How can I explain that 17:14 and 64:60 aren't equivalent

The 2 ratios are almost equivalent, but not quite. In order to tell if they are equivalent, there are a number of ways but the 2 most common are 1, finding the decimal equivalent of the fraction, and 2, finding the scale factor.

1: Take 16, divide by 14. You should get something around 1.142. Take 64, divide by 60. You should get something around 1.066666 ... Not equivalent.

2: Find the scale factor between the 2. To find scale factor, divide the larger numerator and larger denominator by the smaller numerator and smaller numerator. 64/16, 60/14. Not equal.

Put 64/60 into simplest form. 32/30=16/15. 16/15 n 17/14 are not equivalent