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# Fractions and simplification of fractions

A fraction represents a rational number as the ratio of two integers, the numerator and the denominator. The denominator cannot be zero.

$\textrm{Fraction} = \frac{\Tblue{\textrm{Numerator}}}{\Tred{\textrm{Denominator}}}$

The fraction $\Tblue{17}/\Tred{26}$ has numerator $\Tblue{17}$ and denominator $\Tred{26}$.

A fraction is in its simplest form, or irreducible, if the numerator and denominator have no common factor. A fraction has a unique simplest form. To simplify a fraction, find the highest common factor of the numerator and the denominator and divide both by it.

$\Tblue{7}/\Tred{9}$ is irreducible. $\Tblue{18}/\Tred{27}$ is not. The HCF of $\Tblue{18}$ and $\Tred{27}$ is $9$. The fraction can be simplified to $\Tblue{2}/\Tred{3}$. $\frac{\Tblue{18}}{\Tred{27}} = \frac{9\times \Tblue{2}}{9\times \Tred{3}} = \frac{\Tblue{2}}{\Tred{3}}.$

Two fractions are equivalent if they have the same value. They have the same simplest form.

$\Tblue{3}/\Tred{9}$ and $\Tblue{2}/\Tred{6}$ are equivalent; their simplest form is $\Tblue{1}/\Tred{3}$.

Every fraction has infinitely many equivalent forms.