比例計算機 – 外項の積計算
比例と外項の積を解きます。A/B = C/Dの未知の値を求めます。
とは 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 応用
- 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.
よくある質問
とは 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. Enter decimal values directly into the calculator. Fractions like 1/4 should be entered as 0.25.
とは 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 calculator handles direct proportions.