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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,

3 11

is in simplest form, since 3 and 11 have no common factors other than 1 . However,

6 21

is not in simplest form, since 6 and 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.

6 21 = 3 2 3 7 = 2 7

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