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A proportion is an equation stating two ratios are equal: a/b = c/d. Cross-multiplication (a×d = b×c) lets you solve for any missing value. Proportions are used in scaling, cooking, maps, and unit conversion.
Công thức
a/b = c/d → a×d = b×c (cross multiplication) | Solve: d = (b×c)/a
- a,b,c,d
- Proportion Terms (values)
- k
- Scale Factor (ratio)
Hướng dẫn từng bước
- 1If a/b = c/d, then a×d = b×c (cross multiplication)
- 2Solve for d: d = (b×c)/a
- 3Verify: substitute back and check both sides are equal
- 4Scale factor = new value ÷ original value
Ví dụ có lời giải
đầu vào
Recipe for 4 people uses 3 cups flour. How much for 10 people?
Kết quả
3/4 = x/10 → x = 7.5 cups
đầu vào
Map: 2 cm = 50 km. Distance is 7 cm?
Kết quả
x = (7×50)/2 = 175 km
Câu hỏi thường gặp
What is the difference between a ratio and a proportion?
A ratio compares two quantities (3:4). A proportion states two ratios are equal (3:4 = 6:8). Proportions let you solve for missing values.
How do I check if proportions are equal?
Cross-multiply: a×d should equal b×c. If they're equal, the proportion is correct.
Can I use proportions for unit conversion?
Yes. Proportions are ideal for converting units. Set up the known ratio on one side and the unknown on the other, then solve.
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