Theory, formulas, and worked examples
This section mirrors calculator.net's long-form documentation so learners understand the exact rules behind every answer. Formulas are rendered in plain text for screen-reader compatibility; copy/paste them as needed.
Addition
Adding fractions requires a common denominator. One method multiplies the numerators and denominators by each other's denominators:
a/b + c/d = (a×d + c×b)/(b×d)
EX: 3/4 + 1/6 = 18/24 + 4/24 = 22/24 = 11/12
For multiple fractions, multiply the numerator by the product of the other denominators, e.g.
1/4 + 1/6 + 1/2 = 12/48 + 8/48 + 24/48 = 44/48 = 11/12
A faster approach is to use the least common multiple (LCM) of all denominators, then scale numerators accordingly. For denominators 2, 4, and 6 the LCM is 12:
1/4 + 1/6 + 1/2 = 3/12 + 2/12 + 6/12 = 11/12
Subtraction
Subtraction mirrors addition; build a common denominator and subtract the numerators:
a/b − c/d = (a×d − c×b)/(b×d)
EX: 3/4 − 1/6 = 18/24 − 4/24 = 14/24 = 7/12
Multiplication
Multiplication is direct; multiply numerators and denominators:
a/b × c/d = ac/bd
EX: 3/4 × 1/6 = 3/24 = 1/8
Division
Division multiplies by the reciprocal of the divisor:
a/b ÷ c/d = a/b × d/c = ad/bc
EX: 3/4 ÷ 1/6 = 3/4 × 6/1 = 18/4 = 9/2
The reciprocal of 3/4 is 4/3; we swap numerator and denominator.
Simplification
Results simplify by dividing numerator and denominator by their greatest common factor. Example: 220/440 ÷ 220 → 1/2. Mixed fractions convert to improper form first, are simplified, then converted back if needed.
Converting between fractions and decimals
Decimal → fraction: treat each decimal place as powers of 10. For 0.1234, denominator is 10^4 = 10000. Simplify: 1234/10000 → divide by gcd 2 → 617/5000.
Fraction → decimal: divide numerator by denominator. Example: 1/2 = 0.5. Repeating decimals appear when denominators have factors besides 2 or 5.