How To Divide Fractions: Keep, Change, Flip (With Examples)
The short version
- To divide fractions, keep the first fraction, change ÷ to ×, and flip the second fraction upside down. Then multiply across and simplify.
- Whole numbers and mixed numbers need one prep step first: write a whole number over 1 (5 becomes 5/1) and turn a mixed number into an improper fraction (2 1/2 becomes 5/2).
- Only the second fraction gets flipped. Flipping the first one, or both, is the most common reason kids get these wrong.
- Check any answer by multiplying it by the fraction you divided by. You should land back on the number you started with.
Here’s how to divide fractions: keep the first fraction, change the division sign to multiplication, flip the second fraction (swap its top and bottom), then multiply the tops and multiply the bottoms. So 3/4 ÷ 1/2 becomes 3/4 × 2/1, which is 6/4, or 1 1/2.
That’s the whole rule for how to divide fractions. The rest of this guide covers why it works, how to handle whole numbers and mixed numbers, a shortcut that keeps the numbers small, and the handful of mistakes that cause most wrong answers. There are practice problems with answers at the end.
What dividing by a fraction actually means
Division asks “how many of these fit into that?” 12 ÷ 3 asks how many 3s fit in 12. The answer is 4.
Fractions work the same way. 3 ÷ 1/2 asks how many halves fit in 3. Picture 3 pizzas cut in half. You’d have 6 halves, so 3 ÷ 1/2 = 6.
This surprises a lot of kids, because the answer is bigger than the number they started with. That’s normal. When you divide by something smaller than 1, you get a bigger answer, since lots of small pieces fit inside. Keeping this in mind is the best quick check there is. If your child divides by 1/4 and gets a smaller number, something went wrong.
How to divide fractions in 3 steps
Most teachers call this “keep, change, flip.” Some say “multiply by the reciprocal.” They mean the same thing. The reciprocal of a fraction is that fraction flipped over, so the reciprocal of 2/3 is 3/2.
- Keep the first fraction exactly as it is.
- Change the ÷ sign to ×.
- Flip the second fraction.
Then multiply straight across (top × top, bottom × bottom) and simplify.
Example 1: fraction divided by a fraction
5/6 ÷ 2/3
Keep, change, flip: 5/6 × 3/2
Multiply the tops: 5 × 3 = 15
Multiply the bottoms: 6 × 2 = 12
Result: 15/12
Simplify (divide top and bottom by 3): 5/4 = 1 1/4
Quick check: 2/3 is a little smaller than 5/6, so 2/3 should fit into 5/6 a little more than once. 1 1/4 fits that.
Why flipping works
Dividing by 1/4 means asking how many quarters fit in something. Every whole holds 4 quarters, so dividing by 1/4 gives the same answer as multiplying by 4. That’s the reciprocal at work: ÷ 1/4 and × 4/1 are the same move.
Another way to see it is with common denominators. Take 3/4 ÷ 1/2. Rewrite 1/2 as 2/4. Now the question is “how many 2 fourths fit in 3 fourths?” That’s 3 ÷ 2, which is 3/2 or 1 1/2. Same answer as keep, change, flip. The flip method is just the faster route to it.
Dividing fractions with whole numbers
Any whole number can be written as a fraction over 1. After that, it’s the same three steps.
Example 2: fraction divided by a whole number
2/3 ÷ 4
Write 4 as 4/1: 2/3 ÷ 4/1
Keep, change, flip: 2/3 × 1/4
Multiply: 2/12
Simplify: 1/6
This makes sense if you think of sharing. Split 2/3 of a pan of brownies among 4 people and each gets 1/6 of the pan.
Example 3: whole number divided by a fraction
6 ÷ 3/4
Write 6 as 6/1: 6/1 ÷ 3/4
Keep, change, flip: 6/1 × 4/3
Multiply: 24/3
Simplify: 8
Eight pieces of 3/4 fit into 6. Check it: 8 × 3/4 = 24/4 = 6.
How to divide mixed numbers
You can’t flip a mixed number like 1 1/4 as it stands. Turn every mixed number into an improper fraction first: multiply the whole number by the denominator, add the numerator, and keep the same denominator.
Example 4: mixed number divided by a mixed number
2 1/2 ÷ 1 1/4
Convert: 2 1/2 = (2 × 2 + 1)/2 = 5/2, and 1 1/4 = (1 × 4 + 1)/4 = 5/4
Now: 5/2 ÷ 5/4
Keep, change, flip: 5/2 × 4/5
Multiply: 20/10
Simplify: 2
That checks out: two lengths of 1 1/4 make 2 1/2.
A shortcut: simplify before you multiply
After you flip, you can cancel any top number with any bottom number that shares a factor. This keeps the numbers small, which means fewer multiplication slips.
Example 5: cross-simplifying
8/9 ÷ 4/15
Keep, change, flip: 8/9 × 15/4
8 and 4 share a factor of 4: 8 becomes 2, 4 becomes 1
15 and 9 share a factor of 3: 15 becomes 5, 9 becomes 3
Now: 2/3 × 5/1 = 10/3 = 3 1/3
Without canceling, you’d get 120/36, which simplifies to the same 10/3. It’s just more work. One rule for canceling: only do it after the flip, once the problem is multiplication. Canceling across a ÷ sign gives wrong answers.
Word problems that use fraction division
The hardest part of word problems is spotting that they’re division. Look for “how many ___ fit in,” “how many pieces,” or “split equally.”
Recipe: You have 3/4 cup of sugar and a 1/8 cup scoop. How many scoops?
