## Reducing (simplifying) fractions

Take a look at the fraction $\frac{36}{40}$. We say this fraction can be "reduced" because both 36 and 40 have at least one common factor (other than 1). For example, both can be divided by 2.

$\frac{36\div~2}{40\div~2}\,=\,\frac{18}{20}$

$\frac{36}{40}$ is the same amount as $\frac{18}{20}$, but $\frac{18}{20}$ can be reduced even further.

$\frac{18}{20}\,=\,\frac{18\div~2}{20\div~2}\,=\,\frac{9}{10}$

Since 9 and 10 do not have a common factor larger than 1, we say $\frac{9}{10}$ is in simplest form.

A quicker way to reduce $\frac{36}{40}$ would have been to divide both numbers by 4.

$\frac{36}{40}\,=\,\frac{36\div~4}{40\div~4}\,=\,\frac{9}{10}$

Use this applet to verify that two fractions are indeed equivalent.

# Self-Check

Q1: Reduce this fraction: $\frac{18}{24}\,=\,\,\,\,\,$ [show answer]

Q2: Reduce this fraction: $\frac{24}{60}\,=\,\,\,\,\,$ [show answer]

Q3: Reduce this fraction: $\frac{20}{24}\,=\,\,\,\,\,$ [show answer]