How to solve it
- Keep the first fraction as it is.
- Change the division to a multiplication.
- Flip the second fraction: the numerator goes down and the denominator goes up.
- Multiply and simplify.
3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8
Result: 15/8
Common mistake:Wrong: 1/2 ÷ 1/4 = 1/8.Right: 1/2 ÷ 1/4 = 2.Multiplying without flipping answers a different question. Dividing by 1/4 is the same as multiplying by 4.
Dividing fractions comes down to multiplying (multiply fractions): the first fraction times the reciprocal of the second. Below you will find the method with a complete example, what the operation means, the cases that change the procedure and the most common mistake. The denominators do not need to match.
Worked example: 2/3 ÷ 4/5
You have 2/3 of a quart of juice and pour it into bottles that each hold 4/5 of a quart. What part of a bottle do you fill?
- Keep the first fraction. The dividend is not touched.
- Flip the second. The reciprocal of 4/5 is 5/4.
- Multiply. 2/3 × 5/4 = 10/12.
- Simplify. Dividing 10 and 12 by 2, 10/12 = 5/6.
You fill 5/6 of a bottle.
Check. The quotient times the divisor gives back the dividend: 5/6 × 4/5 = 20/30 = 2/3.
What dividing fractions means
Division asks how many times the divisor fits into the dividend. In 3/4 ÷ 1/8 the question is how many eighths fit in three fourths. Since 3/4 = 6/8, 6 fit. When the divisor is a whole number, the question becomes sharing, and 2/5 ÷ 2 = 1/5 is what each of two equal parts gets.
This reading explains why the reciprocal works. Dividing by 1/8 means counting eighths, and there are 8 in one whole, so it is the same as multiplying by 8. If you want to see the reasoning with drawings, the guide on why dividing by a fraction can increase the result uses groups, and the one on the reciprocal of a fraction covers the reciprocal on its own.
Cases that change the procedure
The method is always the same, but it helps to know how to set up each case before flipping. The table gathers the most common ones with the full calculation.
| Case | What you do | Calculation |
|---|---|---|
| Fraction divided by a whole number | The whole number becomes its reciprocal | 5/8 ÷ 5 = 5/8 × 1/5 = 1/8 |
| Whole number divided by a fraction | Write the whole number over 1 | 4 ÷ 2/9 = 4 × 9/2 = 36/2 = 18 |
| Mixed number | Convert to an improper fraction | 2 1/4 ÷ 3/8 = 9/4 × 8/3 = 72/12 = 6 |
| Same denominator | Divide the numerators | 6/8 ÷ 3/8 = 6 ÷ 3 = 2 |
| Zero dividend | The result is zero | 0 ÷ 7/9 = 0 × 9/7 = 0 |
| Negative dividend | The sign carries over | −1/3 ÷ 5/7 = −1/3 × 7/5 = −7/15 |
Every row ends in a multiplication, so you can simplify before multiplying when a numerator and a denominator share a factor. To review canceling, use multiply fractions.
Dividing by zero and the order of the values
Zero behaves differently depending on which side it is on. With a zero dividend the quotient is 0, as long as the divisor is not zero. A zero divisor is not allowed, because 0 and 0/7 have no reciprocal: no number times zero gives 1, and the calculator rejects it with a warning. If the zero is in a denominator, as in 3/0, the starting fraction does not exist.
Order matters too, because division is not commutative. With 3/5 ÷ 6/7 the result is 7/10, and swapping the values, 6/7 ÷ 3/5, gives its reciprocal, 10/7. In a chain like 5/7 ÷ 1/7 ÷ 1/2 you work from left to right and each result is the dividend of the next step, so 5/7 ÷ 1/7 = 5 and 5 ÷ 1/2 = 10. With different parentheses the value changes, and that is what fraction expressions are for.
When to use another page
This calculator accepts fractions, whole numbers, mixed numbers and terminating decimals, up to 20 chained values and 100 digits per number. If the data is a fraction inside another fraction, use complex fractions. To find a total from a part, as in “12 is 3/5 of what amount,” there is find the whole from a fraction. If you only need the reciprocal, the reciprocal field on this page calculates it.
To practice, the division worksheets come with answers, and the division word problems set them in context. If the result is a fraction greater than 1 and you want to reduce it, see simplify fractions. In English, OpenStax explains that dividing fractions means multiplying by the reciprocal of the divisor, and that zero has no reciprocal: Prealgebra 2e, multiply and divide fractions (accessed October 17, 2026).
Frequently asked questions
Does dividing always give a larger result?
No. With a positive dividend, the quotient is larger than the dividend only if the divisor is between 0 and 1: 9 ÷ 1/4 = 36. If the divisor is greater than 1, the result goes down: 9 ÷ 9/2 = 2. With a negative dividend it is the other way around: −7 ÷ 1/2 = −14 is less than −7, but −7 ÷ 2 = −7/2 is greater. The guide on why dividing by a fraction can increase the result explains it with groups.
How do I divide decimals?
Write each decimal as a fraction and apply the same rule. With 0.6 ÷ 0.2 you have 6/10 ÷ 2/10, which gives 3. The calculator accepts terminating decimals in the Mixed numbers and decimals mode, so you can type them as they are.