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Simplifying fractions

Definition.
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.
4 = 2 = 1
20105
Definition.
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.

Examples of tasks to simplify fractions

Example 1.
Simplify the fraction 
4.
8

gcd(4, 8) = 4 then,

4 = 4÷4 = 1.
88÷42

Example 2.
Simplify the fraction 
15.
40

gcd(15, 40) = 5 then,

15 = 15÷5 = 3.
4040÷58

Example 3.
Simplify the fraction 
126.
426

gcd(126, 426) = 6 then,

126 = 126÷6 = 21.
426426÷671

Example 4.
Simplify the fraction 
7.
9

gcd(7, 9) = 1 then,

7 - can not be simplified.
9

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