Simplifying fractions

Any fraction can be fully reduced to its lowest terms by dividing both the numerator and denominator by their greatest common divisor. This is called reducing or simplifying of the fraction.

A fraction in which the numerator and denominator are coprime [this means that for faction mn it's gcd(m,n)=1] is said to be irreducible or in its lowest or simplest terms.

Example 1. Simplify the fraction	4	.
	8

gcd(4, 8) = 4 then,

4	=	4÷4	=	1	.
8		8÷4		2

Example 2. Simplify the fraction	15	.
	40

gcd(15, 40) = 5 then,

15	=	15÷5	=	3	.
40		40÷5		8

Example 3. Simplify the fraction	126	.
	426

gcd(126, 426) = 6 then,

126	=	126÷6	=	21	.
426		426÷6		71

Example 4. Simplify the fraction	7	.
	9

gcd(7, 9) = 1 then,

7	- can not be simplified.
9