help!

[lillybeth]

Can someone show me how to find the percent of change? I used to know but I forgot. Please help! thanks!

 

[lillybeth]

Sorry, i forgot to tell you where i was stuck. ill bet u guys $100000 S. Kahn already figured that out.
I know how to turn a problem into a fraction, but not what to do after that. please help. thanks!

 

[JeffM]

Can someone show me how to find the percent of change? I used to know but I forgot. Please help! thanks!

Percent of change always implies a non-zero reference value, frequently called a base. It is the number from which you measure the change in the number of interest.

\(\displaystyle Let\ r = the\ reference\ value.\)

\(\displaystyle Let\ n = the\ number\ of\ interest.\)

\(\displaystyle Let\ p = the\ percent\ change.\)

\(\displaystyle p \equiv 100 * \dfrac{n - r}{r} \equiv \left(\dfrac{100n}{r}\right) - 100.\)

I like the second form because then you will never get the sign of the change wrong.

Edit: Percent change is a measure of relative change. It is meaningful only if the base or reference value is meaningful in context.

 

[lillybeth]

Percent of change always implies a non-zero reference value, frequently called a base. It is the number from which you measure the change in the number of interest.

\(\displaystyle Let\ r = the\ reference\ value.\)

\(\displaystyle Let\ n = the\ number\ of\ interest.\)

\(\displaystyle Let\ p = the\ percent\ change.\)

\(\displaystyle p \equiv 100 * \dfrac{n - r}{r} \equiv \left(\dfrac{100n}{r}\right) - 100.\)

I like the second form because then you will never get the sign of the change wrong.

Edit: Percent change is a measure of relative change. It is meaningful only if the base or reference value is meaningful in context.

Thanks, but I don't get it. Kind of confusing. Do you want me to give you the problem im working on so we can fill in the letters? Assuming you say yes:
If 40 is increased to 56, what is the percent of change?
a. 80%
b. 29%
c. 40%
d. 71%


So, i'm pretty sure that i subtract 40 from 56 which is 16. Then i make into a fraction. 16/40. Can you tell me what to do next, and/or point out to me if i already did something wrong? Thanks!

 

[MarkFL]

You want to take the ratio of the change to the original amount, then multiply by 100 to convert this ratio to a percentage:

\(\displaystyle \dfrac{56-40}{40}\cdot100=40\%\)

 

[lillybeth]

You want to take the ratio of the change to the original amount, then multiply by 100 to convert this ratio to a percentage:

\(\displaystyle \dfrac{56-40}{40}\cdot100=40\%\)

So the answer is 40 %? I'm sorry but I can't see how you get that by multiplying by 100. I'm really confused. thanks anyway.

 

[MarkFL]

Before we multiply by 100, we have:

\(\displaystyle \dfrac{16}{40}=\dfrac{8\cdot2}{8\cdot5}=\dfrac{2}{5}\)

Now, multiply by 100:

\(\displaystyle \dfrac{2}{5}\cdot100=2\cdot\dfrac{100}{5}=2\cdot \dfrac{5\cdot20}{5}=2\cdot20=40\)

 

[JeffM]

So the answer is 40 %? I'm sorry but I can't see how you get that by multiplying by 100. I'm really confused. thanks anyway.

Percent comes from a Latin phrase "per centum," which means literally "by the hundred." If it makes it easier for you, you can just think of percent meaning hundredths. So we change the base, the reference value, to 100. One hundred becomes a standard reference point for relative changes, a form of standard communication.

\(\displaystyle \dfrac{56 - 40}{40} = \dfrac{16}{40} = \dfrac{40}{100} \equiv 40 * \dfrac{1}{100} \equiv 40\ hundredths \equiv 40\%.\)

See where the equal signs change to equivalence signs. We are now talking definitions.

\(\displaystyle So\ \dfrac{16}{40} = \dfrac{40}{100} = 40\%.\) To go from a fraction to a percent, I simply multiply by 100 by DEFINITION.

But I do not need the intermediate step to convert a fraction into an equivalent one with a denominator of 100.

\(\displaystyle 100 * \dfrac{16}{40} = 40\ percent.\)

There is no more why involved in this definition than there is in why English speakers say that they work at a "desk" rather than working at a "pig."

