Why does order matter in ratios?

Answer 1

The order of a ratio only matters as far as the "title" or "description" of the ratio.

A bottle of squash may say "dilute this in the ratio of 1:5 with water". This would formally be stated as "the ratio of squash to water is 1:5", ie for every 1 part of squash there is, there should be 5 parts of water.

Each part of the ratio refers to a specific part of the description: the first part of the ratio (in this case "1") refers to the first part of the description (in this case "squash") and the second part of the ratio ("5") refers to the second part of the description ("water").

If the ratio is reversed WITHOUT reversing the "titles", it becomes the ratio of squash to water is 5:1 meaning for every 5 parts squash there is only 1 part water - a very concentrated drink that will not be very nice to drink (nor very healthy for the teeth) - which is not the same.

However, reversing the "title" of the ratio as well as the ratio itself is perfectly acceptable as each part of the ratio still refers to the same thing: above would be come the ratio of water to squash is 5:1 meaning that for every 5 parts of water there is 1 part of squash - the "5" still refers to "water" and the "1" still refers to "squash".