PreCalc: If ad = bc then a/b = c/d (hint: assume ad=bc; start w/ ab-1, transform...)

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Bms1998

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I have a couple of problems that I am unsure of how to solve! Any help is much appreciated!

  1. If ad = bc then a/b = c/d (hint: assume that ad=bc then start with ab-1 and transform it into cd-1)
  2. Show that a/b = ak/bk follows from the law that a/b = c/d if and only if ad=bc
 
Bms1998 said:
I have a couple of problems that I am unsure of how to solve! Any help is much appreciated!

  1. If ad = bc then a/b = c/d (hint: assume that ad=bc then start with ab-1 and transform it into cd-1)
  2. Show that a/b = ak/bk follows from the law that a/b = c/d if and only if ad=bc
Click to expand...

If you haven't read our guidelines, or this summary, please do so. It is important that you show us how you are thinking, so we can tell what help you need.

I suspect that you meant to say "start with ab-1 and transform it into cd-1", using exponents. What you typed is quite different. (You can also type it as "ab^-1".) The full guidelines includes advice on how to type math correctly.

But I'm not really sure what that hint means; it is not the quickest way to accomplish the goal. Try doing anything you want (that is valid) to either transform a/b into c/d, or transform ad=bc into a/b = c/d. Show us something (preferably based on what you have been learning, which will give us a hint as to what might be expected), and we can guide you from there.

I think the answer to the second question is meant to use the result of the first.
 
Bms1998 said:
I have a couple of problems that I am unsure of how to solve! Any help is much appreciated!

  1. If ad = bc then a/b = c/d (hint: assume that ad=bc then start with ab-1 and transform it into cd-1)
  2. Show that a/b = ak/bk follows from the law that a/b = c/d if and only if ad=bc
Click to expand...
You need to think carefully about this. You have ad and want to get a/b. So in ad you want to get rid of the d (so divide both sides by d) and you also want to introduce a b in the denominator (so divide by sides by b). So in the end, divide both sides by bd.
 
Jomo said:
You need to think carefully about this. You have ad and want to get a/b. So in ad you want to get rid of the d (so divide both sides by d) and you also want to introduce a b in the denominator (so divide by sides by b). So in the end, divide both sides by bd.
Click to expand...

I think the hint is suggesting, not starting with an equation, but with a/b as an expression, and multiplying by the fraction (bc)/(ad), which is 1.
 
Denis said:
Where is YOUR work?
Show it and we'll check it...
Click to expand...

I don't have any work on this so far. I am preparing to go back to college so I bought a precalculus workbook to teach myself. So I don't even know where to start on these.
 
Dr.Peterson said:
If you haven't read our guidelines, or this summary, please do so. It is important that you show us how you are thinking, so we can tell what help you need.

I suspect that you meant to say "start with ab-1 and transform it into cd-1", using exponents. What you typed is quite different. (You can also type it as "ab^-1".) The full guidelines includes advice on how to type math correctly.

But I'm not really sure what that hint means; it is not the quickest way to accomplish the goal. Try doing anything you want (that is valid) to either transform a/b into c/d, or transform ad=bc into a/b = c/d. Show us something (preferably based on what you have been learning, which will give us a hint as to what might be expected), and we can guide you from there.

I think the answer to the second question is meant to use the result of the first.
Click to expand...

Honestly, I am just not even sure what to think. I am teaching myself this so I don't really know where to start. This is the first chapter of the book too, which is pretty much supposed to just be a review. I am getting my questions out of a workbook that I bought, so yeah the hint didn't mean much sense to me either. & weird I was pretty positive I had put the ^ for exponent because I posted this same thing on Reddit and just copy & pasted, I guess it didn't transfer over.
 
I have some suggestions. Read this

https://www.freemathhelp.com/forum/threads/41536-Read-Before-Posting!!

Now re-post your problems completely and exactly.

Tell us what you want to learn. Is it elementary algebra (this is what is usually taught in high school algebra)?

Tell us the name of the text that you are using so we can determine whether it is appropriate for what you want to learn.

People here want to be helpful, but no one can be helpful in a void.

EDIT: You posted this under pre-calculus, which as far as I am concerned is a rather nonsensical term. What is necessary to study calculus is arithmetic, algebra, and analytic geometry. But you seem to be struggling with algebra.
 
Last edited:
Could you please solve this problem? " If abc=1 then prove that

clip_image002.png
+
clip_image004.png
=1
 
Aadil Ahnaf said:
Could you please solve this problem? " If abc=1 then prove that
clip_image002.png
+
clip_image004.png
=1
Click to expand...

You appear to have tried inserting images without uploading them, and made your question a reply to an existing question rather than a new thread. Please try again!

Also, we don't primarily "solve this problem"; our purpose is to help you solve problems, which requires knowing what help you need. Please see the summary of our guidelines.
 
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