audio read-through 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

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 $\,\bf{3}\,.$

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 $\,1\,$.

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 .

Practice