Generally expresses a “part to part” relationship, though a ratio can be disguised within a “part to whole” relationship.
Part to part: Given that there are 3 oranges for every 2 apples in a basket, the ratio of oranges to apples is 3 parts to 2 parts, or 3:2, or (3/2). The “whole” is 3+2 = 5; there are 5 pieces of fruit in each “group” of 3 oranges and 2 apples.
“Disguised” part to part relationship might be presented as: Given only apples and oranges in a basket, 3 out of every 5 pieces of fruit are oranges. Because the fruit must be either apples or oranges, there must be 3 oranges for every 2 apples in order to arrive at the “whole” 5 pieces of fruit. Thus, the ratio of oranges to apples is 3 parts to 2 parts, or 3:2 or (3/2).M
The constant number by which a ratio is multiplied in order to determine the actual number of items present. Given a ratio of 3 oranges to 2 apples and an actual total of 15 oranges in the basket, the unknown multiplier is (15 oranges / 3 oranges) = 5. Because the unknown multiplier is always constant within a ratio, it can be used to calculate any other actual numbers in that ratio. In this case, we multiply the 2 apples in the ratio by 5 to arrive at an actual total of 10 apples in the basket.
Generally, a ratio presented in the form of an equation. Given a ratio of 3 oranges to 2 apples, and an actual total of 15 oranges, a proportion would read: (3 oranges / 2 apples) = (15 oranges / ? apples).
The ratio and the actual numbers are in proportion; the actual numbers always simplify to the ratio.