What is the mean and extremes of proportions?
The mean and extremes of proportions are terms usually used in the context of solving proportion problems. Let me explain how to find them.
In a proportion, you have two sets of numbers or quantities that are related to each other in a specific ratio. The proportion is written as a/b = c/d, where a, b, c, and d are the numbers or quantities involved.
- Mean: In a proportion, the mean is the product of the means from each ratio. Mathematically, it can be expressed as (a * d) / b = c. So, to find the mean, you multiply the first mean (a) by the second mean (d) and divide it by the first extreme (b). This gives you the third quantity (c).
- Extremes: In a proportion, the extremes are the first and last terms of the ratio. In the proportion a/b = c/d, the extremes are a and d.
To understand this concept better, let's consider an example:
Suppose you have the proportion 2/5 = x/10, and you need to find the mean and extremes.
1. To find the mean, you multiply the means (2 * 10) and divide by the first extreme (5).
(2 * 10) / 5 = 20 / 5 = 4. So, the mean is 4.
2. The extremes in this proportion are 2 and 10.
Therefore, in the proportion 2/5 = x/10, the mean is 4, and the extremes are 2 and 10.
Remember, when solving proportions, you can cross-multiply to find the mean or use the concept of means and extremes discussed above.