비례식 계산기 – 교차 곱 풀기
비례식과 교차 곱을 계산합니다. A/B = C/D에서 미지수를 구하세요.
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.
교차 곱셈 방법
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.
자주 묻는 질문
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.
비율이 소수나 분수를 가질 수 있나?
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.
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 calculator handles direct proportions.