Visual model for dividing 3 by 1/4 using fraction bars.

Explanation:
We are asked to find the value of:

$$
3 \div \frac{1}{4}
$$

Think of division by a fraction as asking: *How many groups of* $\frac{1}{4}$ *are in 3?*

Each whole (like the gray rectangle labeled “1”) is divided into 4 equal parts, and each part is $\frac{1}{4}$. So in one whole, there are 4 pieces of $\frac{1}{4}$.

Therefore:
- In 1 whole → 4 quarters ($\frac{1}{4}$s)
- In 2 wholes → $2 \times 4 = 8$ quarters
- In 3 wholes → $3 \times 4 = 12$ quarters

So, $3 \div \frac{1}{4} = 12$.

Another way: Use the rule for dividing by a fraction:
$$
a \div \frac{b}{c} = a \times \frac{c}{b}
$$

Here, $3 \div \frac{1}{4} = 3 \times \frac{4}{1} = 3 \times 4 = 12$.

Both methods give the same answer.

Final Answer:
12