Dividing Fractions Calculator
Type two fractions or mixed numbers to divide the first by the second, using keep, change, flip, with each step written out.
3/4 ÷ 2/5 =
1 7/8
3/4 ÷ 2/5 = 1 7/8 (15/8), 1.875 as a decimal.
- As a fraction
- 15/8
- As a decimal
- 1.875
How this works: Method, 1 source, Checked against 1 worked example,
How this works
Method
To divide by a fraction, multiply by its reciprocal, the same fraction upside down. Teachers call it keep, change, flip: keep the first fraction, change ÷ to ×, flip the second. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8. Full method
How it’s tested
One worked example for this page is checked by automated tests before every release: given the inputs, the tool must show the expected answer.
Privacy
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Changes
- First published, with nine pages: adding, subtracting, multiplying, dividing and simplifying fractions, fraction to decimal and back, mixed numbers and ratios.
How to divide fractions
To divide by a fraction, multiply by its reciprocal, the same fraction upside down. Teachers call it keep, change, flip: keep the first fraction, change ÷ to ×, flip the second. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8.
Why it works: division asks how many of the second number fit into the first. Dividing by 2/5 is the same as asking how many fifths there are (multiply by 5) and then grouping them in twos (divide by 2), which is multiplying by 5/2.
Dividing by a number less than 1 makes the answer bigger: there are 6 halves in 3, so 3 ÷ 1/2 = 6. Dividing by zero, or by a fraction with a zero numerator, is undefined, and the calculator says so.
a/b ÷ c/d = a/b × d/c = (a × d) / (b × c)
- Grade 6 standards ask students to interpret and compute quotients of fractions, for example that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3 (6.NS.A.1). Source: Common Core State Standards, Grade 6 The Number System (6.NS.A.1).
Fraction quotients
Each division rewritten as a multiplication by the reciprocal, with the simplified answer and its decimal.
| Quotient | As a multiplication | Answer | Decimal |
|---|---|---|---|
| 1/2 ÷ 1/4 | 1/2 × 4/1 | 2 | 2 |
| 3/4 ÷ 1/2 | 3/4 × 2/1 | 1 1/2 | 1.5 |
| 2/3 ÷ 3/4 | 2/3 × 4/3 | 8/9 | 0.8889 |
| 3/4 ÷ 2/5 | 3/4 × 5/2 | 1 7/8 | 1.875 |
| 5/6 ÷ 5/12 | 5/6 × 12/5 | 2 | 2 |
| 1/3 ÷ 2 | 1/3 × 1/2 | 1/6 | 0.1667 |
| 4 ÷ 2/3 | 4 × 3/2 | 6 | 6 |
| 7/8 ÷ 7 | 7/8 × 1/7 | 1/8 | 0.125 |
| 9/10 ÷ 3/5 | 9/10 × 5/3 | 1 1/2 | 1.5 |
| 1 1/2 ÷ 3/4 | 3/2 × 4/3 | 2 | 2 |
Show all 14 rowsShow fewer
| 2 1/4 ÷ 1 1/2 | 9/4 × 2/3 | 1 1/2 | 1.5 |
| 5/9 ÷ 10/3 | 5/9 × 3/10 | 1/6 | 0.1667 |
| 3 ÷ 1/2 | 3 × 2/1 | 6 | 6 |
| 1/8 ÷ 1/2 | 1/8 × 2/1 | 1/4 | 0.25 |
Frequently Asked Questions
What is the reciprocal of a mixed number?
Turn it into an improper fraction first, then flip it. 2 1/2 = 5/2, so its reciprocal is 2/5. Flipping only the fraction part (2 2/1) is a common mistake.
How do I divide a fraction by a whole number?
Multiply the denominator by the whole number: 3/4 ÷ 3 = 3/4 × 1/3 = 3/12 = 1/4. Sharing three quarters between three people gives each a quarter.
Is there a way without flipping?
Yes: give both fractions a common denominator and divide the numerators. 3/4 ÷ 2/5 = 15/20 ÷ 8/20 = 15 ÷ 8 = 15/8, the same answer.