Learn · Grades 6–8

How to Divide Fractions: Keep, Change, Flip

To divide by a fraction, multiply by its reciprocal (the fraction flipped upside down). Teachers call it "keep, change, flip".

Try it with your own problem ↓

The steps

  1. Turn mixed numbers into improper fractions, and a whole number n into n/1.
  2. Keep the first fraction as it is.
  3. Change the division sign to multiplication.
  4. Flip the second fraction (swap its top and bottom).
  5. Multiply across, then simplify.

A worked example

Work out 3/4 ÷ 1/2.

  1. Keep 3/4.
  2. Change ÷ to ×.
  3. Flip 1/2 into 2/1.
  4. Now multiply: 3/4 × 2/1 = 6/4.
  5. Simplify: 6/4 = 3/2 = 1 1/2.

3/4 ÷ 1/2 = 1 1/2. It makes sense: 1/2 fits into 3/4 one and a half times.

Why it works

Division asks how many of the second number fit into the first. How many halves fit into 3/4? Every whole holds two halves, so you multiply by 2: 2 × 3/4 = 6/4 = 1 1/2. Flipping 1/2 into 2 builds in that "two per whole". A quick sense check: dividing by a number smaller than 1 makes the answer bigger.

Try it with your own problem

Open the free The Division House with this example already filled in. It shows every step, and you can type over it with your own numbers.

Work it out: 3/4 ÷ 1/2Opens The Division House with this example

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Common mistakes

Questions people ask

Why does flipping work?

Dividing by 1/2 asks how many halves fit in a number, and there are 2 halves in every whole. So dividing by 1/2 is the same as multiplying by 2.

What is a reciprocal?

The fraction turned upside down. The reciprocal of 2/3 is 3/2, and of 5 (which is 5/1) it is 1/5. A number times its reciprocal is 1.

Can the answer be bigger than the numbers I started with?

Yes, when you divide by a fraction smaller than 1, as in 3 ÷ 1/4 = 12.

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