Simplifying Fractions

To simplify a fraction, we do the prime factorization of the numerator and denominator and any numbers that are on the top and the bottom will “cancel out”, which means they divide to equal 1. We often cross out the numbers that cancel out and get rid of them, the following video will show why we can do this.

Video Source (07:01 mins) | Transcript

The following video goes through more examples of how to simplify fractions.

Video Source (04:42 mins) | Transcript

Remember, even if you cancel everything in the numerator or the denominator it doesn’t mean it is 0. There is still a 1 there. Anything multiplied to 1 is itself, so even when we divide out everything else, we will always have a 1 left.

Additional Resources

Practice Problems

Simplify the following fractions to the lowest terms:

  1. \(\frac{4}{6}\)

  2. \(\frac{10}{25}\)

  3. \(\frac{4}{7}\)

  4. \(\frac{30}{48}\)

  5. \(\frac{42}{70}\)

  6. \(\frac{12}{84}\)


  1. \(\frac{4}{6}=\frac{2\times2}{3\times2}=\frac{2}{3}\) (Written Solution)

  2. \(\frac{10}{25}=\frac{2\times5}{5\times5}=\frac{2}{5}\) (Written Solution)

  3. \(\frac{4}{7}\) is already simplified to lowest terms. (Written Solution)

  4. \(\frac{30}{48}=\frac{2\times3\times5}{2\times2\times2\times2\times3}=\frac{5}{8}\) (Solution Video | Transcript)

  5. \(\frac{42}{70}=\frac{2\times3\times7}{2\times7\times7}=\frac{3}{5}\) (Solution Video | Transcript)

  6. \(\frac{12}{84}=\frac{2\times2\times3}{2\times2\times3\times7}=\frac{1}{7}\) (Written Solution)