You have shared a unit fraction among people. Now turn it around: how many pieces of size $\frac{1}{2}$ fit in 4 wholes? That is $4 \div \frac{1}{2}$.
Key idea
$n \div \frac{1}{b} = n \times b$. Each whole holds $b$ pieces of size $\frac{1}{b}$, so $n$ wholes hold $n \times b$ of them. $4 \div \frac{1}{2} = 8$.
Why it works
Division can ask “how many groups of this size fit?”: $12 \div 3$ asks how many 3s fit in 12. In the same way, $4 \div \frac{1}{2}$ asks how many halves fit in 4. There are 2 halves in each whole, so there are 8 in 4. Check: $8 \times \frac{1}{2} = 4$.
Worked examples
Worked example: Halves in 4
Find $4 \div \frac{1}{2}$.
- How many halves fit in 4?
- 2 halves in each whole: $4 \times 2 = 8$.
- Check: $8 \times \frac{1}{2} = 4$.
Answer: $8$
Worked example: Servings
How many $\frac{1}{3}$-cup servings are in 5 cups of rice?
- $5 \div \frac{1}{3}$: how many thirds in 5?
- 3 thirds in each cup: $5 \times 3 = 15$.
Answer: 15 servings
Common mistake
Believing division always makes a number smaller, so $4 \div \frac{1}{2} = 2$. That answer is $4 \div 2$, splitting 4 into 2 groups. Dividing by a number less than 1 asks how many small pieces fit, and the answer is bigger. Check: $2 \times \frac{1}{2} = 1$, not 4.