Amount we have
3/4 = 3/4
1234
Dividing fractions
How to Flip a Denominator to the Numerator
Flipping a fraction — swapping its top and bottom — produces its reciprocal: 3/4 becomes 4/3, 1/2 becomes 2. The test of a correct flip is that the fraction and its flip multiply back to exactly 1.
- the reciprocal
- swap top and bottom
- flip only the divisor
- product of reciprocals is 1
Interactive tool
Divide fractions step by step
Build the picture first: make equal parts, count groups, then use the rule to check your answer.
Start with the question
3/4 ÷ 1/2
Build the picture in three short moves.
Use the guided buttons below to reveal one idea at a time.
See the division
How many groups of 1/2 fit inside 3/4?
First make both fractions use the same-size pieces. Then count groups of the divisor — not just colored bars.
Step 1 — Make the parts match
These are the same one whole, cut into 4 equal parts.
One group to measure with
1/2 = 2/4
1234
Step 2 — Count groups of 2/4
The blue amount has 3 equal pieces. Each green group needs 2 pieces.
Next, mark 2/4 as one complete group.
1 full group
1/4 left = 1/2 of one more 2/4 group
You measured1 1/2groups.
3/4 ÷ 1/2 = 1 + 1/2 = 1 1/2
Check with the rule
3/4 ÷ 1/2=3/4 × 2/1=6/4=3/2
The calculation steps
- 1.Keep 3/4.
- 2.Flip the divisor: 1/2 becomes 2/1.
- 3.Change division to multiplication: 3/4 × 2/1.
- 4.Simplify before multiplying: 3/2 × 1/1.
- 5.Multiply across: 6/4.
- 6.Simplify the result: 3/2.
- 7.Write the mixed number: 1 1/2.
Quick answer
Swap top and bottom — the product must be 1
To flip 3/4, write the numerator where the denominator was and vice versa: 4/3. The flipped fraction is called the reciprocal, and its defining property is that the pair multiplies to exactly 1 — 3/4 × 4/3 = 12/12 = 1.
Whole numbers flip through a fraction bar: 5 = 5/1 becomes 1/5. Mixed numbers convert first: 1 1/2 = 3/2 flips to 2/3. A negative sign belongs to the value and stays: -2/3 flips to -3/2.
The method
Four steps: fraction form, swap, keep the sign, verify
Write the number as a fraction
A whole number flips too, once it is written over 1: 5 becomes 5/1, so its flip is 1/5. A mixed number must convert to an improper fraction first — 1 1/2 becomes 3/2.
Swap the numerator and the denominator
The flip of 3/4 is 4/3 and the flip of 1/2 is 2/1. The fraction turns over; nothing else about it changes.
Keep any negative sign with the fraction
The flip of -2/3 is -3/2, not 3/2. The sign belongs to the whole value, so it rides along while the numbers trade places.
Check: the product must be exactly 1
A number and its reciprocal multiply to 1: 3/4 × 4/3 = 12/12 = 1. If the flipped fraction does not multiply back to 1, the flip went wrong.
Worked example
A plain fraction: 3/4
3/4 → 4/3 because 3/4 × 4/3 = 12/12 = 1
The numerator and denominator trade places. The check is the definition: only 4/3 multiplies 3/4 back to exactly 1, which is what makes it the reciprocal rather than just any upside-down-looking fraction.
Worked example
A unit fraction: 1/2
1/2 → 2/1 = 2
Flipping 1/2 produces 2/1, which is simply the whole number 2. Unit fractions have the friendliest reciprocals: the flip of 1/n is always the whole number n.
Worked example
A whole number: 5
5 = 5/1 → 1/5
Every whole number is a fraction over 1, so its flip is one over the number. The reciprocal of 5 is 1/5, and 5 × 1/5 = 1 confirms it.
Worked example
A negative fraction: -2/3
-2/3 → -3/2 because -2/3 × -3/2 = 6/6 = 1
The negative sign belongs to the whole fraction, so the reciprocal keeps it: -3/2. Flipping does not switch a sign off — if it did, the product would be negative instead of 1.
The flip exists to undo multiplication
A reciprocal is defined by one property: multiplying the two gives exactly 1. That single requirement forces the swap. For 3/4 × ? = 1, the missing factor must contribute 3 to the denominator (to make 12 = 3 × 4) and 4 to the numerator — it must be 4/3. The flip is not a trick someone invented; it is the only number that can answer the question.
This is why flipping matters almost exclusively inside division. Dividing by a fraction asks "how many of these fit", and keep-change-flip replaces the division with multiplying by the flip: 3/4 ÷ 1/2 becomes 3/4 × 2/1. The divisor turns over because multiplying by its reciprocal is the same operation, done with numbers that follow the multiplication rules.
Flip only the divisor, and only after converting
In a division chain, only the number you are dividing by turns over. In 3/4 ÷ 1/2, the 3/4 stays exactly as it is while 1/2 becomes 2/1. Flipping both turns the quotient into its own reciprocal and silently answers a different question.
Mixed numbers must merge into improper fractions before their flip exists: 1 1/2 is 3/2, so its reciprocal is 2/3. There is no meaningful "flip" of a whole-and-part written side by side. And zero never flips — no number multiplies 0 to reach 1, which is the algebraic reason division by zero is undefined.
Common mistakes when flipping fractions
- Flipping the first fraction in a division: Keep-change-flip keeps the dividend as written. In 3/4 ÷ 1/2, flipping the 3/4 as well produces 4/3 × 2/1 = 8/3 instead of the correct 3/2 — a plausible-looking wrong answer.
- Dropping a negative sign during the flip: The reciprocal of -2/3 is -3/2. The sign travels with the value; losing it turns a division that should land negative into a positive answer while every other step looks correct.
- Flipping a mixed number in place: Writing the flip of 1 1/2 as 2 1/1 or 1 2/1 invents a rule. Convert 1 1/2 to 3/2 first; only then does the swap produce the true reciprocal 2/3.
Keep learning
Related fraction topics
Common questions
Flipping Fractions FAQ
Swap the two numbers of the fraction: the flip (reciprocal) of 3/4 is 4/3 and of 1/2 is 2/1. Write whole numbers over 1 first (5 → 5/1 → 1/5), convert mixed numbers to improper fractions first (1 1/2 → 3/2 → 2/3), and keep any negative sign with the fraction.