Understanding Drawing Scale

Question

I'm a little confused about reading scales.

I do understand that if I see a scale of 1:30, that means that the object is 30 times smaller then in real world or 30:1 where the object is 30 time bigger then in real world.

1. My question is, why an object at a scale of 1:.5 is bigger than another object at a scale of 1:2?

2. How is this 1:.5 scale format usually read?

3. What makes :.5 bigger then :2?

Thanks

Answer 1

1. The ratio 1:.5 is equivalent to the ratio 2:1, i.e. the object is $2$ times bigger than in the real world, which is larger than your 1:2 object which is $2$ times smaller than in the real world.
2. 1:.5 is usually read "one to point five" or, if you wish to use the equivalent ratio of 2:1, as "two to one".
3. :.5 and :2 alone mean nothing, but if you mean a:.5 and a:2, for some positive $a$, then that's because a:.5 is equivalent to 2a:1. i.e multiplying a positive constant by $2$ gives something more than dividing that positive constant by $2$.

Indeed, we can think of a scale as some sort of simple division. After all, your "scale" is actually just a ratio where we can divide and multiply in the commonsense way (we can scale ratios very much like fractions, for example, the ratio a:b is exactly the same as the ratio 2a:2b).