Fraction Calculator
Add, subtract, multiply and divide fractions and mixed numbers — auto-simplified, with decimal and mixed-number conversion. Free, runs in your browser.
Fraction Calculator
How to Use the Fraction Calculator
Enter the first fraction
Type the numerator (top) and denominator (bottom). For a mixed number like 2¾, put 2 in the whole-number box on the left and 3 over 4 in the fraction. Leave the whole box empty for a simple fraction.
Choose an operation
Pick add, subtract, multiply, or divide between the two fractions. The result updates instantly as you type — no submit button needed.
Enter the second fraction
Fill in the second fraction (or mixed number) the same way. Negative fractions are fine — put the minus sign on the whole number, or on the numerator if there is no whole part.
Read the answer
You get the result as a fully simplified fraction, as a mixed number, and as a decimal — all at once. The calculator always reduces to lowest terms automatically.
Working With Fractions
Why Fractions Trip People Up
Fractions are one of the first places arithmetic stops being automatic. Adding 1/2 and 1/3 is not "add the tops and add the bottoms" — that would give 2/5, which is wrong. You have to find a common denominator first (here, 6), rewrite each fraction over it (3/6 and 2/6), and only then add to get 5/6. Multiplication and division follow different rules again: to multiply you multiply straight across, and to divide you "flip and multiply" the second fraction. These rules are simple once learned but easy to mix up, which is exactly why a calculator that shows the fully worked, simplified answer is so useful — for students checking homework, for parents helping with it, and for anyone whose school fractions have gone a little rusty. This tool handles all four operations, reduces every answer to lowest terms automatically using the greatest common divisor, and copes with mixed numbers and negatives without fuss.
"Simplifying" — reducing a fraction to its lowest terms — is the step people most often forget. 6/8 and 3/4 are the same number, but 3/4 is the conventional, tidy form, found by dividing top and bottom by their greatest common divisor (here, 2). This calculator always does that final simplification for you, and it is built on the same shared math engine that powers the site's GCD & LCM calculator — so the simplification you see here is computed exactly the same way. Seeing the answer three ways at once — simplified fraction, mixed number, and decimal — also helps build intuition for how the same quantity looks in each form, which is half the point of learning fractions in the first place.
"A fraction and its decimal are the same number wearing different clothes. Fluency means seeing 3/4, 0.75, and 'three quarters' as one idea."
Mixed Numbers, Decimals, and Real Life
Fractions are not just a school exercise — they are everywhere in the physical world. Recipes call for 2¾ cups of flour; a tape measure is divided into halves, quarters, eighths, and sixteenths of an inch; music is built on whole, half, and quarter notes; woodworking and sewing live and die by fractional measurements. In all of these, you frequently need to add or subtract mixed numbers (¾ cup plus ⅔ cup, or 5⅛ inches minus 1¾ inches) and then express the answer in a usable form. That is precisely what this calculator is for: enter the mixed numbers, pick the operation, and read off the answer as a clean mixed number you can act on, plus the decimal if you would rather measure that way. Everything runs in your browser, instantly and privately, so it is as quick to reach for as a notepad — but it never makes an arithmetic slip.
Egyptians wrote almost everything as sums of 1/n
To add fractions you need a common denominator — you cannot just add the tops.
To multiply, you multiply straight across — tops together, bottoms together.
To divide, flip the second fraction and multiply (multiply by the reciprocal).
Simplifying means dividing top and bottom by their greatest common divisor.
6/8, 3/4 and 0.75 are all the same number in different forms.
The ancient Egyptians wrote almost all fractions as sums of unit fractions (1/n).
The fraction bar (vinculum) dates back to medieval Arab mathematicians.
A mixed number like 2¾ is a whole number plus a proper fraction.
This calculator always reduces to lowest terms automatically.
Results are exact while every numerator, denominator and cross-product stays below 2⁵³ (about 9 × 10¹⁵) — the integer limit of double-precision arithmetic.
Frequently Asked Questions
- Enter the numerator and denominator of each fraction, choose the + operation, and the calculator finds a common denominator, adds them, and simplifies the result automatically. For example, 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6. You see the answer as a fraction, a mixed number, and a decimal at once.
- Yes. Put the whole number (2) in the left-hand box and the fraction (3 over 4) in the fraction boxes. The calculator converts the mixed number to an improper fraction internally, does the arithmetic, and gives you the answer back as a tidy mixed number. This is ideal for recipes and measurements.
- Always. Every result is reduced to lowest terms by dividing the numerator and denominator by their greatest common divisor — so you get 3/4 rather than 6/8. This is the same simplification logic used by the site's GCD/LCM calculator, because both run on the same shared math engine.
