If a, b, p, q are integers, then a part-to-part ratio would be a/b:p/q. For example, ⅗:⅔.
A whole-to-whole ratio could be m:n (m and n are integers; aq:bp from the above example). Taking the above example this ratio would be 9:10 (that is, 3×3:2×5).
The same ratio can also be expressed as 9/10:1 (part-to-whole) by changing one of the ratio parts to 1, and adjusting the other part--dividing both parts by 10.
Another example of part-to-whole could be ⅔:5 which is the same as 2:15.