Fraction Calculator
Add, subtract, multiply & divide fractions with step-by-step working — mixed numbers supported
Fraction Calculator
Enter mixed numbers or simple fractions, pick an operation.
Fraction A
Fraction B
Result
Step-by-Step Working
Enter a numerator and denominator in each fraction. Leave Whole as 0 for simple fractions. Results update automatically.
Additional Tools
Enter a fraction to simplify it and see its GCD.
Convert between fraction, decimal, and percent.
Enter up to 4 fractions. They will be sorted and compared.
Enter up to 6 positive integers to find their LCM (LCD) and GCD with prime factorizations.
Worked Examples
Adding Fractions
Simplifying a Fraction
Recipe Scaling
How to Add, Subtract, Multiply and Divide Fractions
Fractions represent parts of a whole and appear throughout everyday life — cooking measurements, construction dimensions, financial ratios, and academic mathematics. Mastering fraction arithmetic is a foundational skill that unlocks algebra, calculus, and beyond. This calculator handles all four operations with full step-by-step working, so you can check your answers and understand each stage of the process.
Adding and Subtracting Fractions
To add or subtract fractions, both denominators must match. The process is: (1) find the Least Common Denominator (LCD), (2) rewrite each fraction with the LCD, (3) add or subtract the numerators, and (4) simplify the result. For example, 1/4 + 1/6 requires LCD = 12, giving 3/12 + 2/12 = 5/12.
Multiplying Fractions
Multiplication is the simplest fraction operation — multiply numerator by numerator and denominator by denominator, then simplify. You do not need a common denominator. Cross-cancellation (dividing numerator and denominator by a common factor before multiplying) keeps intermediate numbers smaller and makes simplification easier.
Dividing Fractions
Division is performed by multiplying by the reciprocal: a/b ÷ c/d = a/b × d/c. Flip the second fraction, then multiply. This works because dividing by a fraction is the same as asking how many times it fits, which equals multiplying by its inverse.
Mixed Numbers
A mixed number like 2¾ combines a whole part and a fractional part. To operate on mixed numbers, first convert them to improper fractions: 2¾ = (2×4 + 3)/4 = 11/4. After computing, convert back: divide numerator by denominator, the quotient is the whole part and the remainder is the new numerator.
Simplifying Fractions and Finding GCD
A fraction is fully simplified (in lowest terms) when the numerator and denominator share no common factor other than 1. The key tool is the Greatest Common Divisor (GCD), also known as the Highest Common Factor (HCF). Using the Euclidean algorithm, GCD(a,b) = GCD(b, a mod b) until the remainder is 0.
| Operation | Method | Key Formula |
|---|---|---|
| Add / Subtract | Find LCD, convert, operate on numerators | a/b + c/d = (a·d + c·b) / (b·d), then simplify |
| Multiply | Multiply straight across, simplify | (a/b) × (c/d) = (a·c) / (b·d) |
| Divide | Multiply by reciprocal | (a/b) ÷ (c/d) = (a/b) × (d/c) |
| Simplify | Divide by GCD | a/b → (a÷g)/(b÷g) where g = GCD(a,b) |
| Mixed to Improper | w whole + n/d = (w·d + n)/d | Multiply whole by den, add num |
LCD, LCM, and GCD Explained
The Least Common Multiple (LCM) of two numbers is the smallest positive integer divisible by both. When applied to denominators, it becomes the LCD. The GCD divides both numbers exactly. Together they satisfy: GCD(a,b) × LCM(a,b) = a × b. Both can be found efficiently using prime factorization or the Euclidean algorithm.
Fraction to Decimal Conversion
Converting a fraction to a decimal is simple: divide the numerator by the denominator. Some fractions produce terminating decimals (like 1/4 = 0.25), while others produce repeating decimals (like 1/3 = 0.333...). A fraction produces a terminating decimal if and only if its denominator (in simplified form) has no prime factors other than 2 and 5.