How do you divide quantities in a given ratio?

Answer 1

The first part of this answer is algebraic; see the example below for how it works out in practice.

Suppose you have a total quantity N that you want to divide in the ratio a:b:c.

Add a, b and c that is, a+b+c = s.

Calulate N/s, the value of each unit in the ratio.

then a*(N/s), b*(N/s) and c*(N/s) are the required amounts.

Example:

Divide 60 sweets in the ratio 2:3:5

N = 60

s = 2+3+5 = 10

therefore N/s = 60/10 = 6.

[Therefore, each 1 in the ratio is worth 6 sweets].

The required division of the sweets is 2*6, 3*6 and 5*6 = 12, 18 and 30.

This process can be extended to dividing quantities into ratios comprising four or more numbers in an analogous fashion.