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CALCPARK

Fraction Calculator

Add, subtract, multiply and divide fractions and mixed numbers with the working shown step by step, simplified results, decimal and percent equivalents and a comparison.

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How to use it

  1. Choose “Calculate” for two fractions or “Simplify / convert” for one.
  2. Type each fraction as 3/4, a mixed number as 1 1/2 (whole number, space, fraction), a whole number, or a decimal such as 0.75.
  3. Pick +, −, × or ÷. Negative values are fine: −3/4 or 3/−4.
  4. Read the simplified result, the mixed-number form, the decimal and percent, and which of the two inputs is larger.
  5. Follow the numbered working to see the common denominator, the reciprocal and the simplification step by step.

Example

1 1/2 + 2 2/3: convert to 3/2 and 8/3. lcm(2, 3) = 6, so 3/2 = 9/6 and 8/3 = 16/6; 9/6 + 16/6 = 25/6, already in lowest terms, which is 4 1/6 = 4.1(6) = 416.67%. Dividing instead: 3/2 ÷ 8/3 = 3/2 × 3/8 = 9/16 = 0.5625. Comparison: 3/2 < 8/3 because 3 × 3 = 9 < 8 × 2 = 16.

Rules and how the tool computes

a/b + c/d = (a·(L/b) + c·(L/d)) / L,   L = lcm(b, d)
a/b − c/d = (a·(L/b) − c·(L/d)) / L
a/b × c/d = (a·c) / (b·d)
a/b ÷ c/d = (a·d) / (b·c)        (c ≠ 0)
simplify:  divide both by gcd(numerator, denominator); keep the sign in the numerator
compare:   a/b < c/d  ⇔  a·d < c·b   (b, d > 0)

Numerators and denominators are arbitrary-precision integers (BigInt), so 12345678901234567890/7 × 7/12345678901234567890 is exactly 1 and there is no floating-point rounding. Decimals typed as input are converted exactly (0.75 → 75/100 → 3/4). The decimal display finds the repeating block by tracking remainders during long division and shows at most 12 digits, adding an ellipsis when a non-repeating expansion is cut off. Repeating decimals cannot be typed as input here – use the Decimal to Fraction calculator for 0.(3)-style notation.

Sources: Khan Academy – Adding and subtracting fractions with unlike denominators, Wolfram MathWorld – Fraction.

Questions

How do I enter a mixed number?
Whole number, a space, then the fraction: 1 1/2. For a negative mixed number put the minus in front: −1 1/2 means −(1 + 1/2) = −3/2.
Why does the tool use the least common denominator instead of multiplying the denominators?
Both give the same simplified answer. The LCD keeps the intermediate numbers small and matches the way the working is taught: 1/4 + 1/6 is done over 12, not 24.
How are fractions compared?
By cross-multiplication: a/b < c/d exactly when a × d < c × b for positive denominators. 2/3 vs 3/4: 2 × 4 = 8 < 3 × 3 = 9, so 2/3 is smaller.