This fraction calculator adds, subtracts, multiplies, and divides any two fractions and automatically simplifies the answer to lowest terms. It also shows the result as a decimal and, when the answer is an improper fraction, as a mixed number — the three forms teachers most often ask for.
Enter the numerator and denominator of each fraction, choose an operation, and calculate. Negative fractions are supported: just enter a negative numerator. The note under the results shows the unsimplified fraction and the greatest common divisor (GCD) used to reduce it, so you can follow every step.
The Rules for Each Fraction Operation
Each operation follows a fixed rule:
- Addition: a/b + c/d = (ad + cb) / bd. Example: 1/2 + 3/4 = (4 + 6)/8 = 10/8 = 5/4.
- Subtraction: a/b − c/d = (ad − cb) / bd. Example: 3/4 − 1/6 = (18 − 4)/24 = 14/24 = 7/12.
- Multiplication: a/b × c/d = ac / bd. Example: 2/3 × 3/5 = 6/15 = 2/5.
- Division: a/b ÷ c/d = a/b × d/c = ad / bc. Example: 1/2 ÷ 3/4 = 4/6 = 2/3.
Addition and subtraction require a common denominator, which is why both numerators get cross-multiplied first. Multiplication is the simplest rule — straight across. Division works by flipping the second fraction (taking its reciprocal) and multiplying.
Simplifying with the Greatest Common Divisor
A fraction is in lowest terms when its numerator and denominator share no common factor other than 1. To simplify, divide both by their greatest common divisor (GCD).
- Find the GCD with the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing it by the smaller, until the remainder is 0.
- Example: simplify 18/24. GCD(18, 24): 24 mod 18 = 6, 18 mod 6 = 0, so GCD = 6. Then 18 ÷ 6 = 3 and 24 ÷ 6 = 4, giving 3/4.
- If the simplified numerator is larger than the denominator (an improper fraction such as 7/4), it can also be written as the mixed number 1 3/4.
This calculator performs both steps automatically after every operation.
Worked Example: 1/2 + 3/4
Add 1/2 and 3/4 using the cross-multiplication rule (ad + cb)/bd.
Step 1: Multiply diagonally and add: (1 × 4) + (3 × 2) = 4 + 6 = 10. That is the new numerator. Step 2: Multiply the denominators: 2 × 4 = 8. Result so far: 10/8. Step 3: Simplify. GCD(10, 8) = 2, so 10/8 = 5/4. Step 4: Convert to a mixed number: 5 ÷ 4 = 1 remainder 1, so 5/4 = 1 1/4.
As a decimal, 5/4 = 1.25. A quick check: 1/2 is 0.5 and 3/4 is 0.75, and 0.5 + 0.75 = 1.25, confirming the answer.
How to Convert a Decimal to a Fraction
Any terminating decimal converts to a fraction in three steps:
1. Write the digits after the point over a power of 10 — one zero per decimal place. So 0.375 becomes 375/1000 2. Find the greatest common factor of the top and bottom. For 375 and 1000 that is 125 3. Divide both by it: 375 ÷ 125 = 3 and 1000 ÷ 125 = 8, giving 3/8
The eighths are worth memorising outright, because they come up constantly in measurements and recipes: 0.125 = 1/8, 0.25 = 2/8 = 1/4, 0.375 = 3/8, 0.5 = 4/8 = 1/2, 0.625 = 5/8, 0.75 = 6/8 = 3/4, 0.875 = 7/8.
The fifths and halves fill in the rest of the common cases: 0.2 as a fraction is 1/5, 0.4 as a fraction is 2/5, 0.6 as a fraction is 3/5, 0.75 as a fraction is 3/4, 2.5 as a fraction is 5/2, and 3.5 as a fraction is 7/2.
Decimals above 1 keep the whole number and convert only the remainder. 1.5 is 1 and 0.5, which is 1 1/2, or 3/2 as an improper fraction. 2.5 is 2 1/2 or 5/2.
Repeating decimals work differently. 0.333… is exactly 1/3, but 0.333 written with three digits is 333/1000 — close to a third but not equal to it. A repeating decimal needs the algebraic method: for 0.̅3, let x = 0.333…, then 10x = 3.333…, so 9x = 3 and x = 1/3.
| Decimal | Fraction | Simplified | Percentage |
|---|---|---|---|
| 0.05 | 5/100 | 1/20 | 5% |
| 0.125 | 125/1000 | 1/8 | 12.5% |
| 0.2 | 2/10 | 1/5 | 20% |
| 0.25 | 25/100 | 1/4 | 25% |
| 0.375 | 375/1000 | 3/8 | 37.5% |
| 0.5 | 5/10 | 1/2 | 50% |
| 0.6 | 6/10 | 3/5 | 60% |
| 0.625 | 625/1000 | 5/8 | 62.5% |
| 0.75 | 75/100 | 3/4 | 75% |
| 0.875 | 875/1000 | 7/8 | 87.5% |
| 1.5 | 15/10 | 3/2 (1 1/2) | 150% |
| 2.5 | 25/10 | 5/2 (2 1/2) | 250% |
| 3.5 | 35/10 | 7/2 (3 1/2) | 350% |
Multiplying and Dividing Fractions
Multiplication is the easiest fraction operation — no common denominator needed. Multiply straight across:
- 2/3 × 2/3 = (2×2)/(3×3) = 4/9
- 1/2 × 1/3 = 1/6
- 2/3 × 2 = 4/3, which is 1 1/3
When a question asks for the answer "in fraction form", it wants 4/9 rather than 0.4444. That is the whole point of the phrasing.
