# Standard Results/Definitions on Ratio/Proportion

1. Continued proportion

ab and c are said to be in continued proportion

if

So, b2 = ac. Here b is known as the mean proportion.

Similarly, if abc and d are in continued proportion, then we get:

2. Componendo

3. Dividendo

If
4. Componendo and Dividendo

If
5. Invertendo

If
6. Alterando

If
7.
In general, if

Then,  = (any combination of the numerator/any combination of the corresponding denominator)

For example, 1/2 = 3/6 = 4/8 =â€¦= (1 + 3 + 4)/ (2 + 6 + 8) = (3 + 4)/(6 + 8)
8. If we multiply the numerator and the denominator of a ratio by any number N (N â‰  0), then the ratio remains same.

A/B = NA/NB
9. If we divide the numerator and the denominator of a ratio by any number N (N â‰  0), then the ratio remains same.

A/B = (A/N)/(B/N)
10. If a/bc/de/f â€¦etc., are all unequal ratios, then the value of (a + c + e +â€¦)/(b + d + f +â€¦) lies in between the minimum and the maximum of all these ratios.