Writing Fractions in Simplest Form

The simplest form of a fraction is $\,\displaystyle\frac{N}{D}\,$, 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:

Question: Write in simplest form:

$\displaystyle\frac{6}{15}$

Solution:
The fraction

$\,\frac{6}{15}\,$ is not in simplest form, because $\,6\,$ and $\,15\,$ have a common factor of $\,3\,$.
To simplify the fraction, use the following thought process:

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

Note:

$\displaystyle\frac{6}{15} = \frac{3\cdot 2}{3\cdot 5} = \frac{3}{3}\cdot\frac{2}{5} = 1\cdot\frac{2}{5} = \frac{2}{5}\,$

Thus, simplifying a fraction is just getting rid of extra factor(s) of $\,1\,$.

Question: Write in simplest form:

$\frac{2}{6}$

Answer:

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

$\,\frac{1}{3}\,$ is input as 1/3 .

Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Deciding if a Fraction is a Finite or Infinite Repeating Decimal

(an even number, please)