Add, subtract, multiply or divide two fractions and see the full working — the common denominator, the un-reduced result and its lowest terms — as a fraction, mixed number and decimal.
Decimal
0.833333
Mixed
5/6
Calculator
Result
5/6
1/2 + 1/3
Mixed number
5/6
Decimal
0.833333
Common denominator
6
Working
Common denominator (LCM): 6
Combine: 5/6 → simplify to 5/6
+=
How fraction arithmetic works
To add or subtract fractions they must share a denominator. The calculator uses the least common multiple of the two denominators, rewrites each fraction over it, then adds or subtracts the numerators. Multiplication multiplies numerators and denominators straight across; division multiplies the first fraction by the reciprocal of the second.
Every result is reduced to lowest terms by dividing the numerator and denominator by their greatest common divisor, and the sign is kept on the numerator. If the result is top-heavy it is also shown as a mixed number and as a decimal.
How do I enter a mixed number?
Convert it to an improper fraction first: a whole number w with fraction n/d becomes (w·d + n)/d. For example 2 1/3 is 7/3. The result is shown back to you as a mixed number when it is top-heavy.
Why use the least common multiple?
Any common denominator works, but the least common multiple keeps the numbers as small as possible, which makes the arithmetic and the final reduction easier.
Does it simplify the answer automatically?
Yes. The result is always reduced to lowest terms using the greatest common divisor, so 6/12 is reported as 1/2.
Results are estimates. Verify with a professional for important decisions.
About this calculator
This calculator adds, subtracts, multiplies or divides two fractions and shows every step along the way. Use it to double-check homework, understand how a common denominator is found, or convert a fraction to its decimal equivalent in one click.
How to read your results
The main result card shows the simplified fraction — for example 17/12 — along with the equivalent mixed number (1 5/12) and the decimal value. Below the result, the step-by-step breakdown explains the common denominator used for addition or subtraction, or how the numerators and denominators were multiplied together for multiplication or division. Three pie charts visualise each fraction and the result.
Worked example
Add 2/3 and 3/4.
The LCM of 3 and 4 is 12, so 2/3 becomes 8/12 and 3/4 becomes 9/12. Adding gives 17/12, which simplifies to the mixed number 1 5/12 and the decimal 1.417.
Frequently asked questions
Why do you need a common denominator for addition and subtraction?
Fractions can only be added or subtracted when they refer to equal-sized parts. Finding the lowest common multiple (LCM) of the two denominators gives the smallest denominator that both fractions can be rewritten with, so the numerators become directly comparable.
Why does multiplication not need a common denominator?
When multiplying, you combine two fractions into a new fraction by multiplying numerator by numerator and denominator by denominator. No alignment of parts is required — the operation works directly on the two fractions as given.
What does it mean to simplify a fraction?
A fraction is in its simplest (or lowest) terms when its numerator and denominator share no common factor other than 1. The calculator divides both by their greatest common divisor (GCD) automatically, so the result is always fully reduced.
How it's calculated
For addition and subtraction the calculator finds the LCM of the two denominators, rewrites each fraction over that common denominator, and combines the numerators. For multiplication it multiplies numerator by numerator and denominator by denominator. For division it multiplies the first fraction by the reciprocal of the second. In every case the result is then reduced by dividing numerator and denominator by their GCD (computed via the Euclidean algorithm), and a mixed-number form is derived when the absolute numerator exceeds the denominator.
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