Solve for X Fraction Calculator: Proportions and Steps

Solve for X Fraction Calculator

Put x in any one box, enter the other three values, and get an exact fraction, decimal, mixed number and checked steps.

Enter a proportion

Use exactly one x. The other boxes accept integers, decimals, fractions such as 3/8, or mixed numbers such as 1 1/2.

Solution—
—Exact reduced fraction
—Mixed number
—Decimal

Show the steps
    Advanced: solve fractions containing x

    Use coefficients for (ax + b)/(cx + d) = (ex + f)/(gx + h). This can produce a linear or quadratic equation.

    (x + 1)/3 = (2x − 5)/4
    Valid solution set—

    Show the algebra

      How to solve a fraction for x

      For a proportion a/b = c/d, cross multiplication gives a × d = b × c. Isolate x by dividing both sides by its remaining coefficient. The calculator keeps rational inputs exact, reduces the result with the greatest common divisor, and then substitutes the answer back into the original proportion.

      Examples checked by the calculator

      EquationCross productSolution
      3/4 = x/203 × 20 = 4xx = 15
      x/7 = 12/2121x = 84x = 4
      5/x = 15/24120 = 15xx = 8
      (x + 1)/3 = (2x − 5)/44(x + 1) = 3(2x − 5)x = 19/2 = 9.5

      Why this solver is different

      • x may appear in any of the four positions of a simple proportion.
      • Integers, decimals, ordinary fractions and mixed numbers remain exact instead of being rounded before solving.
      • The advanced solver handles x in both numerators or denominators, detects quadratic results, and removes values that make an original denominator zero.
      • Identity equations, contradictions and invalid zero denominators are reported explicitly rather than returning a misleading number.

      Limits

      The main solver requires exactly one x. In advanced mode, each numerator and denominator must be linear in x; cross multiplication may therefore create an equation up to degree two. Decimal results are rounded for display, while the main proportion result is retained as an exact fraction.

      Related tools: use the Fraction Calculator for fraction arithmetic, the Partial Fraction Calculator for decomposition, or the System of Equations Calculator for multiple variables.