Understanding Ratios
A ratio is a comparison of two or more quantities. Ratios can be written as A:B, A/B, or "A to B." They are used in cooking, maps, finance, and science.
To simplify A:B โ divide both by GCD(A,B)
12:8 โ GCD=4 โ 3:2
12:8 โ GCD=4 โ 3:2
Ratio Applications
- Cooking: Scale recipes up or down maintaining taste
- Maps: 1:1000 means 1 cm = 1000 cm in reality
- Finance: Debt-to-equity ratio, price-to-earnings ratio
- Mixing: Cement, paint, chemical solutions
Ratio Concepts and Notation
A ratio compares two quantities of the same kind. The ratio 3:2 can also be written as 3/2 or "3 to 2." Ratios can be simplified just like fractions by dividing both parts by their GCD.
| Ratio | Simplified | As Fraction | As Decimal |
|---|---|---|---|
| 6:4 | 3:2 | 3/2 | 1.5 |
| 15:10 | 3:2 | 3/2 | 1.5 |
| 100:25 | 4:1 | 4/1 | 4.0 |
| 8:12 | 2:3 | 2/3 | 0.667 |
| 50:50 | 1:1 | 1/1 | 1.0 |
Dividing a Quantity in a Given Ratio โ Method
Divide $150 in the ratio 3:2:
Total parts = 3+2 = 5
Value of one part = $150/5 = $30
First share = 3ร$30 = $90
Second share = 2ร$30 = $60
Check: $90 + $60 = $150 โ
Total parts = 3+2 = 5
Value of one part = $150/5 = $30
First share = 3ร$30 = $90
Second share = 2ร$30 = $60
Check: $90 + $60 = $150 โ
Scale Ratios in Maps and Models
Maps use scale ratios to represent real distances:
Map scale 1:50,000 means:
1 cm on map = 50,000 cm = 500 m in reality
If two cities are 8 cm apart on the map:
Real distance = 8 ร 500 m = 4,000 m = 4 km
1 cm on map = 50,000 cm = 500 m in reality
If two cities are 8 cm apart on the map:
Real distance = 8 ร 500 m = 4,000 m = 4 km
Real-World Applications
- Cooking: Recipe scaling โ maintain ratios when doubling or halving ingredients
- Finance: Debt-to-equity ratio, price-to-earnings (P/E) ratio, current ratio
- Maps & models: Scale models of buildings, engineering drawings
- Medicine: Drug dosage ratios (mg per kg of body weight)
- Chemistry: Mixing solutions and chemical compounds in correct proportions