Keep, Change, Flip: The Easiest Way to Divide Fractions

If you learned to divide fractions in school, there’s a good chance someone told you “keep, change, flip” and then moved on without explaining why it works. That’s fine for passing a test, but it’s also why so many people forget the method the moment the test is over.

Here’s the method, then the reason behind it, then the mistakes to avoid.

The Method

To divide one fraction by another:

1. Keep the first fraction exactly as it is
2. Change the division sign (÷) to a multiplication sign (×)
3. Flip the second fraction upside down (swap numerator and denominator)
4. Multiply normally and simplify

Example 1: Simple Fractions

2/3 ÷ 4/5

• Keep: 2/3
• Change: ÷ becomes ×
• Flip: 4/5 becomes 5/4
• Result: 2/3 × 5/4 = 10/12 = 5/6

Example 2: Whole Number Divisor

3/4 ÷ 3

Rewrite 3 as 3/1, then apply KCF:

• Keep: 3/4
• Change: ÷ becomes ×
• Flip: 3/1 becomes 1/3
• Result: 3/4 × 1/3 = 3/12 = 1/4

Example 3: Mixed Numbers

1¾ ÷ ½

Convert mixed numbers first: 1¾ = 7/4

• Keep: 7/4
• Change: ÷ becomes ×
• Flip: 1/2 becomes 2/1
• Result: 7/4 × 2/1 = 14/4 = 7/2 = 3½

Why Does It Work?

This is the part that actually makes the rule stick.

Dividing by a number is the same as multiplying by its reciprocal. Always. This is true for whole numbers too: dividing by 2 is the same as multiplying by 1/2, dividing by 5 is the same as multiplying by 1/5.

For fractions, the reciprocal of 4/5 is 5/4. So dividing by 4/5 is the same as multiplying by 5/4.

Here’s the algebra if you want to see it:

(2/3) ÷ (4/5)
= (2/3) × (1/(4/5))
= (2/3) × (5/4)
= 10/12
= 5/6

1/(4/5) simplifies to 5/4, which is just the flip. That’s all keep-change-flip is doing: converting a division into an equivalent multiplication. You’re not doing anything magic, you’re just applying a rule that’s baked into how division works.

The Common Mistakes

Flipping the wrong fraction. You flip the second fraction, the one you’re dividing by, not the first one. (2/3) ÷ (4/5) becomes (2/3) × (5/4). If you accidentally flip 2/3, you get the wrong answer.

Forgetting to convert mixed numbers first. Keep-change-flip only works directly with proper or improper fractions. Convert 2½ to 5/2 before you start.

Not simplifying the answer. After multiplying, always reduce the result. 10/12 should be simplified to 5/6.

Flipping both fractions. Only the divisor (the second fraction) gets flipped. Flipping both gives you the right setup for a completely different problem.

Practice It

The best way to lock this in is repetition on actual problems. Our Practice Fraction Division page generates unlimited division problems at three difficulty levels, with hints available when you get stuck. Try a few rounds. After ten problems, you won’t need the mnemonic anymore.

If you want to check your work step-by-step, the Fraction Calculator walks through every division with the full keep-change-flip working shown.