High School Part to Whole comparison

[SHASHWAT PRATAP SING]

Since, percentages are fractions and fractions are a comparison of a part to whole. Then, how is this statement--> A is what percent more than B, a part to whole comparison ?
Also a part to whole comparison involves only one quantity (the whole) which is distributed into equal parts and we talk about some parts of that whole, but here in this statement--> A is what percent more than B, we have two quantities so how is this a part to whole comparison.

 

[phinds]

I think "A is what percent more than B" makes sense only when A is larger than B (unless you are OK with the answer being negative in which case, for example, 7.5 is -50% more than 5. I but I doubt that that is ever used in the real world).

ALSO, FYI, percentages are NOT fractions, they are real numbers including those that cannot be expressed as fractions. So, for example, it would be perfectly legitimate to say pi percent or e percent. In practical terms, of course, you have to round off at some point, but that is also true fractional values such as 1/3 = .3333333 ...

 

[FactChecker]

Since, percentages are fractions and fractions are a comparison of a part to whole. Then, how is this statement--> A is what percent more than B, a part to whole comparison ?
Also a part to whole comparison involves only one quantity (the whole) which is distributed into equal parts and we talk about some parts of that whole, but here in this statement--> A is what percent more than B, we have two quantities so how is this a part to whole comparison.

That would compare A-B with the whole of B. It does not have to be part of the whole. It can be more than the whole that it is being compared to.

 

[SHASHWAT PRATAP SING]

That would compare A-B with the whole of B. It does not have to be part of the whole. It can be more than the whole that it is being compared to.

I didn't understand properly, would you please elaborate and explain.

 

[FactChecker]

I didn't understand properly, would you please elaborate and explain.

When you say that A is greater than B, that is comparing some measure of A and B. It might be area or weight, or A and B might just be positive numbers. In any case, two numbers, $r_A, r_B$ associated with A and B, respectively, are being compared. It doesn't need to have anything to do with A being part of B or vise versa. The amount that A is larger than B is $r_A - r_B$. Then the question "A is what percent more than B" is answered by the calculation $100\frac {r_A-r_B}{r_B}$%. That is the correct answer whether A is greater than B or not.

 

[pbuk]

Since, percentages are fractions

In a certain sense, yes, but that's not a complete or a good definition of a percentage.

fractions are a comparison of a part to whole.

In a certain sense, yes, but that's not a complete or a good definition of a fraction.

Then, how is this statement--> A is what percent more than B, a part to whole comparison ?

In the same sense as an improper fraction is a part to whole comparison, but the classification of something as "a part to whole comparison" is not something that is useful and you should not waste your time and effort thinking about it.

If you start off with incomplete, not very good definitions and put them together then you shouldn't be surprised that the resulting statement is not satisfactory.

 

[Mark44]

I think "A is what percent more than B" makes sense only when A is larger than B (unless you are OK with the answer being negative in which case, for example, 7.5 is -50% more than 5. I but I doubt that that is ever used in the real world).

I think you got your numbers reversed, probably meaning that 5 is -50% "more" than 7.5. What is true is that 7.5 is +50% more than 5.

ALSO, FYI, percentages are NOT fractions, they are real numbers including those that cannot be expressed as fractions. So, for example, it would be perfectly legitimate to say pi percent or e percent.

In almost every scenario, a percentage is a fraction, as "per cent" literally means "per 100," where there is an implied denominator of 100. Pi percent would be $\frac \pi {100}$, which is certainly ungainly and something I've never seen before, but as you say, it would be legitimate.

 

[symbolipoint]

Would telling you that a ratio is the comparison of two numbers be helpful to you, @SHASHWAT PRATAP SING ?

 

[phinds]

I think you got your numbers reversed, probably meaning that 5 is -50% "more" than 7.5. What is true is that 7.5 is +50% more than 5.