- Just choose the ÷ operation. Behind the scenes the calculator applies the "flip and multiply" rule — it inverts the second fraction and multiplies. So 1/2 ÷ 1/4 becomes 1/2 × 4/1 = 2. You do not have to remember the rule; the calculator applies it for you and simplifies the result.
- Yes. Put the minus sign on the whole number for a negative mixed number, or on the numerator if there is no whole part. The calculator tracks the sign correctly through all four operations and shows a negative result clearly.
- The decimal form is shown automatically alongside every result — it is simply the numerator divided by the denominator (3/4 = 0.75). If you just want to convert a single fraction, enter it as the first fraction with a "+ 0" second fraction, or multiply by 1, and read off the decimal row.
- A denominator of zero, or dividing by the fraction 0, is undefined in mathematics, so the calculator shows a clear error message instead of a wrong answer. Correct the input and the result reappears instantly.
- Yes, and it is a precise one. Every browser stores numbers in IEEE 754 double precision, which represents integers exactly only up to 2⁵³ = 9,007,199,254,740,991. Adding two fractions cross-multiplies (a/b + c/d = (ad + cb)/bd), so the arithmetic stays exact while those products stay under that limit — comfortably millions over millions. Beyond it the products round, and the simplified fraction shown may no longer be exactly right. For schoolwork and measurements it is never a concern.
- Yes. Everything runs in your browser — nothing you type is uploaded, stored, or logged, and the calculator works offline once the page has loaded. It is as private as scribbling on paper, but without the arithmetic mistakes.
- With Euclid's algorithm, the oldest algorithm still in everyday use: repeatedly replace the larger number by the remainder when it is divided by the smaller, until the remainder is zero — the last non-zero remainder is the GCD. For 6/8 that is gcd(6, 8): 8 mod 6 = 2, 6 mod 2 = 0, so the GCD is 2 and the fraction reduces to 3/4. It appears as Propositions 1 and 2 of Book VII of Euclid's Elements (c. 300 BC) and takes at most a few dozen steps even for very large numbers, which is why the result appears instantly.
Method & sources
How it computes
Exact rational arithmetic on two fractions or mixed numbers: a/b + c/d = (ad + cb)/bd, a/b − c/d = (ad − cb)/bd, (a/b)(c/d) = ac/bd and (a/b) ÷ (c/d) = ad/bc, with every result reduced to lowest terms by dividing numerator and denominator by gcd(n, d) computed with Euclid's algorithm (Elements VII.1–2). A mixed number w n/d is converted to the improper fraction (|w|d + |n|)/d carrying the sign of w. The answer is shown as a simplified fraction, a mixed number and a decimal.
What this tool implements
- Canonical reduced form: the denominator is kept positive, the sign carried by the numerator, and the fraction divided through by the greatest common divisor, so 6/8 always displays as 3/4 and −4/−6 as 2/3.
- Euclid's subtractive-then-remainder algorithm in its modern remainder form — repeatedly replace (a, b) with (b, a mod b) until b = 0 — as in Elements Book VII Propositions 1 and 2 and Knuth TAOCP Vol. 2 §4.5.2.
- Integers are IEEE 754 binary64 doubles, exact only to 2^53 − 1 = 9,007,199,254,740,991; addition and subtraction cross-multiply, so the result is exact only while ad, cb and bd all stay inside that range. The page states this limit and the reason for it.
- Division by the fraction zero and a zero denominator are refused with an error rather than returned as Infinity or NaN; a sign typed on the numerator is ignored when a whole part is present, which is why the page tells the reader to put the minus sign on the whole number.
Sources
- Euclid. Elements, Book VII, Propositions 1 and 2 (the algorithm for the greatest common measure of two numbers), c. 300 BC. Heath TL, translator. The Thirteen Books of Euclid's Elements. 2nd ed. Cambridge: Cambridge University Press; 1926.
- Knuth DE. The Art of Computer Programming, Volume 2: Seminumerical Algorithms. 3rd ed. Reading, MA: Addison-Wesley; 1998. §4.5.1 Fractions and §4.5.2 The greatest common divisor.
- IEEE Std 754-2019, IEEE Standard for Floating-Point Arithmetic. New York: IEEE; 2019. Clause 3.3 binary64 format — 53-bit significand, integers exact to 2^53. https://standards.ieee.org/ieee/754/6210/
- Cajori F. A History of Mathematical Notations, Volume I: Notations in Elementary Mathematics. Chicago: Open Court; 1928. §§20-24 Egyptian unit fractions in the Rhind papyrus; §235 the horizontal fraction bar introduced by al-Hassar and carried into Europe by Fibonacci.
What can make this go out of date
- None at runtime — exact rational arithmetic in the browser, with no published figure or table consulted.
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