Oran Hesaplayıcı – Çapraz Çarpma
Oranları ve çapraz çarpma problemlerini çözün. A/B = C/D'deki bilinmeyeni bulun.
Ne is a Orantı?
A proportion states that two ratios are equal: A/B = C/D. If you know three of the four değerler, you can solve for the missing one using cross-multiplication: A × D = B × C.
For örnek, 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 fiyatlar, and solving map mesafe problems.
Cross-Multiplication Method
The standard method to solve for a missing term in a orantı:
- Set up the orantı: A/B = C/D
- Cross-multiply: A × D = B × C
- Solve for the unknown: D = (B × C) / A
Cross-multiplication works çünkü 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 bardak of flour, 10 servings need (2×10)/4 = 5 bardak.
- Maps: If 1 cm = 50 km and the mesafe on the map is 3.5 cm, the real mesafe is 175 km.
- Finance: If 3 items maliyet $12, then 7 items maliyet (12×7)/3 = $28.
- Science: Solve for unknown concentrations, speeds, or measurements using proportional relationships.
Sık Sorulan Sorular
Ne 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 Ne zaman the other three are known.
Can proportions have decimals or fractions?
Yes. Proportions work with any real sayılar, dahil decimals and fractions. Enter ondalık değerler directly into the hesaplayıcı. Fractions like 1/4 should be entered as 0.25.
Ne is a direct vs inverse orantı?
In a direct orantı (A/B = C/D), as one değer increases, the other increases proportionally. In an inverse orantı (A×B = C×D), as one değer increases, the other decreases. Bu hesaplayıcı handles direct proportions.