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# Reducing Fractions (Simplest Form)

A fraction is in simplest form if the greatest common factor (GCF) of its numerator and denominator is $1$ -- that is, if they share no common factors other than $1$ .

For example,

$\frac{3}{11}$

is in simplest form, since $3\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\text{\hspace{0.17em}}11$ have no common factors other than $1$ . However,

$\frac{6}{21}$

is not in simplest form, since $6\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\text{\hspace{0.17em}}21$ share a common factor of $3$ .

To reduce a fraction, divide both the numerator and denominator by the GCF. (This is also known as "writing a fraction in lowest terms".)

This is sometimes shown as "canceling" the common factors.

$\frac{6}{21}=\frac{\overline{)3}\cdot 2}{\overline{)3}\cdot 7}=\frac{2}{7}$

Note that the result is an equivalent fraction in simplest form.

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