What is the Correct Way to Determine Percentages from Ratios?

[lorik]

Homework Statement

I desperately need to know something which I consider basic but yet I get different answers all the time

for example ratio A:G=1:3 or A:G=1:2 or A:G=1:4
some students are telling me that the ratios should be divided with one another like 1/3=0.33 to get the percebtage of A and the percentage of B ,while some other are implying this 1+3=4~ 1/4=0.25
I really have to know how to correctly give percentage to each symbol .BTW all the numbers start with A:B=1:X so number 1 is always present .Thank you

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

Since this is pretty much just an arithmetic problem, I have moved it to "PreCalculus".

Homework Statement

I desperately need to know something which I consider basic but yet I get different answers all the time

for example ratio A:G=1:3 or A:G=1:2 or A:G=1:4
some students are telling me that the ratios should be divided with one another like 1/3=0.33 to get the percebtage of A and the percentage of B ,while some other are implying this 1+3=4~ 1/4=0.25
I really have to know how to correctly give percentage to each symbol .BTW all the numbers start with A:B=1:X so number 1 is always present .Thank you

Homework Equations

The Attempt at a Solution

What you have written really makes no sense. You have several ratios, of "A" to "G" and then ask about "percentage of A" and "percentage of B". Did you mean ratios of "A" to "B" instead of "G". And A and B as a percentage of what? That seems to be your fundamental problem- you do not realize that it makes no sense to talk about a "percentage" without specifying a base. If, for example, you were to divide a line segment into two intervals, of length A and B, then it would make sense to ask what percentage of the whole interval each of A and B is. In that case the "base" is the whole interval which has length A+ B. If A:B= 1:X then the "whole" is X+1 so find the fractions A/(X+1) and B/(X+ 1) and convert to decimals and then to percenjtages. For example, in your first case, A:B= 1:3. X= 3 so X+ 1= 4. A/(X+ 1)= 1/4= 0.25= 25% and B/(X+ 1)= 3/4= 0.75= 75%.

That is my guess as to what you mean. It would also make sense to ask what percentage of B A is. In that case we would form the fraction A/B. If we are given A:B= 1:3, then A/B= 1/3= .3333... = 33+1/3%.

Those are completely different questions and have different answers. Whenever you talk a percentage, you must state the base or the question makes no sense.

 

[lorik]

Since this is pretty much just an arithmetic problem, I have moved it to "PreCalculus".


What you have written really makes no sense. You have several ratios, of "A" to "G" and then ask about "percentage of A" and "percentage of B". Did you mean ratios of "A" to "B" instead of "G". And A and B as a percentage of what? That seems to be your fundamental problem- you do not realize that it makes no sense to talk about a "percentage" without specifying a base. If, for example, you were to divide a line segment into two intervals, of length A and B, then it would make sense to ask what percentage of the whole interval each of A and B is. In that case the "base" is the whole interval which has length A+ B. If A:B= 1:X then the "whole" is X+1 so find the fractions A/(X+1) and B/(X+ 1) and convert to decimals and then to percenjtages. For example, in your first case, A:B= 1:3. X= 3 so X+ 1= 4. A/(X+ 1)= 1/4= 0.25= 25% and B/(X+ 1)= 3/4= 0.75= 75%.

That is my guess as to what you mean. It would also make sense to ask what percentage of B A is. In that case we would form the fraction A/B. If we are given A:B= 1:3, then A/B= 1/3= .3333... = 33+1/3%.

Those are completely different questions and have different answers. Whenever you talk a percentage, you must state the base or the question makes no sense.

Ok let me make it clear coz you seem to have made my question a rocket science . The question again; the report(or ratio) of clay and limestone is 1 : 3 ,find the percentage of clay and limestone ? ok ?

 

[Mark44]

Ok let me make it clear coz you seem to have made my question a rocket science . The question again; the report(or ratio) of clay and limestone is 1 : 3 ,find the percentage of clay and limestone ? ok ?

This is by no means rocket science. If there is 1 part clay to 3 parts limestone, then in total you have 4 parts. Clay makes up 1/4 of the whole, and limestone makes up 3/4 of the whole.

I am hopeful that you can convert 1/4 and 3/4 to percentages.