# Writing Fractions in Simplest Form

The *simplest form* of a fraction is
$\,\frac{N}{D}\,,$
where $\,N\,$ and $\,D\,$ have no common factors (except $\,1\,$).

Thus, in *simplest form*,
there is no number other than
$\,1\,$ that goes into both
the numerator and denominator evenly.

## Examples

The fraction $\,\frac{6}{15}\,$ is not in simplest form, because $\,6\,$ and $\,15\,$ have a common factor of $\,\bf{3}\,.$

To simplify the fraction, use the following thought process:

- $6\,\,\,$ divided by $\,\bf{3}\,$ is $\,2\,$ (the new numerator is $\,2\,$)
- $15\,$ divided by $\,\bf{3}\,$ is $\,5\,$ (the new denominator is $\,5\,$)
- Thus, $\,\cssId{s20}{\frac{6}{15}} \cssId{s21}{= \frac{6\div\bf{3}}{15\div\bf{3}}} \cssId{s22}{= \frac{2}{5}}\,.$
- Since $\,2\,$ and $\,5\,$ have no common factor other than $1$, the simplest form of $\,\frac{6}{15}\,$ is $\,\frac{2}{5}\,.$

Note:

$$ \cssId{s26}{\frac{6}{15}} \ \ \cssId{s27}{= \ \ \frac{3\cdot 2}{3\cdot 5}} \cssId{s28}{\ \ = \ \ \frac{3}{3}\cdot\frac{2}{5}} \ \ \cssId{s29}{= \ \ 1\cdot\frac{2}{5}} \ \ \cssId{s30}{= \ \ \frac{2}{5}} $$Thus, simplifying a fraction is just getting rid of extra factor(s) of $\,1\,.$

In the exercises below, you will input fractions using a forward diagonal slash. For example, $\,\frac{1}{3}\,$ is input as 1/3 .