Solve a/b = c/d for any missing value using cross multiplication. See step-by-step solution, cross products, scaling factor, equivalent ratios table, and ratio comparison bars.
A proportion is an equation stating that two ratios are equal: a/b = c/d. If you know three of the four values, you can solve for the missing one using cross multiplication — the principle that a × d = b × c. Proportions are one of the most practical tools in mathematics, appearing in everyday tasks like scaling recipes, converting units, reading maps, resizing images, and calculating discounts.
Cross multiplication transforms the proportion into a simple linear equation that can be solved in one step. For example, if 2/3 = x/12, then 2 × 12 = 3 × x, giving 24 = 3x, so x = 8. The same approach works no matter which of the four values is unknown.
This calculator handles all four cases (solve for a, b, c, or d), shows a detailed step-by-step solution, verifies the result by confirming the cross products are equal, and computes the scaling factor between the two ratios. The equivalent-ratios table extends your proportion through several multiples so you can see the pattern at a glance, and the comparison bars visualize how the four values relate to one another. Use the presets to practice classic proportion problems or enter your own values.
Proportion Calculator helps you solve proportion problems quickly while keeping each step transparent. Instead of redoing long algebra by hand, you can enter a (first numerator), b (first denominator), c (second numerator) once and immediately inspect Cross Product (a×d), Cross Product (b×c), Ratio a:b to validate your work.
This is useful for homework checks, classroom examples, and practical what-if analysis. You keep the conceptual understanding while reducing arithmetic mistakes in multi-step calculations.
a/b = c/d → a × d = b × c (cross multiplication). Solve for unknown by isolating it.
Result: Cross Product (a×d) shown by the calculator
Using the preset "1:2 = ?:6", the calculator evaluates the proportion setup, applies the selected algebra rules, and reports Cross Product (a×d) with supporting checks so you can verify each transformation.
This calculator takes a (first numerator), b (first denominator), c (second numerator), d (second denominator) and applies the relevant proportion relationships from your chosen method. It returns both final and intermediate values so you can audit the process instead of treating it as a black box.
Start with the primary output, then use Cross Product (a×d), Cross Product (b×c), Ratio a:b, Ratio c:d to confirm signs, magnitude, and internal consistency. If anything looks off, change one input and compare the updated outputs to isolate the issue quickly.
A strong workflow is manual solve first, calculator verify second. Repeating that loop improves speed and accuracy because you learn to spot common setup errors before they cost points on multi-step algebra problems.
Cross multiplication means multiplying the numerator of each fraction by the denominator of the other: a × d = b × c. This converts the proportion into a simple equation.
Yes. If 1 inch = 2.54 cm, then x inches / 10 cm can be set up as 1/2.54 = x/10 and solved via cross multiplication.
Division by zero is undefined, so the proportion has no solution. The calculator will display "undefined" in that case.
A ratio compares two quantities (a:b), while a proportion states that two ratios are equal (a:b = c:d). Use this as a practical reminder before finalizing the result.
The scaling factor is the number you multiply one side of the proportion by to get the other. For example, in 2/3 = 8/12, the factor is 4 (both numerator and denominator are multiplied by 4).
Yes. The math works the same way. Just be careful with signs: a negative scaling factor means one ratio is the "reverse" of the other.