top is $1$, you're always done.

Can't spot the GCF? Simplify in stages

You don't have to find the GCF on the first try. Divide by any common factor you notice, then look again. $\dfrac{24}{36}$: divide by $2$ to get $\dfrac{12}{18}$, divide by $2$ again for $\dfrac{6}{9}$, then by $3$ for $\dfrac{2}{3}$. Three small steps, same destination as one big one.

Using the GCF just gets you there in a single step. Either way, keep going until no common factor is left.

Worked examples

Try one yourself

Common questions