 # 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.

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

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.

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. $$\frac{12}{84}$$

#### Solutions

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)