Improper to Mixed

Going the other way is a division. Take $\frac{17}{5}$: how many whole fives fit in 17? Three of them, which use up 15, and 2 are left over. So $\frac{17}{5}$ is 3 wholes and 2 fifths: $3\tfrac{2}{5}$.

The rule: divide the top by the bottom. The quotient is the whole part, and the remainder goes over the same denominator as the fraction part. The remainder is always smaller than the denominator, because any time it reaches the denominator, another whole fits.

Why it works: the denominator says how many pieces make one whole, so every group of 5 fifths is one whole. You can check by going back: 3 times 5 is 15, plus 2 is 17. When the remainder is 0, there is no fraction part at all: $\frac{12}{4}$ is just 3.