How to Divide Fractions
Most people learn “keep, change, flip” as a magic spell. It’s easier to remember once you see what division is actually asking: how many of these fit into that?
Measure it first
Choose a division and step through it. The orange bar is the first fraction; the yellow pieces are the second fraction, laid end to end.
3/4 ÷ 1/8 asks: how many pieces of size 1/8 fit into 3/4? The orange bar is 3/4 of a whole.
Keep, change, flip
- Keep the first fraction as it is.
- Change the ÷ sign to ×.
- Flip the second fraction: 1/3 becomes 3/1.
- Multiply top × top and bottom × bottom, then simplify.
Why flipping works
Dividing by 1/3 asks how many thirds fit. Exactly 3 thirds fit into each whole, so the answer is always 3 times as many as there are wholes — that’s multiplying by 3/1. The same holds for any fraction: the number of c/d-sized pieces in one whole is d/c.
Questions
What does “keep, change, flip” mean?
Keep the first fraction, change ÷ into ×, and flip the second fraction upside down (use its reciprocal). Then multiply as usual.
Why does dividing by a fraction make the answer bigger?
Dividing asks how many of something fit. Many small pieces fit into a number, so dividing by a fraction less than 1 gives a bigger result: 3 ÷ 1/2 = 6 halves.
How do I divide mixed numbers?
Turn them into improper fractions first, then keep, change, flip. 1 1/2 ÷ 3/4 = 3/2 × 4/3 = 12/6 = 2.
How do I divide a fraction by a whole number?
Write the whole number over 1 and flip it: 3/4 ÷ 3 = 3/4 × 1/3 = 3/12 = 1/4.