Examples of Continued Proportion
Example 1: Find the third proportional to 8 and 16.
Solution:
Let the third proportion be x
8:16 = 16:x
This implies:
8/16 = 16/x
Cross-multiplying gives:
8x = 162
8x = 256
Solving for x:
x = 256/8 = 32
Thus, the third proportion to 8 and 16 is 32.
Example 2: Finding the Mean Proportional of 5 and 20.
Solution:
Let the mean proportional be y
5:y = y:20
This implies:
5/y = y/20
Cross-multiplying gives:
y2 = 5 × 20
y2 = 100
Solving for y
y = √100 = 10
Thus, the mean proportion between 5 and 20 is 10.
Example 3: Find the mean proportional between 4 and 9.
Solution:
Let the mean proportional be x
4:x = x:9
x2 = 4⋅9
x2 = 36
x = 6
Example 4: Determine the third proportional to 12 and 30.
Solution:
Let the third proportion be x
12:30 = 30:x
12x = 302
12x = 900
x = 75
Continued Proportion
Continued proportion is a mathematical area meaning a sequence of numbers such that the ratio of the first to the second is equivalent to the ratio of the second to the third. This principle extends the idea of simple proportions, allowing for deeper analysis in various mathematical contexts. It plays a vital role in solving complex ratio problems and is applied in fields such as geometry, algebra, and finance.
Understanding continued proportion is essential for students to grasp advanced mathematical relationships and their practical applications.
Table of Content
- What is Continued Proportion?
- Mathematical Representation
- Properties of Continued Proportion
- Theorems and Proofs
- Problem-Solving Techniques
- Real-Life Applications of Continued Proportions
- Difference between Continued Proportion and Simple Proportion