ratio of A/B

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Ryan$

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Hi guys, If I have the amount which it's the ration of A/B , what does it mean? I mean is it the answer of "how many time A bigger than B for instance?"
what's confusing me is , what we call the amount of the ration itself? it's not just an amount, because it's an answer of A/B so we should call it something else .. what math call that amount? thanks alot ...!
I'm talking implicitly what should we call the result of the ration between two things?!
 
The ratio (yes, my fingers always type "ration" before I can stop them too!) of A to B tells what we would need to multiply B by to get A. If A/B= r then A= Br. If A/B= 3, then A is three times as large as B. If A/B= 1/3 then A is only 1/3 as large as B (and B is three times as large as A). I am not sure what you mean by "what should we call the result of the ratio between two things?" "Ratio" is a perfectly good word! That's what I would call it.
 
Ryan

A ratio is, as you say, a way to describe relative measure. It is somtimes shown like this

[MATH]A\ :\ B\ ::\ 2\ :\ 3[/MATH], meaning that

3 measures of A equal 2 measures of B. In other words, the idea comes from measuring or counting things and comparing them to one another, and is mentally related to the physical world. So far, so good.

Sticking with our example, we see that we could have described the same relative measures as

[MATH]\text {Measure of A} = \dfrac{2}{3} \text { Measure of B.}[/MATH]
Why is that true? Because if add up 3 measures of A we get 3 * (2 / 3) measures of B, which is 2 measures of B.

So we can also treat a relative measure as a fraction, which is indeed the more common way to do so nowadays. We call such fractions "ratios" or "proportions."

But math deals with an ideal world set free from the specifics of the real world. And in the vocabulary of that world of ideas, "ratio," "proportion," and "fraction" are synonyms, and a fraction is simply a number. So a ratio is simply another word for a number expressed in fractional form in pure math. In applications, a ratio describes relative measure.
 
but guys ! I'm totally with you !!!
I have a problem with understanding the meaning or the implicitly meaning of division, I mean once "they" say or tell me that how many times you need to do something over other something ? which implicitly means I want the ratio , but it's implicitly and not exactly ... here's my problem!!
 
Ryan$ said:
but guys ! I'm totally with you !!!
I have a problem with understanding the meaning or the implicitly meaning of division, I mean once "they" say or tell me that how many times you need to do something over other something ? which implicitly means I want the ratio , but it's implicitly and not exactly ... here's my problem!!
Click to expand...
I do not understand what any of that means. "Exact" and "implicit" do not have opposite meanings.

But here is how to understand division

[MATH]c \ne 0 \text { and } a = b \div c \equiv \dfrac{b}{c} \iff c \ne 0 \text { and } b = a * c.[/MATH]
That is what division means in the ideal world of math. We apply division as an operation in the real world when that relationship applies.
 
thank you very much for your cooperation !

but if so, then when I apply division? in which cases? I mean if I've a problem, how to know if it's demand to apply division or not?!
in the problem will not give me an explicitly expression to tell me to use division, so I need to know by myself ..
 
Whenever a problem can be reduced to:

[MATH]ax = b \ne 0[/MATH], you divide both sides of the equation by a to find x.
 
Ryan$ said:
thank you very much for your cooperation ! but if so, then when I apply division? in which cases? I mean if I've a problem, how to know if it's demand to apply division or not?! in the problem will not give me an explicitly expression to tell me to use division, so I need to know by myself ..
Click to expand...
Do you have a clear understanding of usage of addition (i.e. when do you apply addition)?

Do you have a clear understanding of usage of subtraction (i.e. when do you apply subtraction )?

Do you have a clear understanding of usage of multiplication (i.e. when do you apply multiplication)?
 
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