3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6 scoops
Ribbon: A ribbon is 5 1/4 feet long. You cut pieces 3/4 foot long. How many pieces?
5 1/4 = 21/4, so 21/4 ÷ 3/4 = 21/4 × 4/3 = 84/12 = 7 pieces
Sharing: 3 friends split 1/2 of a pizza equally. How much does each get?
1/2 ÷ 3 = 1/2 × 1/3 = 1/6 of the pizza
Common mistakes when dividing fractions
| Mistake | What it looks like | The fix |
|---|---|---|
| Flipping the first fraction | 2/3 ÷ 1/4 turned into 3/2 × 1/4 = 3/8 | Keep the first fraction. Only the divisor (the second one) flips. Right answer: 2/3 × 4/1 = 8/3. |
| Flipping both | 2/3 ÷ 1/4 turned into 3/2 × 4/1 = 6 | Flip one fraction, the second one, once. |
| Flipping but not changing the sign | Writing 2/3 ÷ 4/1 and then dividing again | Flip and change go together. After the flip, the problem is multiplication. |
| Flipping a mixed number as is | 1 1/2 treated as 1 2/1 | Convert to an improper fraction first: 1 1/2 = 3/2, which flips to 2/3. |
| Forgetting the whole number is over 1 | 3/5 ÷ 2 turned into 3/5 × 2 = 6/5 | 2 is 2/1, which flips to 1/2. Right answer: 3/5 × 1/2 = 3/10. |
| Canceling before the flip | Canceling across the ÷ sign | Flip first, then cancel. |
The fastest way to catch any of these: multiply the answer by the fraction you divided by. For 5/6 ÷ 2/3 = 5/4, check 5/4 × 2/3 = 10/12 = 5/6. It matches, so the answer’s right.
Practice problems
These go from easier to harder. Simplify each answer, and write improper fractions as mixed numbers.
- 1/2 ÷ 1/4
- 3/5 ÷ 3
- 4 ÷ 2/3
- 7/8 ÷ 3/4
- 5/12 ÷ 10/9
- 3 1/3 ÷ 1 2/3
- 2 1/4 ÷ 3/8
- A 2/3 pound bag of trail mix is split into snack bags that hold 1/6 pound each. How many snack bags can you fill?
Answers
- 1/2 × 4/1 = 4/2 = 2
- 3/5 × 1/3 = 3/15 = 1/5
- 4/1 × 3/2 = 12/2 = 6
- 7/8 × 4/3 = 28/24 = 7/6 = 1 1/6
- 5/12 × 9/10 = 45/120 = 3/8
- 10/3 ÷ 5/3 = 10/3 × 3/5 = 30/15 = 2
- 9/4 ÷ 3/8 = 9/4 × 8/3 = 72/12 = 6
- 2/3 ÷ 1/6 = 2/3 × 6/1 = 12/3 = 4 snack bags
If your child is stuck on dividing fractions
Keep, change, flip is easy to memorize. So when a kid can recite it and still gets these wrong, the trouble is almost always an earlier skill underneath. Here’s where to look.
- Multiplying fractions. Every division problem turns into a multiplication problem. If 3/4 × 2/5 is shaky, division will be too.
- Simplifying and equivalent fractions. A kid who can’t see that 15/12 = 5/4 will get “right but unsimplified” answers marked wrong over and over.
- Mixed numbers. Converting 2 1/4 to 9/4 is its own skill, usually taught in fourth grade.
- Multiplication facts. Slow recall of 7 × 8 or 6 × 9 turns every step into a struggle and burns attention the fraction steps need.
Fractions are where a lot of later math trouble starts. We wrote about that in why algebra problems usually trace back to fourth grade fractions. If you’re not sure which fraction skills your child should already have, our guide to math skills by grade level lays them out. And if fraction homework ends in tears most nights, math anxiety may be part of the picture too.
Frequently asked questions
What is the rule for dividing fractions?
Keep the first fraction, change ÷ to ×, and flip the second fraction. Then multiply the numerators, multiply the denominators, and simplify. For example, 1/3 ÷ 1/6 = 1/3 × 6/1 = 6/3 = 2.
Why do you flip the second fraction when dividing?
Because dividing by a number gives the same result as multiplying by its reciprocal. Dividing by 1/2 asks how many halves fit, and each whole holds 2 halves, so ÷ 1/2 is the same as × 2.
Can you divide fractions without flipping?
Yes. Give both fractions the same denominator, then divide the numerators. 3/4 ÷ 1/2 becomes 3/4 ÷ 2/4, and 3 ÷ 2 = 3/2. When the numbers divide evenly, you can also divide straight across: 6/8 ÷ 3/4 = (6 ÷ 3)/(8 ÷ 4) = 2/2 = 1.
How do you divide fractions with whole numbers?
Write the whole number as a fraction over 1, then use keep, change, flip. 3/4 ÷ 3 = 3/4 × 1/3 = 3/12 = 1/4. And 3 ÷ 3/4 = 3/1 × 4/3 = 12/3 = 4.
How do you divide mixed numbers?
Convert each mixed number to an improper fraction first, then flip the second one and multiply. 1 1/2 ÷ 3/4 = 3/2 × 4/3 = 12/6 = 2.
What grade learns how to divide fractions?
Under the Common Core standards, kids start in fifth grade by dividing unit fractions (like 1/3) by whole numbers and whole numbers by unit fractions. Dividing any fraction by any fraction comes in sixth grade.
Find the actual gap
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