Advanced Math Concepts
Three-Part Ratios (A : B : C)
Three-part ratios describe proportional relationships across three interdependent components simultaneously.
How to Simplify a Three-Part Ratio
To reduce a three-part ratio (such as 18 : 24 : 30), you must find a common divisor that divides into all three terms without a remainder:
- Find GCD of first two numbers: GCD(18, 24) = 6.
- Find GCD of that result and the third number: GCD(6, 30) = 6.
- The overall 3-way GCD is 6.
- Divide every term by 6: 18 ÷ 6 = 3, 24 ÷ 6 = 4, and 30 ÷ 6 = 5.
- The simplified ratio is 3 : 4 : 5.
How to Divide a Total Amount into Three Parts
Suppose an inheritance of $60,000 is split among three siblings in the ratio 2 : 3 : 5:
- Sum the parts: 2 + 3 + 5 = 10 total parts.
- Calculate single part value: $60,000 ÷ 10 = $6,000 per part.
- Allocate shares:
- Sibling 1 (2 parts): 2 × $6,000 = $12,000 (20%)
- Sibling 2 (3 parts): 3 × $6,000 = $18,000 (30%)
- Sibling 3 (5 parts): 5 × $6,000 = $30,000 (50%)
- Check: $12,000 + $18,000 + $30,000 = $60,000.