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Do I have to submit an image at a ratio that exactly matches a print size currently offered by Prints?
Not exactly, there is a little bit of leeway given to you, however a few pixels from the edges will be cropped on the printed version.
Images without borders do not get very much leeway at all, since you should be adding the space to the edges to make it fit perfectly, and because cropping the edges of a bordered print may make the borders look uneven.