Cross Multiplication Calculator
Solve proportions by cross multiplication.
Enter three values in a/b = c/d and find the unknown instantly with a step-by-step cross-multiplication solution.
Cross-multiplication is the standard algebraic technique for solving proportions — equations that set two ratios equal to each other. It’s one of the most versatile tools in applied mathematics.
The Proportion Setup:
a/b = c/d
Cross-Multiplication Rule:
a × d = b × c
To solve for any one unknown, isolate it:
- Solve for a: a = (b × c) / d
- Solve for b: b = (a × d) / c
- Solve for x in a/b = x/d: x = (a × d) / b
Worked Example 1 — Finding an unknown: If 3 apples cost $1.50, how much do 7 apples cost?
- Setup: 3/1.50 = 7/x
- Cross-multiply: 3x = 1.50 × 7 = 10.50
- x = 10.50 / 3 = $3.50
Worked Example 2 — Scaling a recipe: A recipe for 4 servings uses 2.5 cups of flour. How much for 10 servings?
- Setup: 4/2.5 = 10/x
- Cross-multiply: 4x = 2.5 × 10 = 25
- x = 25 / 4 = 6.25 cups
Worked Example 3 — Percentage problems: 35 is what percent of 140?
- Setup: 35/140 = x/100
- Cross-multiply: 140x = 3,500
- x = 25%
Real-World Applications: Unit conversions, map scaling, medication dosing, recipe scaling, currency exchange, grade weighting, and any time you need to maintain a ratio while changing one value. Cross-multiplication is the algebraic backbone of direct proportionality.