If 1/2 * $100.00 = $50.00 or $50.00 per $100.00, does 2 * $100.00 = $200.00 or $200.00 per $100 or...?

[Dr.Peterson]

There is nothing impossible about it. I provided an example for you that, I believe, explains how this situation may be possible!

Does that mean you no longer have a problem with what you asked about?

 

[Explain this!]

Does that mean you no longer have a problem with what you asked about?

My question is still unanswered!

 

[Denis]

Perhaps you should try another math site...

 

[Dr.Peterson]

1. If 1/2 * $100.00 = $50.00 or $50.00 per $100.00, ($50.00/$100.00), does 2 * $100.00 = $200.00 or $200.00 per $100, ($200.00/$100.00) or $200.00 for every $100.00?

If you're asking which of the four things at the end of the sentence is true, I would say only the first, $200.00, belongs on the right side of the equal sign, because the units don't match. I initially thought your were asking whether 2 * $100.00 = $200.00 could be described as a rate in one of the other forms, and it could. Your placement of commas and "or" makes it a little confusing what you are actually asking, which is part of the reason I asked for clarification.

2. How can there be $200.00 per $100.00 or $200.00 for every $100.00? "Per" and "for every" are interchangeable.

Please restate your question. In what sense are you asking, "How can there be ..."? What do you see wrong with this? Or did you say you had resolved this question?

 

[Explain this!]

You are correct...my sincere apologies...

Apologies accepted! Have a good day!

Perhaps you should try another math site...

I'll consider it--thanks for the advice!

 

[Explain this!]

If you're asking which of the four things at the end of the sentence is true, I would say only the first, $200.00, belongs on the right side of the equal sign, because the units don't match. I initially thought your were asking whether 2 * $100.00 = $200.00 could be described as a rate in one of the other forms, and it could. Your placement of commas and "or" makes it a little confusing what you are actually asking, which is part of the reason I asked for clarification.

Please restate your question. In what sense are you asking, "How can there be ..."? What do you see wrong with this? Or did you say you had resolved this question?

In the first example, 1/2 * $100.00, I know that there are two groups of $50.00 in $100.00--$50.00/$100.00, but it appears to be strange to think that there are $200.00 in $100.00 or $200.00/$100.00. This is the strange part of the calculation 2 * $100.00 = $200.00. Can this have a similar meaning as 1/2 * $100.00--$50.00/$100.00 or $50.00 for every $100.00? Does 2 * $100.00 represent $200.00 for every $100.00?

 

[pka]

In the first example, 1/2 * $100.00, I know that there are two groups of $50.00 in $100.00--$50.00/$100.00, but it appears to be strange to think that there are $200.00 in $100.00 or $200.00/$100.00. This is the strange part of the calculation 2 * $100.00 = $200.00. Can this have a similar meaning as 1/2 * $100.00--$50.00/$100.00 or $50.00 for every $100.00? Does 2 * $100.00 represent $200.00 for every $100.00?

Give this thread and several others[ i.e. the inverse of complex numbers] I have the distinct impression that we have been dropped into the midst of the MadHatter's tea party.

 

[Dr.Peterson]

In the first example, 1/2 * $100.00, I know that there are two groups of $50.00 in $100.00--$50.00/$100.00, but it appears to be strange to think that there are $200.00 in $100.00 or $200.00/$100.00. This is the strange part of the calculation 2 * $100.00 = $200.00. Can this have a similar meaning as 1/2 * $100.00--$50.00/$100.00 or $50.00 for every $100.00? Does 2 * $100.00 represent $200.00 for every $100.00?

I think part of the difficulty is that you are thinking that a mathematical expression or equation has only one concrete meaning. Numbers are abstract, and can be applied in different ways in different situations. Also, an expression is just an expression; the meaning of 1/2 * 100 is simply "the number that, multiplied by 2, gives 100", namely 50.

One way to think of 1/2 * $100.00 is to think of dividing $100 into two equal parts, and taking one of them. The expression doesn't literally mean $50/$100, but the fact that 1/2 * $100 = $50 is related to the fact that $50/$100 = 1/2. This is a ratio that says 50 is related to 100 as 1 is related to 2. None of this says that 100 actually consists of two parts. One application of the ratio would be that, say, one item costs half as much as another, so you could say that for every $100 you spend on the latter, you spend $50 on the former. There are no "parts" involved.

The fact that 2 * $100 = $200 merely means that $200 is twice as much as $100. The ratio $200/$100 = 2, in one application, would mean that for every $100 you spend on the second item, you spend $200 on the first. Again, no "parts".

Applications of math determine what math should be used. The math doesn't imply anything about the real world.

 

[Explain this!]

I think part of the difficulty is that you are thinking that a mathematical expression or equation has only one concrete meaning. Numbers are abstract, and can be applied in different ways in different situations. Also, an expression is just an expression; the meaning of 1/2 * 100 is simply "the number that, multiplied by 2, gives 100", namely 50.

One way to think of 1/2 * $100.00 is to think of dividing $100 into two equal parts, and taking one of them. The expression doesn't literally mean $50/$100, but the fact that 1/2 * $100 = $50 is related to the fact that $50/$100 = 1/2. This is a ratio that says 50 is related to 100 as 1 is related to 2. None of this says that 100 actually consists of two parts. One application of the ratio would be that, say, one item costs half as much as another, so you could say that for every $100 you spend on the latter, you spend $50 on the former. There are no "parts" involved.

The fact that 2 * $100 = $200 merely means that $200 is twice as much as $100. The ratio $200/$100 = 2, in one application, would mean that for every $100 you spend on the second item, you spend $200 on the first. Again, no "parts".

Applications of math determine what math should be used. The math doesn't imply anything about the real world.

Thank you--I'll need to gives this information more thought. I'm still somewhat confused. It makes sense to me to think that 1/2 * $100.00 = $50.00 or $50.00 out of every $100.00 if there is a situation that applies to my opinion. If there is a finance charge of $500.00 per $1,000.00 what is the finance charge per $100.00? $500.00/$1,000.00 * $100.00 = 1/2 * $100.00 = $50.00. The finance charge per or for every $100.00 is $50.00--correct?
Doesn't this actually mean $50.00/$100.00?

 

[Dr.Peterson]

Thank you--I'll need to gives this information more thought. I'm still somewhat confused. It makes sense to me to think that 1/2 * $100.00 = $50.00 or $50.00 out of every $100.00 if there is a situation that applies to my opinion. If there is a finance charge of $500.00 per $1,000.00 what is the finance charge per $100.00? $500.00/$1,000.00 * $100.00 = 1/2 * $100.00 = $50.00. The finance charge per or for every $100.00 is $50.00--correct?
Doesn't this actually mean $50.00/$100.00?

Yes, of course! The fractions 500/1000, 50/100, and 1/2 are all equivalent. All represent a rate of 50%.