Add, multiply, or reduce fractions

Denominators must be nonzero. Addition and subtraction use ad + bc over bd (or the minus variant). Multiplication is ac/bd. Division is a/b ÷ c/d = ad/bc, so the second fraction cannot be zero. Simplify ignores the second fraction and divides numerator and denominator by their GCF. Signs follow ordinary integer arithmetic.

a/b + c/d = (ad + bc) / (bd), then reduce by the GCF

a/b × c/d = (ac) / (bd)    and    (a/b) ÷ (c/d) = (ad) / (bc)

Inputs are integers, not mixed numbers (enter 3/2, not 1 1/2). Reduction uses the same Euclidean GCF as the GCF calculator. Mixed-number display is not produced; an improper fraction such as 7/3 is left as 7/3. Decimal output is extra context, not a replacement for the exact fraction.

Numerator of the first fraction

Top of the first fraction. May be negative.

Denominator of the first fraction

Bottom of the first fraction. Zero is rejected.

Operation

Simplify uses only the first fraction. Other operations need both.

Numerator of the second fraction

Top of the second fraction. Unused for simplify.

Denominator of the second fraction

Bottom of the second fraction. Unused for simplify. Cannot be 0 when used.

Assumptions

• Integer numerators and denominators.
• The displayed fraction is reduced by a positive GCF.

Limits

• No mixed-number input or output.
• Very large integers hit JavaScript integer precision.
• Does not solve equations; it only evaluates one operation.

5/6 is exact. The decimal is a convenience. If you need a ratio in A : B form, the ratio page starts from two integers and also reports mix shares.

• Adding numerators and denominators (1/2 + 1/3 = 2/5).

  Add with a common denominator: 3/6 + 2/6 = 5/6.

• Leaving 18/24 unreduced and calling it a different answer from 3/4.

  They are the same rational. This tool always reduces.

• RatioTwo integers in, a reduced ratio out (8 : 12 becomes 2 : 3), plus the quotient A/B and each term’s weight in the sum of absolute values — not “A as a percent of B.”
• GCF (GCD)Enter at least two integers. The result is the largest positive integer that divides all of them — the same GCF used to reduce a fraction or a ratio.
• AveragePaste numbers; the tool sums, counts, and divides. Every observation has weight 1. Min, max, and count sit beside the mean.
• ExponentEvaluate aᵇ. Integers, decimals, negative exponents (reciprocals), and 1/2 (square root, base ≥ 0) are possible, within the reals and floating-point limits.
• LCMEnter at least two nonzero integers. The result is the smallest positive integer that is a multiple of each — useful for common denominators and repeating schedules.
• Square rootEnter a number that is not negative. The tool returns the principal (nonnegative) square root. It is the inverse of squaring, not a cube root or an nth root.

Written by Rédaction HexaCalc (editorial team). Content last updated: August 25, 2026. No third-party medical or financial review is claimed.

This calculation uses a standard mathematical identity. See also the methodology.