Fraction Calculator
Add, subtract, multiply, and divide fractions. Auto-simplifies and converts between improper, mixed-number, and decimal forms.
e.g. 5, 3/4, 1 1/2, or 1-1/2 — negatives prefix the whole expression
Same formats as A
Results auto-simplify by the greatest common divisor and normalise the sign so the denominator is always positive.
How to use this calculator
Enter two fractions, pick an operation, and the result appears in three forms: simplified improper fraction, mixed number, and decimal. Inputs accept whole numbers (5), simple fractions (3/4), and mixed numbers either with a space (1 1/2) or a dash (1-1/2). To enter a negative, put the minus sign at the front: -3/4, -1 1/2.
The four operations
Addition and subtractionrequire a common denominator. The calculator multiplies each fraction's numerator and denominator by the other's denominator, then adds or subtracts and simplifies. So 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6. Multiplication multiplies numerators and denominators directly: (a/b) × (c/d) = (ac)/(bd). Division multiplies by the reciprocal: (a/b) ÷ (c/d) = (a/b) × (d/c) = (ad)/(bc).
Why simplification matters
6/8 and 3/4 are the same number, but 3/4 is the canonical form — it's easier to read, easier to compare, and matches how textbooks write the answer. The calculator simplifies after every operation by computing the greatest common divisor of the numerator and denominator, then dividing both. The result is always in lowest terms with a positive denominator.
Mixed numbers vs. improper fractions
7/4 is an "improper" fraction (numerator larger than denominator). 1 3/4 is the equivalent "mixed" form — a whole part plus a proper fraction. Mixed numbers read naturally in everyday contexts (recipes, woodworking, distances). Improper fractions are easier to compute with because there's only one piece. The calculator shows both so you can pick what fits your use.
Common practical uses
Recipes that need scaling (half a recipe of 3/4 cup is 3/8 cup). Construction measurements that mix feet and inches with sixteenths (cutting a 1 1/2-inch piece off a 5 3/4-inch board). Dividing time blocks (two-thirds of 45 minutes is 30 minutes). Probability problems where outcomes are naturally ratios. The calculator covers all of these cleanly without forcing decimal approximation.
Frequently asked questions
What input formats are accepted?▾
Plain whole numbers (5), simple fractions (3/4), and mixed numbers in either spaced (1 1/2) or dashed (1-1/2) form. Negatives prefix the whole expression with a minus sign — '-1 1/2' or '-3/4'. The calculator parses each input into a normalised fraction before computing, so 4/8 and 1/2 produce identical results.
How does auto-simplification work?▾
After every operation, the calculator computes the greatest common divisor of the resulting numerator and denominator, then divides both by it. So 6/8 becomes 3/4, 12/18 becomes 2/3, and a result that lands on 5/1 displays as 5. The sign is normalised so the denominator is always positive — −1/2, not 1/−2.
Why is dividing by zero rejected?▾
Mathematically undefined. Dividing any fraction by 0 (or by a fraction whose numerator is 0) has no real-number answer. The calculator surfaces a clear error rather than silently returning Infinity. Fractions with a zero denominator (like 3/0) also fail at the input stage for the same reason.
How are negative mixed numbers handled?▾
The minus sign applies to the whole expression — so '-1 1/2' means −(1 + 1/2) = −3/2, not (−1) + 1/2 = −1/2. This matches how mixed numbers are written in textbooks and avoids the ambiguity of a sign inside the expression. The calculator stores the result with a positive denominator and the sign on the numerator.
What's the difference between improper, mixed, and decimal forms?▾
An improper fraction has a numerator larger than its denominator (7/4). A mixed number splits that into a whole part and a remainder (1 3/4). The decimal form is the division written out (1.75). All three represent the same value — the calculator shows all three so you can pick the one that fits your context.
Are repeating decimals shown exactly?▾
No — the decimal output uses 10 significant digits. Fractions like 1/3 display as 0.3333333333, which is a finite approximation of the true repeating decimal. For exact arithmetic, use the simplified fraction or mixed-number forms — those carry no rounding error.
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