Add, subtract, multiply, and divide fractions — with simplified result, mixed-number form, and decimal equivalent, plus a built-in simplifier and decimal-to-fraction converter.
Results update live as you type.
Result (simplified)
Unsimplified
5/6
before reducing
Simplified
5/6
GCF 1 — already lowest
Mixed number
5/6
proper fraction
Decimal
0.8333
≈ to 4 d.p.
| Operation | Rule | Example |
|---|---|---|
| Add | Common denominator, add numerators | 1/2 + 1/3 = 5/6 |
| Subtract | Common denominator, subtract numerators | 3/4 − 1/2 = 1/4 |
| Multiply | Numerators × numerators, denominators × denominators | 2/3 × 3/4 = 1/2 |
| Divide | Multiply by the reciprocal (flip the second) | 1/2 ÷ 1/4 = 2 |
| Simplify | Divide by GCF of numerator and denominator | 12/18 = 2/3 |
| Mixed → improper | Whole × denom + numerator | 1 1/2 = 3/2 |
The Rules
For addition and subtraction you need a common denominator; the simplest one is the least common multiple of the two existing denominators. For multiplication you just multiply numerators together and denominators together. For division, multiply by the reciprocal of the second fraction (the "keep, change, flip" rule). After any operation, divide both numerator and denominator by their greatest common factor to express the result in lowest terms.
Working
About This Tool
A fraction calculator performs the four basic arithmetic operations — addition, subtraction, multiplication, and division — on fractions of any kind: proper (numerator < denominator), improper (numerator ≥ denominator), and negative. It returns the result in three useful forms: the simplified fraction, the mixed-number form, and the decimal equivalent. Built-in helpers also simplify any single fraction to its lowest terms and convert any decimal to a fraction.
Fractions are foundational throughout school and into university mathematics. They underpin ratios and proportions, probability, algebraic manipulation, trigonometry (think π/6, π/4, π/3), and any real-world setting where you need to express a part of a whole: cooking recipes, measurement tolerances, financial percentages. Comfort with fractions is what distinguishes confident from anxious mathematicians.
This online fraction calculator works in exact arithmetic — no decimal rounding is introduced until the final decimal-equivalent display, so 1/3 + 1/6 returns exactly 1/2 rather than 0.5000…01. The simplification algorithm uses the Euclidean GCD, the same method taught in schools and used by every computer algebra system. The visual bar chart shows each fraction relative to a single "whole" so you can see at a glance whether the result is bigger or smaller than each input.
Use this free fraction calculator for homework, exam revision, cookery, woodworking, or anywhere you need precise rational arithmetic. All calculation is local — no sign-up, no tracking, no data sent to any server.
Four Operations
Add, subtract, multiply, divide — with automatic simplification of the result.
Mixed & Decimal Output
See the result as a simplified fraction, mixed number, and decimal.
Built-in Simplifier
Reduce any single fraction to lowest terms — and see the GCF used.
Decimal Converter
Convert any decimal to its fraction equivalent in lowest terms.
100% Free & Private
No account, no tracking — every calculation runs locally in your browser.
Visual Comparison
Bar chart shows each fraction as a slice of one whole — see the answer.
Four inputs and one operator give you a complete answer in seconds.
Type the numerator (top) and denominator (bottom) of fraction A. Negative numerators are fine — that's how the calculator handles negative fractions.
Choose + − × ÷ from the dropdown between the two fractions. The footer of the card always shows the active operation.
Fill in the second numerator and denominator. The result appears immediately to the right of the equals sign in fraction form.
The summary card shows the unsimplified result, the simplified form, the mixed number, and the decimal — all four representations at once.
The bar chart shows each fraction as a portion of one whole. If the result overflows the bar (improper fraction), it shows in amber so you can spot it.
Use the Simplify sub-tool to reduce a single fraction, or Decimal to Fraction to convert any decimal back to lowest-terms fraction form.
