🍕 Fraction calculator — the pieces, put together
← Math & EverydayHalf a pizza plus a third of another sounds simple until the bottoms of the fractions don't match. Add, subtract, multiply, divide or simplify fractions here — and see the exact answer, a picture of what it means, and the steps that get you there.
The answer, in every shape
Fill in a numerator and a denominator to see the answer.
Because fractions refuse to stay in one shape
Three quarters and two thirds are perfectly reasonable numbers on their own. Put them next to a plus sign, though, and suddenly there's a small puzzle: quarters and thirds are different-sized pieces. You can't count them together until you agree on the size of a piece.
That's where fraction maths gets slippery. The right answer might be 17/12, 1 5/12, or about 1.4167, and all three are describing the same quantity. One looks like a school exercise, one looks like something you'd say while cooking, and the decimal is useful when you're comparing numbers quickly.
This calculator does the arithmetic, but it also shows the pieces. Use it to check homework, adjust a recipe, compare measurements, or just remember why dividing by a half can make an answer bigger rather than smaller. The goal isn't only to get a number. It's to make that number make sense.
Tiny slices, surprisingly big tricks
🍕 One pizza can have infinitely many fraction labels
1/2, 2/4, 50/100 and 500/1000 all describe the same amount of pizza. The number of slices can change as much as you like, but if the filled share stays the same, you haven't gained dinner. Just more ways to write it.
Half, two quarters and four eighths: the same half a pizza.
🔁 Three thirds make one — exactly
1/3 + 1/3 + 1/3 = 1. No awkward 0.9999… to worry about. Thirds repeat forever when written as decimals, but as fractions the arithmetic stays exact. It's a good reason to keep the original fraction around.
The infinite decimal 0.999… is exactly 1 as well — thirds just make that easier to see.
🍰 The bigger bottom number can mean the smaller slice
1/12 of a cake is smaller than 1/8 of the same cake. The denominator tells you how many equal pieces the cake was cut into. More pieces means smaller pieces, if you're taking just one.
One eighth against one twelfth of an equal whole.
✖️ Dividing by a half doubles your answer
3 ÷ 1/2 = 6. Sounds upside down until you change the question to “How many halves fit into three wholes?” The answer is six. Dividing by a fraction doesn't always make a number smaller.
Three wholes, cut into halves: six halves in total.
🧩 These two almost-equal pizza shares differ by one tiny piece
2/3 and 5/8 look close. They are: 2/3 − 5/8 = 1/24 of a whole. Put them into twenty-four equal slices and the entire disagreement is one slice.
The whole difference, out of twenty-four slices.
How does this fraction calculator work?
Fractions are whole numbers on top of other whole numbers, with one important rule: the denominator cannot be zero. The top tells you how many equal pieces you have; the bottom tells you how many equal pieces make a whole.
The calculator keeps the answer as an exact fraction while it works. That's why 1/3 + 1/3 stays exactly 2/3, even though each third has a repeating decimal expansion.
Adding fractions: match the size of the pieces
For fractions with different denominators, first find a common denominator. The least common denominator is the least common multiple (LCM) of the two denominators.
a/b + c/d = (a × (L/b) + c × (L/d)) / L, where L = lcm(b, d)
The general identity is (ad + bc)/(bd), but working with the least common denominator can give a smaller, easier-to-follow intermediate step.
Example: 3/4 + 2/3 = 9/12 + 8/12 = 17/12 = 1 5/12.
Subtracting fractions: same idea, minus instead of plus
a/b − c/d = (ad − bc)/(bd)
A least common denominator can again keep the workings tidy. If the second fraction is larger than the first, the result is negative — and that's a valid answer.
Example: 5/6 − 1/4 = 10/12 − 3/12 = 7/12.
Multiplying fractions: top times top, bottom times bottom
a/b × c/d = (a × c)/(b × d)
Unlike addition and subtraction, multiplication doesn't need a common denominator. The result is then reduced to simplest form.
Example: 2/3 × 9/10 = 18/30 = 3/5.
Dividing fractions: multiply by the reciprocal
a/b ÷ c/d = a/b × d/c = (a × d)/(b × c) — provided c is not zero.
Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8.
This also explains why 3 ÷ 1/2 = 6: there are six halves in three wholes.
