Division asks two kinds of question. $12 \div 3$ can mean "how many 3s fit in 12?" or "share 12 into 3 equal groups." In Grade 5 you used both meanings with whole numbers and unit fractions. The "how many fit?" meaning works for any fractions.
Key idea
$\frac{3}{4} \div \frac{1}{8}$ asks: how many $\frac{1}{8}$s fit in $\frac{3}{4}$? Write both with the same denominator and count pieces: $\frac{6}{8} \div \frac{1}{8} = 6$.
Why it works
Once both numbers are counted in eighths, the question is about pieces of one size: 6 eighths ÷ 1 eighth works like 6 apples ÷ 1 apple. The size of the pieces does not matter any more, just as $600 \div 100 = 6 \div 1$ when you count in hundreds.
Worked example: Whole groups
How many $\frac{2}{3}$-cup scoops are in 2 cups of rice? Find $2 \div \frac{2}{3}$.
- Write 2 in thirds: $2 = \frac{6}{3}$.
- Each scoop is 2 thirds. How many groups of 2 thirds are in 6 thirds? $6 \div 2 = 3$.
Answer: 3 scoops.
Worked example: Part of a group
Find $\frac{5}{6} \div \frac{1}{3}$.
- Use sixths for both: $\frac{1}{3} = \frac{2}{6}$, so the question is $\frac{5}{6} \div \frac{2}{6}$.
- How many groups of 2 sixths fit in 5 sixths? Two full groups use 4 sixths, and 1 sixth is left.
- The leftover is 1 of the 2 sixths a group needs: half a group.
- So $2$ groups and $\frac{1}{2}$ of a group.
Answer: $2\frac{1}{2}$
Common mistake
Expecting the answer to be small. When you divide by a fraction less than 1, many small pieces fit, so the quotient is bigger than the number you started with: $\frac{3}{4} \div \frac{1}{8} = 6$. Quick check: if you divide by a number less than 1 and get a smaller answer, something went wrong.
The sharing meaning works too: "if $\frac{3}{4}$ cup is $\frac{1}{8}$ of a batch, how much is a whole batch?" Eight eighths make the batch, so it is $8 \times \frac{3}{4} = 6$ cups. Same answer, as it must be.