Exact fractions with steps

Calculators

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About this tool

Calculate two exact rational values. Enter an integer, a fraction a/b or a mixed number w n/d. A mixed number’s leading minus applies to the whole value: -2 1/3 means -(2 + 1/3).

Common uses

Check exact rational arithmetic without floating-point loss.
Verify common denominators, reduction and negative mixed-number notation.

How to use it

1.Enter two bounded integers, fractions or proper mixed numbers; use one internal space in mixed numbers.
2.Choose addition, subtraction, multiplication or division and calculate.
3.Inspect normalized inputs, LCM or reciprocal steps, final GCD and the exact fraction; distinguish the decimal display from the exact value.

Worked fraction examples

Add unlike denominators

1/6 + 1/4

5/12; 0.416666666667

LCM(6,4)=12. The equivalent fractions are2/12 and3/12, giving5/12; GCD(5,12)=1. The12-place decimal0.416666666667 is rounded.

Multiply a negative mixed number

-2 1/3 × 3/5

-7/5; -1 2/5; -1.400000000000

-2 1/3 means-7/3. Multiplying by3/5 gives-21/15; GCD(21,15)=3, so the reduced value is-7/5, or-1 2/5.

Limits and notes

Each integer component accepts up to 128 ASCII digits, with at most 400 characters per operand. Outer whitespace is trimmed; mixed numbers use one internal ASCII space, a positive denominator and 0 ≤ n < d. Fractions may have negative denominators. Decimals, exponents and expressions are not accepted.
Mixed-number signs apply to the whole magnitude; proper fractions stay fractions, and whole results stay integers.
This decimal is rounded; the fraction is the exact result. Ties round away from zero.
Browser-local arithmetic only. No history is stored, no inputs are uploaded, and no mathematical expression is executed.

Frequently asked questions

How is a negative mixed number interpreted?

Calculate two exact rational values. Enter an integer, a fraction a/b or a mixed number w n/d. A mixed number’s leading minus applies to the whole value: -2 1/3 means -(2 + 1/3).

Can the denominator be zero?

A zero denominator is rejected even when the numerator is zero; division by any zero-valued right operand is also rejected.

Is the displayed decimal exact?

The reduced fraction is exact. The decimal is displayed to12 places, with ties rounded away from zero; the page states whether that display is exact or rounded.