mixed numbers subtraction vertically

Question

In the following subtraction we are subtracting $2$ mixed numbers vertically. I know how it works except the last step.

$$ 7 \frac{1}{3} - 4 \frac{1}{2} = 3 + \frac{-1}{6} = 2 + \frac{5}{6} = 2 \frac{5}{6}$$

I am confused about this step: $ 3 + \frac{-1}{6} = 2 + \frac{5}{6}$ How does this work?

Answer 1

For "normal" subtraction, we all learned in elementary school to "borrow" a 1 from the next highest place if we needed to.

In this case, we're sort of doing the same thing. When we have $3 + -1/6$, we "borrow" a 1 to make $2 + 6/6 + -1/6$, which then becomes $2 + 5/6$.

Answer 2

Write it as $$ 3 - \frac{1}{6}= 2 + 1 - \frac{1}{6}= 2 + \frac{6}{6} -\frac{1}{6} = 2 + \frac{6-1}{6} = 2+\frac{5}{6} $$

Answer 3

3+-1/6=2+(1-1/6)=2+(6/6-1/6)=2+5/6