Kalkulator Proporcji – Mnożenie Krzyżowe
Rozwiąż proporcje i mnożenie krzyżowe. Znajdź nieznaną wartość w A/B = C/D.
What is a Proportion?
A proportion states 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: A × D = B × C.
For example, if A=3, B=4, and C=9, then D = (B × C) / A = (4 × 9) / 3 = 12. This tool is useful for scaling recipes, calculating unit prices, and solving map distance problems.
Cross-Multiplication Method
The standard method to solve for a missing term in a proportion:
- Set up the proportion: A/B = C/D
- Cross-multiply: A × D = B × C
- Solve for the unknown: D = (B × C) / A
Cross-multiplication works because multiplying both sides of A/B = C/D by B×D gives A×D = B×C. This is valid as long as B and D are not zero.
Real-World Applications
- Cooking: Scale a recipe from 4 servings to 10: if 4 servings need 2 cups of flour, 10 servings need (2×10)/4 = 5 cups.
- Maps: If 1 cm = 50 km and the distance on the map is 3.5 cm, the real distance is 175 km.
- Finance: If 3 items cost $12, then 7 items cost (12×7)/3 = $28.
- Science: Solve for unknown concentrations, speeds, or measurements using proportional relationships.
Często Zadawane Pytania
What is cross-multiplication?
Cross-multiplication is a method to solve proportions. In A/B = C/D, you multiply diagonally: A×D = B×C. This lets you solve for any unknown term when the other three are known.
Can proportions have decimals or fractions?
Yes. Proportions work with any real numbers, including decimals and fractions. Wpisz decimal values directly into the Kalkulator. Fractions like 1/4 should be Wpiszed as 0.25.
What is a direct vs inverse proportion?
In a direct proportion (A/B = C/D), as one value increases, the other increases proportionally. In an inverse proportion (A×B = C×D), as one value increases, the other decreases. This Kalkulator handles direct proportions.