How Many Fit

A division asks a question: how many of one number fit into another? $\frac{12}{3}$ is 4 because four 3s fit into 12. Ask the same question with a fraction: $3 \div \frac{1}{4}$ asks how many quarters fit into 3.

3 wholes, each holding 4 quarters: 12 quarters in all.

Each whole holds 4 quarters, so 3 wholes hold 12 quarters. $3 \div \frac{1}{4}$ is 12. In the same way, $2 \div \frac{1}{3}$ is 6, because each whole holds 3 thirds.

Notice that the answer is bigger than the number you started with. That surprises people, because dividing by a whole number makes things smaller. But when the pieces are smaller than 1, more of them fit than there are wholes, so dividing by a fraction below 1 makes the answer bigger.