What is Proportion?
A proportion states that two ratios are equal: A/B = C/D. To find the missing value, use cross-multiplication.
A/B = C/D
Cross multiply: A Ć D = B Ć C
If D is unknown: D = (B Ć C) / A
Cross multiply: A Ć D = B Ć C
If D is unknown: D = (B Ć C) / A
Real-World Examples
- Cooking: If 2 cups make 4 servings, how many cups for 10 servings?
- Maps: If 1 inch = 50 miles, 3 inches = how many miles?
- Pricing: If 5 apples cost $3, how much do 8 apples cost?
Types of Proportion
| Type | Description | Formula | Example |
|---|---|---|---|
| Direct proportion | As A increases, B increases proportionally | A = kB | Speed and distance (same time) |
| Inverse proportion | As A increases, B decreases | A Ć B = constant | Speed and time (same distance) |
Cross-Multiplication Method
Solve: 3/4 = x/20
Cross multiply: 3 Ć 20 = 4 Ć x
60 = 4x
x = 60/4 = 15
Verification: 3/4 = 15/20 = 0.75 ā
Cross multiply: 3 Ć 20 = 4 Ć x
60 = 4x
x = 60/4 = 15
Verification: 3/4 = 15/20 = 0.75 ā
Worked Real-World Examples
Recipe Scaling
Recipe for 4 people needs 2 cups flour.
How much for 10 people?
4/2 = 10/x ā 4x = 20 ā x = 5 cups
How much for 10 people?
4/2 = 10/x ā 4x = 20 ā x = 5 cups
Map Distance
Scale 1:25,000. On map, distance = 4 cm.
Real distance? 1/25000 = 4/x ā x = 100,000 cm = 1 km
Real distance? 1/25000 = 4/x ā x = 100,000 cm = 1 km
Currency Exchange
$1 = ā¬0.92. How much is $350?
1/0.92 = 350/x ā x = 350 Ć 0.92 = ā¬322
1/0.92 = 350/x ā x = 350 Ć 0.92 = ā¬322
Real-World Applications
- Cooking: Scale recipes up or down while maintaining flavor ratios
- Maps & models: Convert map distances to real distances
- Finance: Currency conversion, tax calculation, investment allocation
- Medicine: Drug dosage by body weight (mg per kg)
- Construction: Concrete mixing ratios, paint colour mixing