Proportion ماشین‌حساب

نحوه استفاده از این ماشین حساب

1. A را وارد کنید
2. B را وارد کنید
3. C را وارد کنید
4. D (leave blank to solve) را وارد کنید
5. روی دکمه محاسبه کلیک کنید
6. نتیجه نمایش داده شده در زیر ماشین حساب را بخوانید

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:

1. Set up the proportion: A/B = C/D
2. Cross-multiply: A × D = B × C
3. 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.

Frequently Asked Questions