Fraction Calculator
Add, subtract, multiply, divide, or simplify fractions with exact whole-number math: steps, mixed number, and decimal included.
Details
Your sum
Tap any sign to change it. × and ÷ are worked out before + and −.
Answer
7/12
1/3 + 1/4
This adds, subtracts, multiplies and divides fractions, and simplifies a single fraction to its lowest terms.
It handles mixed numbers and improper fractions, returns the answer in both forms plus a decimal, and shows the working step by step.
What a fraction is
A fraction is a part of a whole. In 3/4, the bottom number says how many equal pieces the whole was cut into, and the top says how many of them you have.
The bottom is the denominator and the top is the numerator. A useful way to remember it: the denominator *denominates*, meaning it names the size of the pieces.
Fractions come in a few forms that describe the same amounts differently, and knowing which one an answer should be in is half of what fraction questions are testing.
The bigger the denominator, the smaller each piece. That is why 1/8 is less than 1/4, even though 8 is the larger number — a fact that catches out almost everyone at first.
What to enter
- What do you want to do?
- Work out a sum with fractions, or simplify a single one to its lowest terms.
- Operation
- Add, subtract, multiply or divide. Each has its own rule, and only addition and subtraction need a common denominator.
- Number type
- Proper, improper or mixed. The calculator accepts any of them and returns the answer in every form.
The three kinds of fraction
- Proper
- Top smaller than bottom, like 3/4. Its value is less than 1.
- Improper
- Top bigger than bottom, like 7/3. Its value is more than 1. Nothing is actually improper about it, and it is the easier form to calculate with.
- Mixed number
- A whole number beside a proper fraction, like 2 1/3. Easier to picture, harder to compute with, which is why you convert to improper before multiplying or dividing.
- Equivalent fractions
- Different numbers, same value: 1/2, 2/4 and 50/100 are all identical. Multiplying top and bottom by the same number never changes the value.
- Simplest form
- Divided down until nothing else fits. 12/18 simplifies to 2/3 by dividing both by 6, their greatest common factor.
What this assumes
Answers are given in lowest terms, and as a mixed number where the value exceeds 1.
A denominator of zero is undefined, since it would mean cutting a whole into no pieces.
How to calculate with fractions
Adding and subtracting need matching denominators. Multiplying and dividing do not, which makes them easier despite feeling harder.
- bd
- A common denominator, though not always the smallest one
- d/c
- The second fraction flipped, which is what turns division into multiplication
To add or subtract, match the bottoms. Find a common denominator, convert both fractions, then add or subtract the tops only. The bottom stays as it is.
To multiply, go straight across. Tops together, bottoms together. No common denominator needed, which is why multiplying is the easiest operation.
To divide, flip and multiply. Turn the second fraction upside down, then multiply. Dividing by 1/4 is the same as multiplying by 4.
Simplify at the end. Divide top and bottom by their greatest common factor, and convert to a mixed number if the answer is over 1.
See a worked example: 1/2 + 1/3, and why the bottoms must match first
- First fraction
- 1/2
- Second fraction
- 1/3
You cannot add halves to thirds directly; the pieces are different sizes.
The smallest number both 2 and 3 divide into is 6, so convert: 1/2 becomes 3/6 and 1/3 becomes 2/6.
Now the pieces match, so add the tops: 3 + 2 = 5, giving 5/6.
The denominator stays 6. Adding the bottoms as well would give 2/5, which is smaller than either fraction you started with and obviously wrong.
5/6
Frequently asked questions
Convert them to a common denominator first, then add only the tops. For 1/2 + 1/3, use sixths: 3/6 + 2/6 = 5/6.
The smallest common denominator is the least common multiple of the two bottoms. Multiplying the denominators together always works too, it just leaves more simplifying to do.
Because dividing by a number is the same as multiplying by its reciprocal. Dividing by 1/4 asks how many quarters fit into something, and there are four quarters in every whole.
So 1/2 ÷ 1/4 = 1/2 × 4 = 2. There are two quarters in a half, which you can check on a picture.
They are the same value written differently. 7/3 is improper; 2 1/3 is the mixed form.
Mixed numbers are easier to picture, improper fractions are far easier to calculate with. Always convert to improper before multiplying or dividing, then convert back at the end if asked.
Divide the top by the bottom. 3/4 = 3 ÷ 4 = 0.75, and multiplying by 100 gives 75%.
Some fractions never terminate: 1/3 is 0.333… forever. In those cases the fraction is the exact value and the decimal is only an approximation, which is why exam answers often stay as fractions.
Divide the top and bottom by their greatest common factor. For 12/18 that is 6, giving 2/3.
If you cannot spot the GCF, keep dividing by any common factor you can see. 12/18 → 6/9 → 2/3 gets to the same place in more steps.
1/4, even though 8 is the larger number. A bigger denominator means the whole was cut into more pieces, so each piece is smaller.
To compare any two fractions, put them over a common denominator: 1/4 is 2/8, which is clearly more than 1/8.
Problems people actually run into
Adding the denominators as well as the numerators
1/2 + 1/3 is not 2/5. The denominator names the size of the pieces, so it is not something you add.
The sanity check that catches it instantly: 2/5 is smaller than 1/2, and adding a positive amount cannot make the total smaller than what you started with.
Finding a common denominator before multiplying
Multiplying and dividing need no common denominator at all. Going to the trouble of finding one is wasted work and introduces extra chances to slip.
Only addition and subtraction require matching bottoms. For multiplication, go straight across and simplify at the end.
Results are estimates for general information only and are not professional financial, medical, or legal advice. Read our full disclaimer.
Last updated: September 4, 2026