# How do you simplify 4/5-4/7?

Jun 18, 2018

$\frac{8}{35}$

#### Explanation:

Whenever we do addition or subtraction with fractions, we must have a common denominator.

The easiest way to achieve a common denominator is to multiply the top and bottom of the first by $7$, and the top and bottom of the second by $5$. We get

$\frac{4}{5} \left(\frac{7}{7}\right) - \frac{4}{7} \left(\frac{5}{5}\right)$

Notice, we are not changing the value since we are essentially multiplying by $1$. We now have

$\frac{28}{35} - \frac{20}{35}$

Now that we have common denominators, we can just subtract the numerators. We'll get

$\frac{8}{35}$

Since the numerator and denominator have no common factors, this fraction is in simplest form.

Hope this helps!