Ratios are simply fractions.  I can hear the groans from here.  Everyone loved fractions in school, right?   This is one of those cases where simple is good, complicated is not good.  I will keep it as simple as possible and let you know where to get more information if you like. 

In photographic prints, the photographer selects a crop that best suits the composition of what they are shooting.  Usually, this is done after the photo has been uploaded to the computer.  When the file is taken directly from the camera, the ratio is 3:2.   

Often, the artist will use standard ratios.  I prefer to use these standard ratios because they make printing and displaying much easier. Let's start with the most common ratio, 8x10.  Most people have, at one time or another, seen, bought, or framed an 8x10 photo.   An 8x10 photo is 8 inches wide by 10 inches tall or vice versa.  A 4:5 ratio, meaning the most minuscule fraction ⅘ is the ratio, or you have multiplied the ratio by 2. When talking about 8x10, you can multiply by 2, and you get 16x20.  So if you see one of my photos that is an 8x10 and you want something larger, the next size you would have to look at would be a 16x20.  This is how the ratios work to help everyone work with the exact measurements.  Below are some standard sizes commonly used. 

What are Common Aspect Ratios and Print Sizes (in inches) 

1:1 ratio common print sizes: 6×6, 12×12 

1:2 ratio common print sizes: 6×12, 8×16 

3:2 ratio common print sizes: 2×3, 6×9, 12×18, 16×24, 20×30 

5:4 ratio common print sizes: 8×10, 16×20, 24×30 

6:5 ratio common print sizes: 10×12, 20×24 

7:5 ratio common print sizes: 5×7, 10×14, 20×28