How to divide fractions
Quick answer
Keep the first fraction, change the division sign to multiplication, and flip the second fraction upside down. Then multiply across and simplify. For example, 2/3 ÷ 4/5 = 2/3 × 5/4 = 5/6.
Step by step
- KeepLeave the first fraction exactly as it is.
- ChangeTurn the ÷ sign into a × sign.
- FlipSwap the top and bottom of the second fraction. This flipped fraction is called the reciprocal: 4/5 becomes 5/4.
- Multiply and simplifyMultiply the tops together and the bottoms together, then reduce the answer to lowest terms.
Three words do all the work: keep, change, flip. Once you’ve done it twice, you won’t need to look it up again.
Example: 2/3 ÷ 4/5
- Keep 2/3
- Change ÷ to ×
- Flip 4/5 to 5/4
2/3 × 5/4 = 10/12, which simplifies to 5/6.
Dividing a fraction by a whole number
Write the whole number as a fraction over 1, then do the same steps.
3/4 ÷ 2 = 3/4 ÷ 2/1 = 3/4 × 1/2 = 3/8
Dividing a whole number by a fraction
3 ÷ 1/2 = 3/1 × 2/1 = 6
That makes sense if you think of it as a question: how many halves fit into 3? Six of them.
Dividing mixed numbers
Turn each mixed number into an improper fraction first.
1½ ÷ ¾ → 3/2 ÷ 3/4 → 3/2 × 4/3 = 12/6 = 2
To convert, multiply the whole number by the bottom and add the top: 1½ becomes (1 × 2 + 1)/2 = 3/2.
Why flipping works
Dividing by a number is the same as multiplying by its reciprocal. Dividing by 2 is the same as multiplying by ½, and dividing by ¾ is the same as multiplying by 4/3. Keep-change-flip is just a quick way to write that.
After flipping, everything is ordinary fraction multiplication.
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