Given:
The ratio of two numbers is 5:2.
To Find:
What are the other ratios which are equivalent to the above ratio?
Solution:
The given problem can be solved using the concepts of ratio and proportions.
1. It is given that the ratio of two numbers is 5:2.
2. Consider two numbers a and b such that the simplest ratio between the two numbers is a:b.
=> Ratio of the numbers a and b = a:b,
=> According to the properties of ratios the operation a:b can also be written as a/b.
=> a/b can also be written as.
=> a/b can also be written as.
=> Similarly a/b can be conclusively written as. (Where n is not equal to 0).
3. The ratio of two numbers will always remain the same even if the numerator and the denominator are multiplied with the same factor. In such cases, the ratio always remains the same.
4. 5:2 = 5/2 can also be written as,
=> ... , . (Where n is not equal to zero).
Therefore the ratios 10:4, 15:6, 20:8, 25:10,.., 5n:2n are equal to the ratio 5:2.