G:N = 4:3,  N:R = 5:3, G:N:R = ?

A principle of proportions is:

If both parts of a proportion are multiplied by the
same positive number, the proportion is unchanged.

N is in the middle of G:N:R.  N corresponds to 3 in the first
proportion, and to 5 in the second proportion.  We must get
these to the same number, using the above principle of
proportions.

The least common multiple of the two numbers corresponding to 
N, which are 3 and 5, is 15.

3 needs to be multiplied by 5 to become 15.
5 needs to be multiplied by 3 to become 15.

Therefore:

G:N = 4:3 = (4×5):(3×5) = 20:15

N:R = 5:3 = (5×3):(3×3) = 15:9

Now that N corresponds to the same number, 15,
in both proportions, we can put them together as

G:N:R = 20:15:9

Edwin