Definition:Reducible Fraction

Definition

Let $q = \dfrac a b$ be a vulgar fraction.

Then $q$ is defined as being reducible if and only if $q$ is not in canonical form.

That is, if and only if there exists $r \in \Z: r \ne 1$ such that $r$ is a divisor of both $a$ and $b$.

Such a fraction can therefore be reduced by dividing both $a$ and $b$ by $r$.

Examples

Example: $\frac 4 6$

The vulgar fraction $\dfrac 4 6$ is an example of a reducible fraction:

$\dfrac 4 6 = \dfrac {2 \times 2} {2 \times 3} = \dfrac 2 3$

Also see

• Definition:Irreducible Fraction

• Results about reducible fractions can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): reducible fraction
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): reducible fraction