Question

12 out of 20 doctors agree 15 out of 30 doctors agree are the ratios equivalent

Answer 1

No.

You may see it without computations: if 12 out of 20 doctors agree, it means that a bit more than half of the doctors agree (half of the doctors would be 10 out of 20).

In the second case, exactly half of the doctors agree, since 15 if the half of 30.

So, in the first case you have than more than half the doctors agree, while in the second case exactly half of the doctors agree.

Anyway, you can obviously perform more rigorous computations as well, and you have different methods available:

You can transform both ratios to have the same denominator:

`(12)/(20) = (12* 3)/(20 * 3) = (36)/(60)`

`(15)/(30) = (15* 2)/(30 * 2) = (30)/(60)`

And obviously

`(36)/(60) \\eq (30)/(60)`

You can check the inequality by cross multiplying denominators:

`(12)/(20) \\eq (15)/(30) \to 12* 30 \\eq 15 * 20 \to 360 \\eq 300`

You can convert fractions to decimal numbers:

`(12)/(20) = 0.6 \\eq 0.5 = (15)/(30)`