About the Fraction Calculator
A fraction calculator adds, subtracts, multiplies, and divides fractions and reduces the answer to lowest terms. Fractions are exact in a way decimals are not — one third is 0.333… forever as a decimal but perfectly precise as 1/3 — which is why they remain standard in mathematics, cooking, and construction.
The formula
a/b + c/d = (ad + bc) / bd and a/b × c/d = ac / bdThe numerator is the top number, the denominator the bottom. Addition and subtraction need a common denominator; multiplication and division do not.
How to use this calculator
- 1Enter your Numerator 1. The field starts at
1, which you can overwrite. - 2Enter your Denominator 1. The field starts at
2, which you can overwrite. - 3Enter your Numerator 2. The field starts at
1, which you can overwrite. - 4Enter your Denominator 2. The field starts at
4, which you can overwrite. - 5Read the result straight away — it recalculates as you type, so there is no button to press. Use Share to copy a link that reopens the page with your exact numbers filled in.
Worked example
| Input | Value |
|---|---|
| Numerator 1 | 1 |
| Denominator 1 | 2 |
| Numerator 2 | 1 |
| Denominator 2 | 4 |
Result
Sum: 3 / 4
Those are the values the page loads with, so you can reproduce this result yourself and then change one field at a time to see what drives the outcome.
Understanding your result
Multiplication is the easy operation: multiply the numerators, multiply the denominators, done. Division is the same thing after flipping the second fraction, because dividing by 1/2 is identical to multiplying by 2. Addition and subtraction are the awkward ones, since the fractions must be rewritten over a shared denominator before the numerators can be combined.
Reducing to lowest terms means dividing both parts by their greatest common factor. 6/8 becomes 3/4 because both divide by 2. The reduced form is the conventional answer and the easiest to compare — spotting that 3/4 is larger than 5/7 is much harder in unreduced form.
Things worth knowing
- You do not need the lowest common denominator to add fractions. Multiplying the denominators always works; it just leaves more reducing to do.
- Dividing by a fraction means multiplying by its reciprocal. Flip the second fraction and change the sign to multiplication.
- Convert mixed numbers to improper fractions before calculating: 2 1/3 becomes 7/3.
- A denominator of zero is undefined, exactly as division by zero is.
- Any whole number is a fraction over 1, which is how you combine 3 and 1/2 into a single expression.
Frequently asked questions
How do I add fractions with different denominators?+
Rewrite both over a common denominator, then add the numerators. For 1/2 + 1/4, convert 1/2 to 2/4 and add to get 3/4. Multiplying the two denominators always gives a usable common denominator.
How do I divide one fraction by another?+
Invert the second fraction and multiply. So 1/2 ÷ 1/4 becomes 1/2 × 4/1 = 4/2 = 2. Dividing by a smaller fraction correctly gives a larger answer.
What does simplifying a fraction mean?+
Dividing the numerator and denominator by their greatest common factor so no common factor remains. 12/18 simplifies to 2/3 because both divide by 6. The value is unchanged.
How do I turn a fraction into a decimal?+
Divide the numerator by the denominator: 3/8 is 3 ÷ 8 = 0.375. Some fractions produce repeating decimals, such as 1/3 = 0.333…, which is why the fraction form is more precise.