Use a formula or algorithm for finding the greatest common factor. When in their simplest form, the numbers in a ratio have a GCF of 1. this is often easy to spot without formally checking; for instance, if any of the numbers are prime, then they are in their simplest ratio.
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That is the simplest form.
The ratio of 338 to 382 in its simplest form is 169 to 191
35 out of 100 as a ratio as a fraction in simplest form is 7/20.
The ratio 44 to 12 in simplest form is 11 to 3.
9/2 is in its simplest form