what is 9-3 and 1/3

Yeah, It's more than one way to skin a cat - and I'd prefer your solving strategy over mine :)

$$9-3\frac{1}{3}$$

Transform the mixed numbers into improper fraction. Use this formula (can you see why it's true):

$$a\frac{b}{c}=\frac{ac + b}{c}$$

We get:

$$9 - \frac{3*3+1}{3}=$$

$$9 - \frac{10}{3}=$$

Transform the integer into a fraction with a common denominator (bottom), and calculate the answer:

$$9 - \frac{10}{3}=$$

$$\frac{27}{3}- \frac{10}{3}= \frac{17}{3}$$

Really nice presentation Tetration.   

I would do it slightly differently.  There is no need to change the mixed numeral into an improper fraction.

I have spread it out so that it is easy to follow but most of these steps are not normally written.

This really is a good method to use.    

$$\\9-3\frac{1}{3}\\\\ \mbox{you are taking away more than 3 so it must be }-3-\frac{1}{3}\\\\ =9-3-\frac{1}{3}\\\\ =6-\frac{1}{3}\\\\ $Now 6 minus a bit must equal 5 and a bit, so what do we do next$\\ $I'll change the 6 into 5+1$\\\\ =5+1-\frac{1}{3}\\\\ =5+\frac{3}{3}-\frac{1}{3}\\\\ =5+\frac{2}{3}\\\\ =5\frac{2}{3}$$