Multiply by the Reciprocal

Flip a fraction upside down and you get its reciprocal: the reciprocal of $\frac{2}{5}$ is $\frac{5}{2}$. To divide by a fraction, multiply by its reciprocal. $\frac{7}{10} \div \frac{2}{5}$ becomes $\frac{7}{10}\cdot \frac{5}{2}$, which is $\frac{35}{20}$, and that simplifies to $\frac{7}{4}$.

Why does flipping work? Dividing by $\frac{1}{5}$ asks how many fifths fit, and 5 fit in every whole, so it is the same as multiplying by 5. Dividing by $\frac{2}{5}$ counts pieces twice as big, so half as many fit: multiply by 5, then halve. Multiplying by 5 and halving is multiplying by $\frac{5}{2}$.

Only the divisor, the fraction you divide by, is flipped; the first fraction stays as it is. On the board a division is written with a fraction bar, so a fraction divided by a fraction shows as one fraction stacked over another.