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Simplifying Fractions Calculator

Fraction Simplification Calculator with step-by-step solution reduces a fraction to an irreducible form.

Fraction

Result

4224 = 4112

Step by step solution


Method 1
1. Calculate the greatest common divisor of the numerator and denominator
    GCD (2, 24) = 2

2. Divide the numerator and denominator on GCD
   2 : 2 = 1
   24 : 2 = 12


3. Substitute the results of the division into the numerator and denominator.We get a fraction
4112

Method 2
1. Calculate the prime factors of the numerator and denominator
   2 = 2
   24 = 2 · 2 · 2 · 3


2. We write the numerator and denominator as the product of their prime factors
   4224 = 422 · 2 · 2 · 3
3. We cross out the prime factors that are repeated in both the numerator and the denominator
   4224 = 422 · 2 · 2 · 3 = 42 2 · 2 · 2 · 3
4.We write the remaining prime factors in the numerator and denominator. If several factors remain in the numerator or denominator, then you need to multiply them together.
   4224 = 422 · 2 · 2 · 3 = 42 2 · 2 · 2 · 3 = 412 · 2 · 3 = 4112

How to simplify fractions?

Method 1

  1. Calculate the greatest common divisor of the numerator and denominator.
  2. Divide the numerator and denominator on GCD.

For example, let's simplify the fraction 4530

Calculate the greatest common divisor of the numerator and denominator
    GCD (45, 30) = 15

Divide the numerator and denominator on GCD
   45 : 15 = 3
   30 : 15 = 2


Substitute the results of the division into the numerator and denominator.We get a fraction
32


Method 2

  1. Calculate the prime factors of the numerator and denominator.
  2. Cross out the repeating factors and multiply the remaining ones.

For example, let's simplify the fraction 4530

Calculate the prime factors of the numerator and denominator
   45 = 3 · 3 · 5
   30 = 2 · 3 · 5


We write the numerator and denominator as the product of their prime factors
   4530 = 3 · 3 · 52 · 3 · 5
We cross out the prime factors that are repeated in both the numerator and the denominator
   4530 = 3 · 3 · 52 · 3 · 5 = 3 · 5 · 33 · 5 · 2
We write the remaining prime factors in the numerator and denominator. If several factors remain in the numerator or denominator, then you need to multiply them together.
   4530 = 3 · 3 · 52 · 3 · 5 = 3 · 5 · 33 · 5 · 2 = 32

See also