How to Divide Fractions: Keep, Change, Flip
Pennpaper Team
Dividing fractions can feel strange at first because the shortcut turns division into multiplication. The shortcut is called keep, change, flip.
Quick idea
Dividing by a fraction means multiplying by its reciprocal. The reciprocal flips the numerator and denominator.
Steps
- Keep the first fraction the same.
- Change the division sign to multiplication.
- Flip the second fraction to make its reciprocal.
- Multiply across and simplify.
Worked example
Divide three fourths by two fifths.
Full solution
Step-by-step walkthrough
Step 1
Keep three fourths.
Step 2
Change division to multiplication.
Step 3
Flip two fifths into five halves.
Step 4
Multiply to get fifteen eighths, then write it as a mixed number if needed.
Common mistake
Only flip the second fraction. If you flip both fractions, you are solving a different problem.
Practice problems
- Divide 1/2 by 1/4.
- Divide 2/3 by 5/6.
- Divide 3/5 by 2/7.
Answers
- 2
- 4/5
- 21/10 or 2 1/10
Ask Pennpaper to explain it live
If the steps make sense but you still feel stuck, start a Pennpaper lesson and ask the tutor to draw the problem on the whiteboard. Seeing the symbols move step by step is often what makes the concept click.