Find the Ratio: 0.0625 : 0.09375

Date: 05/15/2003 at 15:31:38
From: Faisal
Subject: Ratio

I am in grade 6 and am having problems with ratio. Please help me 
find the ratio between 0.0625:0.09375 and please tell me how to do it.

Thank you, Dr. Maths,
Faisal

Date: 05/15/2003 at 17:22:25
From: Doctor Ian
Subject: Re: Ratio

Hi Faisal,

There are a few different ways you might approach this.  One is to
divide the larger number by the smaller one.  For example, if you
have a ratio of 

  12:138

doing the division
        
         1 1.5
      ________
  12 ) 1 3 8.0
       1 1
       ---
        1 8
        1 2   
        ---
         6 0
         6 0
         ---
           0

shows us that this is the same as the ratio 1:11.5.  What do you get
when you try this with your numbers? 

A second thing we can do is scale the values in the ratio by the same
amount until they don't look quite as intimidating. For example, a
ratio of 2:5 is the same as a ratio of 20:50 or a ratio of 200:500. 
(Do you see why?)  

So we can keep multiplying both terms by 10 until we get rid of the
decimal point:

       0.0625  :    0.09375
       0.625        0.9375
       6.25         9.375
      62.5         93.75
     625          937.5
    6250         9375            <-- Same ratio, different values

This looks easier to reduce, doesn't it?  We can look for common
factors, and eliminate them, e.g., 

    6250 : 9375

  = 1250 * 5 : 1875 * 5          

  = 1250 : 1875

Where before we scaled _up_ by a factor of 10, now we're scaling
_down_ by a factor of 5.  But it's the same idea. 

Can you find other factors that these values have in common, and
eliminate them? 

A third thing you can do is look for patterns that might work out
nicely.  In this case, I happen to know that 1/8 is 0.125, which means
that 5/8 is 0.625, so that means that 0.0625 is 1/10 of that, or 5/80.
So what if I multiply both items by 80? 

    0.0625 : 0.09375
   *    80        80
    ------   -------
         5       7.5

That's a lot easier to deal with, isn't it?  This third approach
requires you to be pretty comfortable with fraction/decimal 
conversions, so don't feel that this is something that should have
jumped out at you. Mostly I was just trying to give you a sense of
some of the different ways that you can tackle ratio problems.

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/