Simplifying fractions: divide by the same number
A fraction is in simplest form when its numerator and denominator have no common positive factor greater than one.
a/b = (a ÷ gcd(|a|, b)) / (b ÷ gcd(|a|, b))
Example: The greatest common divisor of 12 and 18 is 6, so 12/18 = 2/3. You have changed how the fraction is written, not its value.
Mixed numbers and improper fractions
A mixed number contains whole units plus a fractional part. For a non-negative whole part w, numerator n and positive denominator d:
w n/d = (w × d + n)/d
Example: 1 1/2 = (1 × 2 + 1)/2 = 3/2.
A leading negative sign applies to the entire mixed number, so −1 1/2 = −3/2.
To express a non-negative improper fraction as a mixed number, divide its numerator by its denominator: the quotient is the number of wholes, and the remainder becomes the fractional part. For negative fractions, work with the absolute value and put one minus sign in front of the entire result.
Decimal and percentage forms
decimal value = numerator ÷ denominator
percentage value = (numerator ÷ denominator) × 100%
Those forms are helpful for comparisons, but decimals can repeat forever. The calculator displays them as approximations when rounded; the reduced fraction remains the exact answer.
The mathematical result is exact. The visual bar, decimal and percentage are interpretations of the same result and may be rounded for display. Nothing is rounded before the fraction is simplified.
A few things to know
- Numerators and denominators are whole numbers; each can be up to 15 digits long.
- A denominator of zero is refused, because dividing by zero is undefined.
- Dividing by a fraction that is worth zero — even one written as 0/5 — is refused too.
- The minus sign belongs to the whole fraction, so −1 1/2 means −(1 + 1/2) = −3/2.
- The decimal and percentage are rounded for reading; the fraction is the exact answer.
- Everything is calculated in this browser tab. No dates, numbers or fractions are sent anywhere.
Frequently asked questions
How do you add fractions with different denominators?
First find a denominator that both fractions can use, ideally the least common denominator. Rewrite each fraction with that denominator, add the numerators and simplify the result. For example, 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6. Adding the top numbers and bottom numbers directly would give the wrong answer.
How do you subtract fractions?
Use the same common-denominator approach as addition, but subtract the numerators. For example, 3/4 − 1/2 = 3/4 − 2/4 = 1/4. If the second fraction is larger, the result can be negative.
How do you multiply two fractions?
Multiply the numerators together and the denominators together, then simplify. For example, 2/3 × 3/4 = 6/12 = 1/2. You don't need matching denominators to multiply fractions.
Why do you flip the second fraction when dividing?
Dividing by a fraction asks how many of that fraction fit into the first amount. Multiplying by the reciprocal gives the same answer: 3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2. The reciprocal is the second fraction with its numerator and denominator swapped. You cannot divide by zero.
What does it mean to simplify a fraction?
It means writing the same value using the smallest whole-number numerator and denominator. Divide both parts by their greatest common divisor: 12/18 becomes 2/3 because both 12 and 18 can be divided by 6. The share hasn't changed, only its label.
What is the difference between an improper fraction and a mixed number?
An improper fraction has a numerator at least as large as its positive denominator, such as 7/4. A mixed number says the same amount using wholes and a remainder: 7/4 = 1 3/4. Neither form is more correct; each is useful in a different situation.
Can fractions be negative?
Yes. −1/2 means half a unit below zero. A minus sign in front of a mixed number applies to the whole amount, so −1 1/2 is −3/2, not −1/2. This calculator keeps that sign attached to the complete value.
Why do some fractions become repeating decimals?
Some exact fractions can't be written with a finite number of decimal digits. 1/3 is exactly one third, but its decimal goes on as 0.3333…. The calculator keeps the fraction exact and labels any rounded decimal as an approximation, so the displayed precision doesn't change the answer.
Is zero allowed in a fraction?
Zero is allowed in the numerator: 0/5 = 0. Zero is not allowed in the denominator, because division by zero is undefined. Dividing one fraction by a second fraction whose entire value is zero is also undefined.
Why is 1/4 + 1/4 not 2/8?
Both quarters are the same size, so you count two of them: 1/4 + 1/4 = 2/4 = 1/2. The denominator stays at four because the whole is still divided into quarters. You only combine the numerators when the pieces have matching denominators.
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