Math
Dividing Fractions Calculator
Divide a fraction, mixed number, whole number, or decimal by another.
The calculator applies keep-change-flip (multiply by the reciprocal), cross-cancels, and gives the quotient as a simplified fraction, mixed number, decimal, and percent with every step written out.
Type a fraction (3/4), a mixed number (2 1/3), a whole number, or a decimal (1.75). Repeating decimals work too: 0.(3).
The fraction you are dividing by. Cannot be zero.
Try an example
Result
Result (simplified)
—
- Mixed number
- —
- Decimal
- —
- Percent
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- Reciprocal of divisor
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Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
How to divide fractions: keep, change, flip
Dividing by a fraction is the same as multiplying by its The number you get by flipping a fraction; 3/4 becomes 4/3, and 5 becomes 1/5.. Keep the first fraction, change the division sign to multiplication, and flip the second fraction (swap its The top number of a fraction; it counts how many parts you have. and The bottom number of a fraction; it says how many equal parts make one whole.). Then multiply straight across and simplify.
Why flipping works
3/4 ÷ 2/5 asks how many 2/5-size pieces fit into 3/4. Multiplying both numbers by 5/2 turns the divisor into 1 without changing the quotient, so the answer is 3/4 × 5/2 = 15/8 = 1 7/8. Roughly one and seven-eighths pieces of size 2/5 fit into 3/4.
Dividing with whole numbers and mixed numbers
| Problem | Keep-change-flip | Quotient |
|---|---|---|
| 3/4 ÷ 2/5 | 3/4 × 5/2 | 15/8 = 1 7/8 |
| 6 ÷ 2/3 | 6/1 × 3/2 | 18/2 = 9 |
| 2/3 ÷ 4 | 2/3 × 1/4 | 2/12 = 1/6 |
| 2 1/2 ÷ 1 1/4 | 5/2 × 4/5 | 20/10 = 2 |
| 1/2 ÷ (-1/4) | 1/2 × (-4/1) | -4/2 = -2 |
How to use it
- Type the number being divided in the first box and the number you are dividing by in the second box.
- Use fractions (2/5), A whole number written next to a fraction, like 2 1/3. (1 1/4), whole numbers (6), or decimals (0.4).
- Read the simplified quotient with its mixed-number, decimal, and percent forms.
- Open Show the work to see the reciprocal, the rewritten multiplication, cross-cancelling, and simplification.
How to read the answer
The quotient tells how many times the divisor fits into the dividend. Dividing by a fraction less than 1 gives a bigger answer than you started with; dividing by something larger than 1 gives a smaller one. A negative quotient means exactly one of the two numbers was negative.
Common mistakes and edge cases
- Flip only the second fraction (the divisor). Flipping the first one gives the reciprocal of the right answer.
- Do not cross-multiply as if solving a proportion. Division is multiply-by-the-reciprocal.
- Convert mixed numbers to A fraction whose top number is at least as big as its bottom number, like 7/3. before flipping. Flipping 1 1/4 as 1 4/1 is wrong; 1 1/4 = 5/4, whose reciprocal is 4/5.
- A whole number's reciprocal puts the number in the denominator: the reciprocal of 4 is 1/4.
- Division by zero has no answer; the calculator reports it instead of guessing.
Worked examples
Fraction by fraction
3/4 ÷ 2/5
Result (simplified)
15/8
Whole number by fraction
6 ÷ 2/3
Result (simplified)
9
Fraction by whole number
2/3 ÷ 4
Result (simplified)
1/6
Mixed numbers
2 1/2 ÷ 1 1/4
Result (simplified)
2
Negative divisor
1/2 ÷ (-1/4)
Result (simplified)
-2
Zero dividend
0 ÷ 5/8
Result (simplified)
0
Decimal divisor
3/5 ÷ 0.3
Result (simplified)
2
Divide by zero
3/4 ÷ 0 is undefined
Result (simplified)
Error
Frequently asked questions
What does keep, change, flip mean?+
Keep the first fraction as it is, change the division sign to multiplication, and flip the second fraction to its reciprocal. Then multiply.
What is the reciprocal of a fraction?+
Swap the numerator and denominator. The reciprocal of 2/5 is 5/2, and the reciprocal of a whole number like 4 is 1/4. A number times its reciprocal is always 1.
How do you divide a fraction by a whole number?+
Write the whole number over 1, flip it, and multiply: 2/3 ÷ 4 = 2/3 × 1/4 = 2/12 = 1/6.
How do you divide mixed numbers?+
Convert both to improper fractions first, then keep-change-flip: 2 1/2 ÷ 1 1/4 = 5/2 × 4/5 = 20/10 = 2.
Why is dividing by a fraction the same as multiplying by its reciprocal?+
Multiplying the dividend and divisor by the same number does not change the quotient. Multiplying both by the divisor's reciprocal turns the divisor into 1, leaving dividend × reciprocal.
Why can't I divide by zero?+
Division asks how many times the divisor fits into the dividend. Zero fits into any number infinitely many times and never adds up to it, so there is no single answer.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026