Division for ratios

  1. Why is division used for ratios? For example, if we have 1 dog for every 2 cats, then why can this relation be modeled by the division? Since the ratio can essentially have the value of 1/2 or 2, then what is the significance of these two distinct numbers in relation to the ratio? How does the value of the fraction 1/2, which is 0.50, relate to the ratio 1 dog to 2 cats? If we said we had a 0.50 ratio of dogs to cats, what does that mean?
     
  2. jcsd
  3. There are different reasons. First of all the ratio is a much easier number to understand, depending if it is greater or smaller than 1 (and how much grater/smaller it is) you can have an immediate idea of what's going on. If you are using small numbers (as in your example) it is clear that the ratio doesn't really add any information. However if the numbers you are dealing with are high it is much more complicated to evaluate the relationship between the two quantities just "by eye".

    Moreover, the ratio gives you the percentage. For example, as you said, if I know that the ratio dogs/cats is 0.37 then this means that the number of dogs is the 37% of the number of cats.
     
  4. Because it works.

    Because 1 dog for every 2 cats is the same as ## \frac12 ## a dog for every 1 cat.

    The significance of ## \frac12 ## is that we have ## \frac12 ## a dog for every 1 cat, and the siginficance of 2 is that we have 2 cats for every 1 dog.

    That we have 0.5 dogs for every cat (which is the same as 1 dog for every 2 cats, or 2 cats for every 1 dog etc...)
     
  5. phinds

    phinds 8,735
    Gold Member

    What would you prefer to use? Do you want everyone to spell it out in words every time?
     
  6. HallsofIvy

    HallsofIvy 40,504
    Staff Emeritus
    Science Advisor

    A "ratio" is defined as a fraction which is an implied division.
     
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