 

[lillybeth]

Before we multiply by 100, we have:

\(\displaystyle \dfrac{16}{40}=\dfrac{8\cdot2}{8\cdot5}=\dfrac{2}{5}\)

Now, multiply by 100:

\(\displaystyle \dfrac{2}{5}\cdot100=2\cdot\dfrac{100}{5}=2\cdot \dfrac{5\cdot20}{5}=2\cdot20=40\)

oh. ok. i see. Thanks so much!!! I owe you, but being an aquaintance over an internet sight, i don't know how!

 

[lillybeth]

Percent comes from a Latin phrase "per centum," which means literally "by the hundred." If it makes it easier for you, you can just think of percent meaning hundredths. So we change the base, the reference value, to 100. One hundred becomes a standard reference point for relative changes, a form of standard communication.

\(\displaystyle \dfrac{56 - 40}{40} = \dfrac{16}{40} = = \dfrac{40}{100} \equiv 40 * \dfrac{1}{100} \equiv 40\ hundredths \equiv 40\%.\)

See where the equal signs change to equivalence signs. We are now talking definitions.

\(\displaystyle So\ \dfrac{16}{40} = \dfrac{40}{100} = 40\%.\) To go from a fraction to a percent, I simply multiply by 100 by DEFINITION.

But I do not need the intermediate step to convert a fraction into an equivalent one with a denominator of 100.

\(\displaystyle 100 * \dfrac{16}{40} = 40\ percent.\)

There is no more why involved in this definition than there is in why English speakers say that they work at a "desk" rather than working at a "pig."

thanks!

 

[MarkFL]

...I owe you, but being an aquaintance over an internet sight, i don't know how!

I tell you what, I will ask you to receive just a wee bit of constructive criticism.

Perhaps it is the moderator in me coming out, but I would ask that when you post a topic, please use a title that indicates the nature of the problem within. For example, I would have titled this topic something like "Finding the percentage of change." When viewing a sub-forum, it just looks nice to see titles that indicate what kind of problem is being discussed.

I offer this advice not because your titles bother me, but because of my experience on many forums, I know that a descriptive topic title makes your topic just a bit more likely to get views and subsequent help. People tend to appreciate little things like that which show effort on your part to present your problem in the best way.

On one of the forums I help to moderate, I see this quite a bit, and I edit the titles for the reasons I cited.

Thanks for listening!

Mark.

 

[lillybeth]

I tell you what, I will ask you to receive just a wee bit of constructive criticism.

Perhaps it is the moderator in me coming out, but I would ask that when you post a topic, please use a title that indicates the nature of the problem within. For example, I would have titled this topic something like "Finding the percentage of change." When viewing a sub-forum, it just looks nice to see titles that indicate what kind of problem is being discussed.

I offer this advice not because your titles bother me, but because of my experience on many forums, I know that a descriptive topic title makes your topic just a bit more likely to get views and subsequent help. People tend to appreciate little things like that which show effort on your part to present your problem in the best way.

On one of the forums I help to moderate, I see this quite a bit, and I edit the titles for the reasons I cited.

Thanks for listening!

Mark.

You kind of forced me to listen, but that's ok. I apreciate cunstructive critisism. I will try to make my titles better, but the reason that I usually make my titles short is because I am in a hurry to get the question out there because I have a very limited time to get my work done. Thanks anyway!

 

[pappus]

an additional remark only

Percent comes from a Latin phrase "per centum," which means literally "by the hundred." ...

"per cento" is Italian and was used by the medi-eval Italian bankers (you probably know Fibonacci) and means of course "by the hundred".

The Italian used the abbreviation cto. If you have to write "cto" quite often and if you have to write it very fast this "cto" becomes \(\displaystyle \displaystyle{{}^c t_o}\)

And you certainely can imagine how this sign "%" is derived from \(\displaystyle \displaystyle{{}^c t_o}\).

Thanks for the opportunity to show off.

 

[MarkFL]

You kind of forced me to listen, but that's ok. I apreciate cunstructive critisism. I will try to make my titles better, but the reason that I usually make my titles short is because I am in a hurry to get the question out there because I have a very limited time to get my work done. Thanks anyway!

