The most intuitive and precise rule of three calculator. Instant calculation, step by step arithmetic breakdown, and interactive visual formulas.
1. Formula: D = (B × C) / A
2. Calculation: D = (30 × 25) / 15
3. Product: 750 / 15
4. Result: 50
Cross multiplication allows you to calculate the fourth proportional value from three known quantities using fraction equality and proportion equations.
In any proportion A / B = C / D, the product of the extremes (A × D) is always equal to the product of the means (B × C). This equality of fractions forms the mathematical foundation of cross multiplication.
To find the missing value (unknown variable), multiply the two diagonally opposing known values and divide by the third remaining value.
Two proportional quantities maintain a constant equal ratio. The proportionality constant directly links these quantities together.
Two quantities are directly proportional when the ratio between every corresponding pair of values remains constant. This constant is called the proportionality coefficient.
For example, grocery pricing per kilogram: 2 kg cost $6, 4 kg cost $12. The proportionality coefficient is 3 ($/kg).
A proportionality table lists proportional quantities across columns, where every column yields the exact same ratio.
| Quantity (kg) | 2 | 4 | 6 | 10 |
|---|---|---|---|---|
| Price ($) | 6 | 12 | 18 | 30 |
| Ratio | 3,0 | 3,0 | 3,0 | 3,0 |
The ratio remains constant: these are directly proportional quantities.
Cross multiplication solves 5 common daily scenarios: recipe scaling, currency exchange, map scales, travel speed, and unit price comparisons.
A recipe tailored for 4 people requires 250 g of flour. How much flour is needed for 7 people?
Proportion: 4 people → 250 g
Goal: 7 people → ? g
Cross Multiplication Solution
4 / 250 = 7 / x
x = (250 × 7) / 4
x = 1750 / 4
x = 437.5 g of flour
Everything you need to know about cross multiplication, algebraic formulas, and proportion calculations.
Cross multiplication is an arithmetic technique used to determine an unknown fourth value from three known proportional values. It relies on the equality of diagonal cross products: A × D = B × C.
Place the proportional quantities into a 2×2 table under the equation A / B = C / D. Multiply the two known diagonal values (extremes and means), then divide by the third known value to isolate the unknown.
Yes, cross multiplication works with decimal numbers exactly as with integers. Set up the proportion, cross multiply diagonals, and divide by the remaining value. Example: 2.5 / 7.5 = 4 / x → x = (7.5 × 4) / 2.5 = 12.
A proportion expresses the equality between two ratios (A / B = C / D). A percentage is a specific proportion where the second denominator is 100: P = (value × 100) / total.
Yes, cross multiplication applies directly to fractions. For a/b = c/d, the cross products a × d = b × c allow you to verify fraction equivalence or solve for missing numerators and denominators.
Two ratios A / B and C / D are proportional when their cross product forms a strict equality: A × D = B × C. If the diagonal products are equal, the ratios are proportional.
Set up the proportion equation with the three known numbers and the variable x. Multiply the two known diagonal values, then divide by the third number: x = (B × C) / A.
Cross multiplication is designed for direct proportionality. It does not apply to inverse proportionality (where the product of values, rather than their ratio, is constant).
1) Confirm that quantities are directly proportional, 2) keep units aligned consistently in the grid, 3) multiply diagonals before dividing, and 4) verify that the resulting ratio matches the initial ratio.
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