Fraction Calculator
Add, subtract, multiply and divide fractions, with the result in lowest terms.
Last updated
Your details
Result
- 1/2 + 1/3
- 5/6
- As a decimal
- 0.833333
- As a percentage
- 83.3333%
- Lowest common denominator used
- 6
In lowest terms
Let's work it out…
a/b + c/d = (ad + cb) / bd
1/2 + 1/3
= 3/6 + 2/6
= 5/6
Formula — written step by step
Adding a half and a third…
a/b + c/d = (ad + cb) / bd
1/2 + 1/3
= 3/6 + 2/6
= 5/6
5/6
Fractions can only be added when the pieces are the same size, so both are rewritten over a common denominator first. Multiplying the denominators always gives one; the lowest common multiple gives the smallest one.
A worked example
Three quarters minus a half
- First
- 3/4
- Second
- 1/2
- Common denominator: 4
- 3/4 − 2/4
- = 1/4
1/4 — or 0.25
One half is rewritten as two quarters. Nothing about the value changes; only how it is written.
Dividing by a fraction
- First
- 1/2
- Second
- 1/4
- Flip the second fraction: 1/4 becomes 4/1
- 1/2 × 4/1
- = 4/2
2
Dividing by a quarter asks how many quarters fit into a half. Two do — which is why dividing by a fraction smaller than one makes the answer bigger.
How to use this calculator
- Enter the top and bottom of each fraction. Negative numerators are fine; a denominator of zero is not.
- Choose the operation. Add and subtract find a common denominator first; multiply and divide do not need one.
- The answer appears in lowest terms, with the decimal and percentage beside it.
- When the result is top-heavy, the mixed number is shown too — 5/3 as 1 2/3.
Why adding fractions needs a common denominator
A fraction is a count of equally sized pieces: 3/4 is three pieces, each a quarter of the whole. You can only add counts when the pieces are the same size, which is why 1/2 + 1/3 is not 2/5. Rewrite both over sixths and it becomes 3/6 + 2/6, which is plainly 5/6.
Multiplication needs no such step, because multiplying fractions asks a different question — a third of a half — and the answer follows from multiplying tops and bottoms directly.
Lowest terms, and why they matter
Every fraction has infinitely many equivalent forms: 1/2, 2/4 and 50/100 are the same number. Dividing both parts by their greatest common divisor gives the one form that cannot be reduced further, which is what this calculator reports.
It matters because lowest terms make comparison possible at a glance. Deciding whether 17/51 is larger than 1/3 is work; noticing that 17/51 reduces to 1/3 is not.
Frequently asked questions
What is an improper fraction?
One whose numerator is at least as large as its denominator, such as 5/3. It is perfectly valid — the name is a historical quirk, not a criticism. The equivalent mixed number, 1 2/3, is shown alongside it.
Why does dividing by a fraction make the number bigger?
Because you are asking how many of the small thing fit into the large one. Six divided by a half is twelve, because twelve halves fit into six. The rule "multiply by the reciprocal" is that question rearranged.
Can I use negative fractions?
Yes. Put the minus sign on the numerator. The result carries the sign on the numerator too, which is the conventional form.