Proportion Calculator
Solve proportions and find missing values in ratios: a/b = c/d
Enter Proportion
a/b = c/d
Solution
Missing Value (d)
12.0000
3/4 = 9/12.00
First Ratio (a:b)
3:4 = 0.7500
Second Ratio (c:d)
9:12.00 = 0.7500
Calculation
d = (b × c) ÷ a
d = (4 × 9) ÷ 3
d = 12.0000
Cross Multiplication
a × d = b × c
3 × 12.00 = 4 × 9
36.00 = 36.00 ✓
Understanding Proportions
A proportion is an equation stating that two ratios are equal: a/b = c/d. This means a:b has the same relationship as c:d.
Solving Proportions
To find a missing value, use cross multiplication:
- a × d = b × c (cross products are equal)
- To solve for d: d = (b × c) ÷ a
- To solve for c: c = (a × d) ÷ b
- To solve for b: b = (a × d) ÷ c
- To solve for a: a = (b × c) ÷ d
Real-World Applications
- Recipe Scaling: 3 cups flour : 4 cups water = 9 cups flour : ? cups water
- Map Scale: 1 inch : 50 miles = 3 inches : ? miles
- Currency Exchange: $1 : €0.85 = $100 : ? euros
- Unit Conversion: 2.54 cm : 1 inch = ? cm : 5 inches
Example
If 3 pencils cost $4, how much do 9 pencils cost?
- 3/4 = 9/d
- d = (4 × 9) ÷ 3 = 12
- Answer: $12 for 9 pencils