Fraction calculator with steps
Add, subtract, multiply and divide fractions and mixed numbers. Shows the common denominator, the simplification and the decimal equivalent.
- Runs in your browser
- Nothing you enter is sent
- Free, no account
11/4 + 5/6
Simplified fraction
43/12
Mixed number
3 7/12
Decimal
3.58(3)
brackets mark the repeating block
Percentage
358.3333%
Numerator
43
Denominator
12
Step-by-step working
Write both values as improper fractions.
11/4 + 5/6A mixed number a b/c becomes (a × c + b)/c; a whole number n becomes n/1.
Find the least common denominator (LCD) of the two denominators.
LCD(4, 6) = 12LCD = 4 × 6 ÷ GCD(4, 6) = 24 ÷ 2 = 12
Rewrite both fractions over that denominator.
11/4 = 33/12 and 5/6 = 10/12Multiply the first by 3/3 and the second by 2/2 — both equal 1, so the values do not change.
Add the numerators and keep the denominator.
33/12 + 10/12 = 43/12Check for common factors — there are none, so this is already in lowest terms.
GCD(43, 12) = 1Convert the improper fraction to a mixed number.
43/12 = 3 7/12Because 43 ÷ 12 = 3 remainder 7.
Divide the numerator by the denominator for the decimal value.
43 ÷ 12 = 3.58(3)The digits in brackets repeat forever — this is a recurring decimal.
How to use the fraction calculator
- Type the first value. Whole numbers (
5), simple fractions (7/8), mixed numbers (2 3/4) and decimals (1.25) are all accepted. - Choose add, subtract, multiply or divide.
- Type the second value the same way.
- Read the answer as a simplified fraction, a mixed number, a decimal and a percentage — with every step of the working shown underneath.
Negative values go in front of the whole expression: -2 1/2 and -7/8 both work.
The calculator stores fractions as pairs of arbitrary-precision integers, so results are exact — nothing
is lost to floating-point rounding along the way.
The rules, in the order the calculator applies them
Adding and subtracting
Fractions can only be added when the pieces are the same size, so both fractions are rewritten over a common denominator first. The calculator uses the least common denominator — the LCM of the two denominators — which keeps the numbers small and usually removes the need to simplify afterwards.
For example, 2 3/4 + 5/6 becomes 11/4 + 5/6. The LCM of 4 and 6 is 12, so the fractions become 33/12 and 10/12, giving 43/12, which is 3 7/12.
Multiplying
Multiply straight across: numerator by numerator, denominator by denominator. No common denominator is needed. Any shared factor between the top and bottom of the product is cancelled at the end.
Dividing
Dividing by a fraction is the same as multiplying by its reciprocal — flip the second fraction and change the ÷ into a ×. This works because dividing by 3/4 asks “how many three-quarters fit in here?”, which is the same as multiplying by 4/3.
Simplifying
A fraction is in lowest terms when the numerator and denominator share no common factor. Dividing both by their greatest common divisor gets there in a single step, which is exactly what the last line of the working shows.
Common fraction ↔ decimal ↔ percent equivalents
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.33% |
| 2/3 | 0.666… | 66.67% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.1666… | 16.67% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 1/10 | 0.1 | 10% |
| 1/16 | 0.0625 | 6.25% |
Where fraction arithmetic actually comes up
- Cooking — halving a recipe that calls for 2/3 cup means computing 2/3 ÷ 2 = 1/3.
- Woodwork and construction — imperial measurements live in sixteenths of an inch, and adding 3/16 to 5/8 needs a common denominator.
- Music — note lengths are fractions of a bar, and a bar has to add up exactly.
- Probability — combining independent events multiplies fractions directly.
- Homework — showing the working matters as much as the answer, which is why every step is listed and copyable.
Why exact arithmetic matters here
Many online fraction tools convert to a decimal, do the sum, then guess a fraction back from the result. That produces answers like 0.3333333333 for 1/3 and can turn 1/3 + 1/6 into something that is not quite 1/2. This calculator never leaves integer arithmetic: it keeps the numerator and denominator as big integers, reduces by the greatest common divisor, and only converts to a decimal at the very end for display. Everything runs on your own device — nothing is uploaded.
Questions
How do I enter a mixed number?
Type the whole part, a space, then the fraction — for example 2 3/4. Improper fractions like 11/4, plain integers like 5 and decimals like 1.25 are all accepted too.
How does it find the common denominator?
It uses the least common multiple of the two denominators, then rescales each fraction. The working shows the LCM, both rescaled numerators and the final reduction by the greatest common divisor.
Are the results exact?
Yes. Every fraction is stored as a pair of arbitrary-precision integers, so nothing is lost to floating point. The decimal shown alongside is a rounded view of that exact value.
Can it handle negative fractions?
Yes — put the minus sign in front of the whole expression, such as -2 1/2 or -7/8. The sign is kept on the numerator internally and displayed in front of the answer.