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# Simplifying Fractions Calculator

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

Fraction

### 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 $⁤\frac{45}{30}$

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
$⁤\frac{3}{2}$

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 $⁤\frac{45}{30}$

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
$⁤\frac{45}{30}$$=$$⁤\frac{3 · 3 · 5}{2 · 3 · 5}$
We cross out the prime factors that are repeated in both the numerator and the denominator
$⁤\frac{45}{30}$$=$$⁤\frac{3 · 3 · 5}{2 · 3 · 5}$$=$$⁤\frac{\overline{)3}·\overline{)5}· 3}{\overline{)3}·\overline{)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.
$⁤\frac{45}{30}$$=$$⁤\frac{3 · 3 · 5}{2 · 3 · 5}$$=$$⁤\frac{\overline{)3}·\overline{)5}· 3}{\overline{)3}·\overline{)5}· 2}$$=$$⁤\frac{3}{2}$