I was just wondering if anyone would be able to confirm a few quick questions I have in relation to making statements about ratios / rates.
My understanding is that a ratio is a comparison of 2 or more quantities by division. It is also to my understanding that a true ratio compares the quantities of two variables/terms that share the same unit such that the ratio is dimensionless. For example when comparing the height of an individual to the length of their left leg where both measurements are taken in cm.
It is also my understanding that if the quantities of two variables are being compared do not share the same unit then the ratio is referred to as a rate. For example comparing the quantity miles traveled in a car to the distance travels in hours.
Therefore, for a rate, for example 35miles per hour. Would of be incorrect to say that the ratio of miles to hours is 35:1? Since ratios only compare quantities between variables sharing the same unit? Another example would be say the rate of centimetres to meters which is 100cm per meter, would it be incorrect to say that the ratio of centimetres to meters is 100 to 1?
It seems like a bit of a contradiction to say that a ratio is a comparison of quantities between variables with shared units when a rate is just a ratio of variables who don’t share units? I wondered if anyone could clear this up.