# How do you simplify the fraction 40/90?

Nov 30, 2016

$\frac{40}{90} = \frac{4}{9}$

#### Explanation:

Find the greatest common divisor of the numerator and denominator:

$40 = {2}^{3} \cdot 5$
$90 = 2 \cdot {3}^{2} \cdot 5$

The greatest common divisor is the product of commn factos with the lowest exponent:

$G C D = 2 \cdot 5 = 10$

Then divide the numerator and denominator by the GCD:

$\frac{40}{90} = \frac{\frac{40}{10}}{\frac{90}{10}} = \frac{4}{9}$