Chapters
How to Simplify Fractions?
Simplifying a fraction means transforming it into a simpler equivalent fraction.
To simplify a fraction, we divide the numerator and denominator by the same number.
We start simplifying by testing the first prime numbers: 2, 3, 5, 7, ... That is, we try to divide the numerator and denominator by 2 as long as possible, then move on to 3, and so on.
We repeat the process until there are no more common divisors.
Example: Simplify
1 First, we divide the numerator and denominator by 
2 The numerator and denominator of the result obtained have again as a common divisor
3 The new numerator and denominator of the result obtained have 
as a common divisor
4 Since the new numerator and denominator of the result obtained have no common divisors, we have that the simplification of is 
, that is:
If the terms of the fraction end in zeros, we will start by removing the common final zeros from the numerator and denominator.
Example: Simplify 
1 We divide the numerator and denominator by 
2 The new numerator and denominator of the result obtained have as a common divisor
3 Since the new numerator and denominator of the result obtained have no common divisors, we have that the simplification of is 
, that is:
If the number by which we divide is the greatest common divisor of the numerator and denominator, we arrive at an irreducible fraction.
Example: Simplify 
1 We divide the numerator and denominator by 
2 Since the new numerator and denominator of the result obtained have no common divisors, we have that the simplification of is 
, that is:
Fraction Simplification Exercises
Simplify the following fractions
1 First, we divide the numerator and denominator by 
1 First, we divide the numerator and denominator by
2 The numerator and denominator of the result obtained have as a common divisor
3 Since the new numerator and denominator of the result obtained have no common divisors, we have that the simplification of is 
, that is:
1 First, we divide the numerator and denominator by
2 The numerator and denominator of the result obtained have as a common divisor
3 The numerator and denominator of the result obtained have as a common divisor again
4 Since the new numerator and denominator of the result obtained have no common divisors, we have that the simplification of is 
, that is:
1 First, we divide the numerator and denominator by
2 The numerator and denominator of the result obtained have as a common divisor
3 The numerator and denominator of the result obtained have as a common divisor again
4 Since the new numerator and denominator of the result obtained have no common divisors, we have that the simplification of is 
, that is:
1 First, we divide the numerator and denominator by
2 The numerator and denominator of the result obtained have as a common divisor
3 Since the new numerator and denominator of the result obtained have no common divisors, we have that the simplification of is 
, that is:
Fraction Simplification Exercises with G.C.D.
Simplify the following fractions using the greatest common divisor
1 First, we express the numerator and denominator as a product of prime numbers
2 To obtain the 
of both numbers, we multiply the common factors with the smallest exponent
3 We divide the numerator and denominator by 
1 First, we express the numerator and denominator as a product of prime numbers
2 To obtain the of both numbers, we multiply the common factors with the smallest exponent
3 We divide the numerator and denominator by 
1 First, we express the numerator and denominator as a product of prime numbers
2 To obtain the of both numbers, we multiply the common factors with the smallest exponent
3 We divide the numerator and denominator by 
1 First, we express the numerator and denominator as a product of prime numbers
2 To obtain the of both numbers, we multiply the common factors with the smallest exponent
3 We divide the numerator and denominator by 
1 First, we express the numerator and denominator as a product of prime numbers
2 To obtain the of both numbers, we multiply the common factors with the smallest exponent
3 We divide the numerator and denominator by 
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