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All calculatorsMethodology

Fraction Calculator

Add, subtract, multiply or divide fractions and mixed numbers exactly, simplify a fraction, turn a decimal into a fraction, or switch improper and mixed forms.

Interactive calculator · Method FRACTION-EXACT-1.0 · Last reviewed: 2026-11-04

Calculate your scenario

a/b + c/d = (a×d + c×b)/(b×d); a/b − c/d = (a×d − c×b)/(b×d); a/b × c/d = (a×c)/(b×d); a/b ÷ c/d = a/b × d/c.

Your inputs

Try an example

Default worked example. Edit the inputs to calculate your scenario.

Default worked example

Simplified fraction 5/4
Mixed number 1 1/4
Exact decimal 1.25
Decimal (10 places) 1.25
GCD divided out 2

1/2 + 3/4 = (1×4 + 3×2)/(2×4) = 10/8; dividing top and bottom by their GCD 2 gives 5/4; 1 × 4 + 1 = 5, so 5/4 = 1 1/4.

How to use the calculator

Choose a task, type the first value (and for arithmetic the operation and second value) as a fraction, mixed number with a space (1 1/2), integer or decimal, and read the reduced result.

What the result means

1/2 + 3/4 = (4 + 6)/8 = 10/8, which reduces by 2 to 5/4 = 1 1/4 = 1.25.

Formula and units

a/b + c/d = (a×d + c×b)/(b×d); a/b − c/d = (a×d − c×b)/(b×d); a/b × c/d = (a×c)/(b×d); a/b ÷ c/d = a/b × d/c. The result is reduced by dividing numerator and denominator by their greatest common divisor (Euclid's algorithm). A decimal with k places is read as an integer over 10^k; a repeating decimal 0.x(y) is read exactly. The mixed number is the whole quotient plus the remainder over the denominator.

Worked examples

1/2 + 3/4: First value (3/4, 1 1/2, -2, 0.75 or 0.(3)): 1/2; Second value (arithmetic only): 3/4; Task: arith; Operation (arithmetic only): add.
Example result: Simplified fraction: 5/4; Mixed number: 1 1/4; Exact decimal: 1.25; Decimal (10 places): 1.25; GCD divided out: 2.

Repeating decimal 0.1(6) as a fraction: First value (3/4, 1 1/2, -2, 0.75 or 0.(3)): 0.1(6); Second value (arithmetic only): 3/4; Task: decimal; Operation (arithmetic only): add.
Example result: Simplified fraction: 1/6; Mixed number: 1/6; Exact decimal: 0.1(6); Decimal (10 places): 0.1666666667; GCD divided out: 15.

Limitations and common mistakes

Arithmetic is exact with whole-number numerators and denominators of any size (inputs up to 40 characters); nothing is rounded except the 10-place decimal line. A repeating block is shown in parentheses, e.g. 0.(3) = 0.333…; periods longer than 60 digits are cut off and marked. In mixed numbers the sign applies to the whole value (-1 1/2 = -3/2). The operation and second value are ignored outside arithmetic mode.

Adding fractions by adding tops and bottoms (1/2 + 3/4 ≠ 4/6); convert to a common denominator first.

Sources and assumptions

Method FRACTION-EXACT-1.0; last formula review 2026-11-04. Sources and their supported claims. Calculation methodology.