Skill: Divide a whole number by a unit fraction

To divide a whole number by a unit fraction, ask:

How many pieces of size $\frac{1}{b}$ fit inside the whole number?

A unit fraction has $1$ in the numerator, such as $\frac14$ or $\frac13$. Dividing by $\frac{1}{b}$ is the same as multiplying by $b$:

$$n\div\frac{1}{b}=n\times b$$

Example: $4\div\frac13$

Step 1: Understand the divisor.
The fraction $\frac13$ means one piece out of three equal pieces. So we are counting how many thirds are in $4$ wholes.

Step 2: Count the thirds in one whole.
Each whole contains $3$ thirds:

$$1=\frac13+\frac13+\frac13$$

Step 3: Count the thirds in four wholes.

$$4\times 3=12$$

So,

$$4\div\frac13=12$$

Step 4: Check with multiplication.
Division and multiplication are inverse operations:

$$12\times\frac13=\frac{12}{3}=4$$

Therefore, $\boxed{4\div\frac13=12}$.