Math Is Fun Forum

Why did you use square root?

if you have a calculator then enter .9176 press y^x key and then press 2.2

I have to always divide the smallest number of a larger ratio into the bigger number ? If so I'm always going to get a decimal.

Firstly it does not really matter if you get a decimal and second you do not necessarily have to be concerned about whether the
number/ratio you are trying to transform is smaller or larger.

On the other hand whole numbers are nice to work with and it may be easier to try to get a result which only has whole numbered
components. In this case you are scaling the thing down as I understand it so there is perhaps a greater chance of ending up with
a number which requires digits after the decimal point. (It is a fact of life that numbers requiring a decimal point are more common.)

Here is an example of a ratio conversion that converts a higher set of numbers to a lower set with whole numbers only:

3 : 6 : 9   is the same as  1 : 2 : 3  (here I have divided each element of the ratio by 3 I could have multiplied by one third)

(obviously that example does not have the same ratio as your problem)

If the second ratio contained only two elements and I wanted to find the third then it can only be done if the two I have given are
in the correct ratio. If I chose 4 : 7 : ? then that would not be possible for 3 : 6 : 9 however if I change the 7 to an 8 then we get
4 : 8 : 12

In your example in the earlier post the problem is that the two numbers you gave for the new ratio are already incorrect relative
to each other. In other words one must be changed. Either the original measurements are wrong or the two numbers in the
second ratio are not in the right ratio relative to each other. The fact that the second number is larger than the first, but the other
way round in the other ratio immediately alerts a mathematician to an inconsistent proportion.

If I have the ratio 3 : 6 : 9 and I want a model to be 1 : 7 : ???  then the first number has to go from 3 to 1, but the second has
to go from 6 to 7, with the same multiplication. Well this is not going to work because 3 multiplied by a third equals 1
but if I do the same multiplication to the second number 6 get transformed to 2. One cannot go up and the other down.
In fact the two numbers that we give for the second ratio have to be in the correct ratio of the first two numbers of the first ratio.
It would probably by a good idea to look at Bob's post including the image file he posted (if you haven't already done so).
Trying to explain this using plain text only is not easy and could cause confusion.

Anyway I hope that has cleared the matter up rather than muddied the waters even further.