How to Divide Fractions: Keep, Change, Flip

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

1. Keep the first fraction the same.
2. Change the division sign to multiplication.
3. Flip the second fraction to make its reciprocal.
4. 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

1. Divide 1/2 by 1/4.
2. Divide 2/3 by 5/6.
3. Divide 3/5 by 2/7.

Answers

1. 2
2. 4/5
3. 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.

Related guides

• How to Multiply Fractions
• How to Solve Fraction Word Problems
• How to Convert Fractions to Decimals