Is 30:12 and 40:16 the same ratio

It is not the same because t he ratio for 30 to 12 simplified is to 5 to 3. The ratio for 40 to 16 simplified is 5 to 2. Because 5 to 3 is not the same as 5 to 2, the ratios are not equivalent. You check this by multiplying 5 times 2 and 5 times 3. Once you do this, you will see that the products are not equivalent. Therefore, the ratios are not the same.

We pull the whole numbers from the fractions:

30:12=2 6/12=2 1/2

40:16=2 8/16=2 1/2

so yes they are equivalent