$\dfrac{a+b}{c} = \dfrac{a}{c} + \dfrac{b}{c}$

We know that we can split a fraction like what we did above, but you can't do this in

$\dfrac{a}{b+c} = \dfrac{a}{b} + \dfrac{a}{c}$

This is a false property, it will be a mistake if you do it! However, it holds for certain values of integers $a,b,$ and $c.$ If $a,b,c \leq 10$ and $a,b,c$ are non-negative integers, then for how many **ordered triples** $(a,b,c)$ is $\frac a{b+c} = \frac ab + \frac ac$ seen to be true?