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.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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