Fraction Calculator guide
How to Divide Fractions: Keep, Change, Flip
To divide fractions, keep the first fraction, change the division sign to multiplication, and flip the second fraction upside down. For 1/2 ÷ 3/4, that becomes 1/2 × 4/3 = 4/6, which simplifies to 2/3.
The rule
Keep, change, flip.
Keep the first fraction exactly as it is. Change the ÷ to a ×. Flip the second fraction upside down.
Then multiply as normal. That is the whole procedure.
A worked example
Take 1/2 ÷ 3/4.
Keep 1/2. Change ÷ to ×. Flip 3/4 to 4/3.
Now it reads 1/2 × 4/3, and multiplying straight across gives 4/6.
Simplify by dividing top and bottom by 2: 2/3.
Why flipping works
This rule is usually taught as something to memorise, which makes it feel like a trick. It is not — there is a straightforward reason.
Dividing by a number is the same as multiplying by its reciprocal. Dividing by 2 is the same as multiplying by ½; you already use that without thinking about it.
The reciprocal of a fraction is that fraction turned upside down, because 3/4 × 4/3 = 12/12 = 1. So dividing by 3/4 is the same as multiplying by 4/3.
"Flip" is just "take the reciprocal", said faster.
Only the second fraction flips
This is the most common error, so it is worth stating on its own: the first fraction does not change.
For 1/2 ÷ 3/4, it is 1/2 × 4/3. It is not 2/1 × 4/3, and it is not 2/1 × 3/4.
The word "keep" at the start of the rule exists specifically to remind you of this. If you find yourself flipping both, you have almost certainly reversed the answer.
Why the answer often gets bigger
Dividing 1/2 by 3/4 gives 2/3, which is larger than 1/2. That looks wrong if you expect division to shrink things.
The question "1/2 ÷ 3/4" really means "how many three-quarters fit into one half?" The answer is less than one whole three-quarter — two thirds of one, in fact.
A clearer example: 6 ÷ ½ asks how many halves fit into 6. There are 12. Dividing by a number less than 1 always makes the answer bigger, because you are counting how many small things fit inside a larger one.
Dividing by a whole number
Any whole number can be written as a fraction over 1, and then the same rule applies.
3/4 ÷ 2 becomes 3/4 ÷ 2/1, which flips to 3/4 × 1/2 = 3/8.
Which makes sense: splitting three quarters between two people gives each three eighths.
