I need a math assist

[AppleGreen]

I haven't posted in forever, but I still read regularly. We decided to give a new charter school a go for my oldest (in 8th grade), but brought him home after 3 weeks. I will probably post a "what was I thinking! freak out and How am I ever going to do this?" when the dust settles, but in the meantime I need help solving a math problem. We are using MM7A to shore up some skills. I am stumped on the following problem:

 

Which of the numbers 0,1,3/2,2 or 5/2 make the equation y/y-1=3 true?

 

I cannot get the answer in the answer key. Can someone explain the solution and why to me? I'll go drink more coffee to see if that wakes my brain up a bit more and try not to freak out that I can't solve this simple problem and should indeed be homeschooling my child.

 

Thank you in advance!

 

Apple :)

[kiana]

Does the answer key say 3/2? 

 

If y = 3/2, then y-1 = 1/2, and 3/2 divided by 1/2 is 3. 

[Snickerdoodle]

[AppleGreen]

Thank you, thank you! I realized what I was doing wrong and so appreciate the help.

[Snickerdoodle]

 

The equation is y/y -1 = 3

 

 

[y]  divided by  [y-1]  equals [3]

[kiana]

But wouldn't you have to divide before subtracting

 

The equation is y/y -1 = 3

 

Since 3/2 is equal to 1.5 I'll use that in the equation

 

1.5 / 1.5 -1 = 3

1-1=3

0=3

 

Pretty sure she meant y/(y-1).

 

You are correct that the equation as written would evaluate to (y/y) - 1 = 1-1 = 0 for every nonzero value of y (which would mean there would not be a solution), but that interpretation wouldn't make sense (imo) with the question asked. Therefore I answered the question that I believed she meant to ask rather than the one she actually asked. 

[AppleGreen]

Ok, that is why I was confused. The problem does not have parentheses. So I solved it as 3/2/3/2-1=3. I wrote the reciprocal, so I had 3/2*2/3-1=3. The 3/2*2/3 reduced to 1, so I was left with 1-1=3 or 0=3. I see how to solve it by subtracting 3/2-1 and then dividing, but did not do that because in Lial's last year they taught to rewrite the problem without the fraction bar and solve. That yielded the first answer, which was not equal to 3.

 

I see someone even solved on the board for me, so I am going to examine that one over my lunch. I am somewhat math phobic, so I feel incredibly unintelligent when I can't figure out pre algebra.

 

I really appreciate people's feedback and help!

[kiana]

Ok, that is why I was confused. The problem does not have parentheses. So I solved it as 3/2/3/2-1=3. I wrote the reciprocal, so I had 3/2*2/3-1=3. The 3/2*2/3 reduced to 1, so I was left with 1-1=3 or 0=3. I see how to solve it by subtracting 3/2-1 and then dividing, but did not do that because in Lial's last year they taught to rewrite the problem without the fraction bar and solve. That yielded the first answer, which was not equal to 3.

 

I see someone even solved on the board for me, so I am going to examine that one over my lunch. I am somewhat math phobic, so I feel incredibly unintelligent when I can't figure out pre algebra.

 

I really appreciate people's feedback and help!

 

Was it written as a fraction? Like

 

y

----

y-1

 

?

 

Because if it was written as y/y-1 (in one line, just like that), then the actual answer would be "none of them". 

[AppleGreen]

Was it written as a fraction? Like

 

y

----

y-1

 

?

 

Because if it was written as y/y-1 (in one line, just like that), then the actual answer would be "none of them".

Yes, in the book it appears:

 

 

Y

------ = 3

Y-1

[desertflower]

If you plug in 3/2 it works.  3/2 / [3/2 - 1]  - 3.  do the denominator first, which will give you 1/2.  then you are left with 3/2 / 1/2 = 3.  so, multiply 3/2 and 2 (reciprocal).  this leaves 6/2 = 3.

 

thoughts?  Now how to get to 3/2..........   :) 

[Snickerdoodle]

 

 

Now how to get to 3/2..........   :)

 

Did you see the image I posted?
 

[desertflower]

I can't really see it.  it's small on my end and I'm not tech savvy.........

 

I'm glad you got it!  :) 

[Snickerdoodle]

If you click on it, it will get bigger.  

[kiana]

Yes, in the book it appears:

 

 

Y

------ = 3

Y-1

 

Yes. In order to put this on one line, you need to use parentheses in the denominator as follows: y/(y-1). 

 

If you write y/y-1, because of order of operations, it would look like this as a fraction:

 

y

--    - 1

y

 

Now, as to what was wrong with your first attempt -- you had:

 

3/2

---------

3/2 - 1

 

and attempted to cancel the 3/2. You cannot do this. 

 

When you cancel common factors from a fraction, what you really are doing is dividing the whole top and bottom by that number. For example, in 10/14, when you reduce it to 5/7 you are dividing the top and bottom by 2. This is legal -- it is the same as multiplying the fraction by 1/2 over 1/2, which is 1. 

 

If you try to cancel the 3/2 here, you are dividing the top and only PART of the bottom by 3/2. That's illegal.

[desertflower]

yes!  thank you snickerdoodle.  that's the way I did it, but wasn't sure if just multiplying by y-1 was legal.  I tend to make up my own rules.  :) 

 

 

[kiana]

yes!  thank you snickerdoodle.  that's the way I did it, but wasn't sure if just multiplying by y-1 was legal.  I tend to make up my own rules.  :)

 

It is legal as long as you remember at your final step that y cannot under any circumstances equal 1. 

 

For this one it does not matter, but if you were given a similar problem where your final solution ended up being "y = 1" you would need to recognize that it was not a real answer (because when you try to plug 1 in to check you end up dividing by 0) and cross it out. 

[desertflower]

That's right. Because 3 is actually over 1, so just cross multiply.

 

I love algebra problems! I'm a bit rusty though. :)

[letsplaymath]

Yes, in the book it appears:

 

 

Y

------ = 3

Y-1

 

Something the math books often forget to tell you (or just assume you already know) is that the fraction line acts like automatic parentheses around the whole top and the whole bottom. Every fraction line, all the time, but it usually doesn't make much difference until we get to algebra.