Cross Multiplication
The most intuitive and precise rule of three calculator. Instant calculation, step-by-step arithmetic breakdown, and interactive visual formulas.
Step-by-Step Resolution
1. Formula: D = (B × C) / A
2. Calculation: D = (30 × 25) / 15
3. Product: 750 / 15
4. Result: 50
Quick Real-World Presets
How to Find an Unknown Value?
Cross multiplication allows you to calculate the fourth proportional value from three known quantities using fraction equality and proportion equations.
The Extremes and Means Principle
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.
Fourth Proportional Formulas
Understanding Proportions and Ratios
Two proportional quantities maintain a constant equal ratio. The proportionality constant directly links these quantities together.
Direct Proportionality
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).
Proportionality Table
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.
Everyday Cross Multiplication Examples
Cross multiplication solves 5 common daily scenarios: recipe scaling, currency exchange, map scales, travel speed, and unit price comparisons.
Scaling a Culinary Recipe
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
Tous nos calculateurs
Chaque outil est optimisé pour un type de calcul précis. Choisissez celui qui correspond à votre besoin.
Percentage
Calculez un pourcentage, une valeur partielle ou un total par produit en croix.
1 Unknown
Résolvez une proportion à une inconnue — entrez 3 valeurs, trouvez la 4ᵉ.
2 Values
Complétez un tableau de proportionnalité et vérifiez le coefficient.
Fractions
Comparez, simplifiez ou trouvez le terme manquant de deux fractions.
Proportionality
Vérifiez si des grandeurs sont proportionnelles et calculez le coefficient.
Speed
Calculez la vitesse, la distance ou le temps avec conversion km/h ↔ m/s.
Dosage
Calculez un dosage médicamenteux, une dilution ou une concentration.
Recipe
Adaptez les quantités d'une recette pour plus ou moins de personnes.
Price
Comparez les prix unitaires et trouvez le meilleur rapport qualité-prix.
Scale
Convertissez les mesures d'un plan ou d'une carte en distances réelles.
Excel
Générez la formule Excel ou Google Sheets pour un produit en croix.
Frequently Asked Questions
Everything you need to know about cross multiplication, algebraic formulas, and proportion calculations.
What is cross multiplication in mathematics?
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.
How do you set up cross multiplication with four values?
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.
Can cross multiplication be used with decimal numbers?
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.
What is the difference between a proportion and a percentage?
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.
Does cross multiplication work with fractions?
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.
How do you check if two ratios are proportional?
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.
How do you find a missing quantity in a proportional situation?
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.
Is cross multiplication always suitable for solving proportions?
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).
How can you avoid errors in proportionality calculations?
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.