Allow me to paint for you a scenario:

Imagine you are a math helper at a math forum. Your time is also limited (as is everyone's), and you see two new topics posted in the differential equations forum. They are titled:

• Solving a Cauchy-Euler equation
• Help!

Now, I can't speak for everyone, but I'm going to give my time first to the topic with the descriptive title. I know how to solve Cauchy-Euler differential equations, so I know I can probably offer some advice.

That's all I'm trying to say, to offer you advice about how to best attract the attention of potential helpers. Even more of a turn-off to me, and so probably to others as well, are titles like:

• Please Help!!!!!!!!!!! I need this in a hurry!!!!!!!!!!!!!!!!!!!!!

Right off the bat, I see a person who procrastinated and expects their poor habits to suddenly become our crisis. My inner voice says "Pffft."

Anyway, you know how we "old folks" are...we love to give advice!

By the way, I wouldn't have said a word if I didn't care and/or think you could possibly benefit in some small way from my experience. I could go on and on about the things people do that decrease their chances of getting prompt help on the forums...but I won't.

Best Regards,

Mark.

 

[JeffM]

"per cento" is Italian and was used by the medi-eval Italian bankers (you probably know Fibonacci) and means of course "by the hundred".

The Italian used the abbreviation cto. If you have to write "cto" quite often and if you have to write it very fast this "cto" becomes \(\displaystyle \displaystyle{{}^c t_o}\)

And you certainely can imagine how this sign "%" is derived from \(\displaystyle \displaystyle{{}^c t_o}\).

Thanks for the opportunity to show off.

Thanks. I did not know any of that. I had wondered from time to time how anyone got % from "per centum". Now I know. Of course Italian "per cento" does come from Latin "per centum," which is actually used in many old texts.

As for Fibonacci, I did not have the pleasure of his acquiantance: I am old, but not quite that old.

 

[lookagain]

You want to take the ratio of the change to the original amount,
then multiply by 100 to convert this ratio to a percentage:

\(\displaystyle \dfrac{56-40}{40}\cdot100=40\%\)

This is incorrect. It should be:

"You want to take the ratio of the change to the original amount,

then multiply by 100% to convert this ratio to a percentage:

\(\displaystyle \dfrac{56-40}{40}\cdot100 \% \ = \ 40\%\)


- - - - - - - - - - - - - - - - - - - - - - -


And this also needs to be addressed:

\(\displaystyle So\ \dfrac{16}{40} = \dfrac{40}{100} = 40\%.\)
The fraction, 40/100, is multiplied by 100%, not 100, to arrive at the correct answer of 40%.


To go from a fraction to a percent, I simply multiply by 100 by DEFINITION.
No, you multiply by 100%. That is another form of 1, as 100% = 100/100.

And also this:

\(\displaystyle 100 * \dfrac{16}{40} = 40\ percent.\)


This is incorrect. It should be:

\(\displaystyle 100 \ percent* \dfrac{16}{40} = 40\ percent.\)

or


\(\displaystyle \dfrac{16}{40}*100 \ percent \ = \ 40 \ percent.\)

Please note all of the additional edits.

 

[MarkFL]

This is incorrect. It should be:

"You want to take the ratio of the change to the original amount,

then multiply by 100% to convert this ratio to a percentage:

\(\displaystyle \dfrac{56-40}{40}\cdot100 \% \ = \ 40\%\)

I am now in the corner constructed by Denis, adorned in the conical and festive headgear. :!:

 

[lookagain]

I am now in the corner constructed by Denis, adorned in the conical and festive headgear. :!:

MarkFL,

please note the updates to my post #16 above. You and JeffM will be arriving
at that corner together.

 

[MarkFL]

MarkFL,

please note the updates to my post #16 above. You and JeffM will be arriving
at that corner together.

Yes, we are already sharing the tall stool, passing notes and conspiring to escape..

Seriously though, you are absolutely correct.

 

[lillybeth]

"per cento" is Italian and was used by the medi-eval Italian bankers (you probably know Fibonacci) and means of course "by the hundred".

The Italian used the abbreviation cto. If you have to write "cto" quite often and if you have to write it very fast this "cto" becomes \(\displaystyle \displaystyle{{}^c t_o}\)

And you certainely can imagine how this sign "%" is derived from \(\displaystyle \displaystyle{{}^c t_o}\).

Thanks for the opportunity to show off.