Everything you need to know about fraction arithmetic and how to interpret your result.
To add fractions you need a common denominator. The simplest choice is the least common multiple of the two denominators. Rewrite each fraction with that denominator, add the numerators, then simplify. For example 1/2 + 1/3: the LCM of 2 and 3 is 6, so we get 3/6 + 2/6 = 5/6. This calculator does the LCM step automatically and gives you the simplified result.
Exactly like addition, but subtract the numerators instead. Find a common denominator, rewrite each fraction, subtract numerators, simplify. 3/4 − 1/2 = 3/4 − 2/4 = 1/4. If the second fraction is larger than the first, the result will be negative.
Multiplication is the easiest operation: just multiply the numerators together and the denominators together: (a/b) × (c/d) = (ac)/(bd). Then simplify. 2/3 × 3/4 = 6/12 = 1/2. You can also "cross-cancel" before multiplying: notice 3 appears in both numerator and denominator and cancel them out first, giving 2/4 = 1/2.
The standard rule is "keep, change, flip": keep the first fraction, change ÷ to ×, and flip (invert) the second fraction. So (a/b) ÷ (c/d) = (a/b) × (d/c) = ad/bc. 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2. The "flipped" fraction is called the reciprocal.
A mixed number combines a whole number with a proper fraction — for example 1 1/2 (one and a half) or 2 3/4. Any improper fraction (where numerator ≥ denominator) can be written as a mixed number by dividing: 5/3 = 1 remainder 2, so 5/3 = 1 2/3. To convert back: 1 2/3 = (1 × 3 + 2)/3 = 5/3.
Find the greatest common factor (GCF) of the numerator and denominator, then divide both by it. For example 12/18: GCF(12, 18) = 6, so 12/18 = (12÷6)/(18÷6) = 2/3. A fraction is in lowest terms when the GCF of numerator and denominator is 1. The simplify sub-tool in this calculator does exactly this — and shows the GCF it used.
For terminating decimals: multiply by a power of 10 to remove the decimal point, then put it over the same power of 10, and simplify. 0.75 = 75/100 = 3/4 after dividing both by 25. For repeating decimals (e.g. 0.333…) use the algebraic technique: let x = 0.333…, then 10x = 3.333…, subtract to get 9x = 3, so x = 1/3.
Just divide the numerator by the denominator. 3/4 = 3 ÷ 4 = 0.75. Some fractions produce terminating decimals (3/4, 7/8); others repeat indefinitely (1/3 = 0.333…, 1/7 = 0.142857142857…). A fraction p/q in lowest terms terminates if and only if the denominator's only prime factors are 2 and 5.
An improper fraction has a numerator that is greater than or equal to its denominator — for example 5/3, 7/4, or 8/8. Improper fractions are perfectly valid; they just represent a value greater than (or equal to) 1. They are usually rewritten as mixed numbers for everyday use (5/3 → 1 2/3) but kept as improper fractions during algebraic manipulation, where the mixed form is awkward.
A fraction means "this many parts out of this total". You can only directly add or subtract parts of the same total — 2 sevenths plus 3 sevenths is 5 sevenths, easy. But 1/2 + 1/3 needs both to be expressed in the same "size" of part first. The least common multiple of 2 and 3 is 6, so we rewrite each as sixths and then the addition makes sense: 3/6 + 2/6 = 5/6. Multiplication and division don't need a common denominator because they work on the parts and the whole together.
Yes. Put a minus sign in front of the numerator: -3/4 means negative three-quarters. The calculator handles the signs correctly — for example -1/2 + 1/4 = -1/4. Negative denominators work too, but the calculator normalises the sign to the numerator when displaying the result (so 1/-2 is rendered as -1/2).
Dividing by zero is undefined. If you set the second fraction's numerator to zero and pick ÷, the result is undefined and the calculator shows a dash. Similarly, a fraction with denominator zero is undefined — treat it the same way. Mathematically, you cannot divide a quantity into "zero equal parts".