To multiply a fraction by a whole number, put the whole number over 1 first: 2 becomes 2/1, so 2/3 × 2/1 = 4/3.
The word "of" signals multiplication. "1/2 of 1/3" means 1/2 × 1/3 = 1/6.
Division is multiplication by the reciprocal — flip the second fraction and multiply:
- 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2
- 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2
That second result explains why dividing by a fraction smaller than 1 makes the answer bigger: asking how many quarters fit into a half sensibly gives 2.
How to Subtract Fractions (and Add Them)
How to subtract fractions, and add them: both need a common denominator first, which is what makes them harder than multiplication.
With the same denominator, just add or subtract the numerators: 1/4 + 2/4 = 3/4.
With different denominators, convert both to the least common denominator:
- 1/2 + 1/3: the LCD of 2 and 3 is 6, so 3/6 + 2/6 = 5/6
- 1/2 − 1/4: the LCD is 4, so 2/4 − 1/4 = 1/4
- 3/4 − 2/3: the LCD is 12, so 9/12 − 8/12 = 1/12
A shortcut that always works, though it may need simplifying afterwards: cross-multiply and use the product of the denominators. For a/b + c/d, the answer is (ad + bc)/bd. For 1/2 + 1/3 that gives (3 + 2)/6 = 5/6 directly.
The most common mistake is adding denominators — writing 1/2 + 1/3 = 2/5. A quick sanity check catches it: 2/5 is 0.4, which is less than 1/2 on its own, so it cannot be right.
Improper Fractions and Mixed Numbers
An improper fraction has a numerator at least as large as its denominator, like 7/4. A mixed number writes the same value as a whole number plus a proper fraction, like 1 3/4.
Improper to mixed: divide and keep the remainder. 7 ÷ 4 is 1 remainder 3, so 7/4 = 1 3/4.
Mixed to improper: multiply the whole number by the denominator and add the numerator. For 1 3/4, that is (1 × 4) + 3 = 7, over the same denominator 4, giving 7/4.
Always convert mixed numbers to improper fractions before multiplying or dividing. Trying to multiply 1 3/4 × 2 1/2 in mixed form is where errors creep in — convert to 7/4 × 5/2 = 35/8 first, then turn 35/8 back into 4 3/8 at the end.
Neither form is more correct. School answers usually want mixed numbers, while algebra and further calculation are easier with improper fractions.
Frequently Asked Questions
What is 0.375 as a fraction?
3/8. Write 0.375 as 375/1000, then divide both parts by their greatest common factor of 125: 375 ÷ 125 = 3 and 1000 ÷ 125 = 8.
What is 0.875 as a fraction?
7/8. As 875/1000, divided top and bottom by 125. It is also 87.5%, and the largest of the common eighths below 1.
What is 0.125 as a fraction?
1/8. From 125/1000, dividing both by 125. That makes it 12.5%, and doubling it repeatedly gives the rest of the eighths: 1/4, 1/2.
What is 1.5 as a fraction?
3/2, or 1 1/2 as a mixed number. Keep the whole number 1 and convert 0.5 to 1/2; as an improper fraction that is (1 × 2 + 1)/2 = 3/2.
What is 2/3 times 2/3 in fraction form?
4/9. Multiply straight across — numerators 2 × 2 = 4 and denominators 3 × 3 = 9 — with no common denominator needed. In decimal that is 0.4444, but "in fraction form" means 4/9.
How are fractions divided?
Flip the second fraction and multiply. 3/4 ÷ 1/2 becomes 3/4 × 2/1 = 6/4 = 3/2. Dividing by a fraction smaller than 1 gives a larger answer, because you are asking how many of the smaller part fit inside the first.
How do you subtract fractions?
Convert both to a common denominator, then subtract the numerators. For 3/4 − 2/3 the least common denominator is 12, giving 9/12 − 8/12 = 1/12. Never subtract the denominators.
What is an improper fraction?
One where the numerator is at least as big as the denominator, such as 7/4. It equals the mixed number 1 3/4 — divide 7 by 4 to get 1 with remainder 3. Convert mixed numbers to improper form before multiplying or dividing.
How do I convert a fraction to a percentage?
Divide the numerator by the denominator and multiply by 100. So 1/8 = 0.125 × 100 = 12.5%, and 3/8 = 37.5%. Fractions above 1 give percentages above 100: 5/4 is 125%.
How do you add fractions with different denominators?
Cross-multiply to get a common denominator: a/b + c/d = (ad + cb)/bd. For 1/3 + 1/4, compute (1×4 + 1×3)/(3×4) = 7/12. Then simplify if the numerator and denominator share a common factor.
How do you divide fractions?
Keep the first fraction, change division to multiplication, and flip the second fraction — often remembered as "keep, change, flip." So 1/2 ÷ 3/4 becomes 1/2 × 4/3 = 4/6 = 2/3. Dividing by a fraction less than 1 always produces a larger result.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. For 3/8, compute 3 ÷ 8 = 0.375. Some fractions produce repeating decimals — 1/3 = 0.333… — because the denominator has prime factors other than 2 and 5.
What is an improper fraction and a mixed number?
An improper fraction has a numerator larger than (or equal to) its denominator, like 7/4. A mixed number writes the same value as a whole number plus a proper fraction: 7/4 = 1 3/4. Divide numerator by denominator; the quotient is the whole part and the remainder is the new numerator.
Why can a denominator never be zero?
A fraction represents division, and division by zero is undefined in mathematics. There is no number that, multiplied by 0, gives a nonzero numerator, so expressions like 5/0 have no value. This calculator returns an error whenever a denominator is zero.