I wanted to find the answer to this as this was bugging me for some time.

so I think of ratios as success vs failure(or vice versa when adding 'dog') always just like everyone else does, but I remember a long time ago in some elementary books, they say to convert a fraction like 1/5 to ratio, simply make it 1:5 as in success vs total.

to me, this seems really stupid as there is practically 0 reason to express the same exact thing using 2 different symbols, and it's the exact reason many years ago I was confused when I first started poker I would express flush draws as 1:3(or 3:1 dog) instead of 1:2 until I realized in a poker book that I should be expressing it as success vs failure, not success vs total(attempts).

another example is gender ratio, 1:1 would be 50% is male and 50% is female or 1/2 as a fraction, but if someone wanted to convert this fraction 1/2 using the elementary way, the ratio is now 1:2 which obviously makes no sense and is actually 33.xx% to 66.xx% in terms of male to female using the proper gender ratio, not 50/50.

so why isn't success vs total simply written as a fraction? which idiot ever thought of this?

I've never seen this, and as far as I know it isn't true. Can you find any current reference that does this?

In my experience, success versus total is always written as either a fraction, a percentage, or a decimal.

That is, if I get 2 hits in my first four at bats, I am 2/4, 50%, or .500.

If I wanted to convert this to odds I compare my successes to my failues, in this case 2 of each, so 2:2 which reduces to 1:1.

Sherman

sure, let me do a simple internet engine search and I can find several sites that teach elementary math that do this:

http://www.mathleague.com/help/ratio/ratio.htm
http://www.mathgoodies.com/lessons/v..._percents.html
http://www.mathgoodies.com/lessons/v...g_percent.html
http://www.jimloy.com/arith/fractn.htm

if you have little siblings who are in elementary school, or have kids..etc. open their math text book and you will probably find the same unfortunately.

some idiocy.
that's how I always do it as well, but that isn't the point, the point is that elementary math teaches it wrong and I find it very idiotic that they do. the problem is that the elementary way they teach this is that they are expressing the same exact thing but with different symbols, when they should just be using a fraction and leaving colons for the REAL ratios, not pseudo fractionratio like they apparently teach in elementary math.

No. That is a specific kind of ratio called "odds".

This is perfectly valid mathematically. All fractions are ratios. Again, you are confusing a specific kind of ratio (odds) with ratios in general.

I didn't see any of your examples using the term "odds" so there is nothing being taught incorrectly there. The two terms odds and ratio are not interchangeable, and any confusion comes from attempting to do so.

good post, but a gender ratio should be referred to as gender "odds" using your explanation.

Not really, a ratio has to be defined as to what you are comparing. If you want a ratio of "men to women" that would be 1:1. If you want a ratio of "males to all people" that would be 1:2. If you want the fraction of males in all people, that would be 1/2.

Odds is primarily a gambling term, meaning how often will you get one outcome compared to the other outcome. So 2:1 means one outcome will happen twice as often as the other outcome. And usually you would follow the ratio with the words "against" or "underdog" to describe that the undesirable result is the largest number.

I agree that teaching kids that 1:2 is the same things as 1/2 is misleading and will cause them confusion later on. A fraction is just numbers. A ratio requires definition of what you are comparing, or context (like poker players) can provide a shared understanding without explicit definitions.

I've basically already said this, the problem is that people write ratios and never predefine them, but rather figure people will read them as the same way they are intending. Which for the most part is true of course, I just think the way they teach ratios in elementary math, they leave out the other ways it can be expressed which later on creates confusion, and that's what I have a problem with like how you concluded your post.

Then we agree.

I think this sort of problem (i.e. not defining a reference group) is larger than just elementary math books. For example, every day the weather person tells us that there is an X% chance of rain. I wonder to myself, "Percent of what?" It could be a number of things:

1) Percent of all the days like today?
2) Percent of the area?
3) Percentage of the next 24 hours?

I tend to interpret it as #1, but I don't think the answer is completely clear. As another example consider that some birth control pills are 99.9% effective. I ask, "99.9% of what?"

1) Percent of the women who use them?
2) Percent of the times one is inseminated?

The answer is not clear to me because no reference group is made. Just as in spadebidder's example, you can say the ratio of men to women is just under 1:1, or you can say the ratio of men to people is just under 1:2. But a reference group is necessary.

On a lighter note, the wife of a colleague of mine is an elementary ed teacher. She was trying to teach her students percentages recently when one student commented, "Mrs. XX, when are we ever going to have to use percentages in real life anyway?"

Sigh.

Sherman

LOL. Obviously I find this bit of news later today:

http://news.yahoo.com/s/livescience/...derstoodbymany

Your first link, as far as I can tell, does not confuse X:Y and X/Y

Your second link does not seem to talk about odds format (ratios) at all.

So I'm going to stop looking at the links now.

odds are typically expressed as: "the # of will nots":"wills"

As an example. There are 47 unseen cards. You have 10 outs. So the odds against hitting are 37:10. (read 37 to 10) (37 will nots:10 wills)

Using this same example, your probability of one of your outs coming in is 10/47, or .21 (21%). The probability is: wills/wills+will nots, or 10/10+37.

You can convert a probability back to odds againts as follows: Say you have a 25% chance of hitting your draw. 100% - 25%=75% of not hitting your draw. So, back to odds is 75:25.