Suzq Posted January 13, 2012 Share Posted January 13, 2012 I am going to show my ignorance here. We have been using Saxon math since Saxon 5/6 and now my son is doing the Advanced math book. We have both the DIVE teacher and the Saxon Teacher. thisi s the first year that we keep running stuck and not being able to figure out how they arrived at some of their answers. The Saxon Teacher seems to repeat just about what is in the Solutions manual. As she is solving she will say something like " now we will clean this up " and then skip some steps that we apparently are supposed to remember from previous learning. However, we don't remember and I cannot explain to my son how they arrive at their answer. For example, ( lesson 37, problem 19 part c ) it says t = (1/2) to the -3/2. Translate this as one half to the power of negative three halves. The next step is t = one over two to the power of negative three halves. I cannot explain how they moved from the first step to the next one. Why is the three halves still negative even after moving it below the fraction line? After this we understand the rest of the answer. It is just that one step. Any ideas? We have this every so often that we cannot quite figure how they move from one step to the next. I wonder if I am doing a disservice to my son as I am not well versed in math and I run stuck at my explanations. He has scored above 80 and usually above 90 on all the tests except for one. Therefore we keep moving along. What do you think? Should we be going back and re-doing some lessons? I don't know if I am even clear on my question here but I welcome any advice. Thanks, Quote Link to comment Share on other sites More sharing options...
emubird Posted January 13, 2012 Share Posted January 13, 2012 Are you sure it's not a mistake? What answer are they trying to get? (I'm having a little difficulty figuring out what the problem is, due to the lack of decent typesetting that's possible on this board.) Quote Link to comment Share on other sites More sharing options...
regentrude Posted January 13, 2012 Share Posted January 13, 2012 For example, ( lesson 37, problem 19 part c ) it says t = (1/2) to the -3/2. Translate this as one half to the power of negative three halves. The next step is t = one over two to the power of negative three halves. I cannot explain how they moved from the first step to the next one. Why is the three halves still negative even after moving it below the fraction line? After this we understand the rest of the answer. It is just that one step. Any ideas? Laws of exponents. Let's look at it two ways, first as a quotient: (a/b)^x= (a^x)/(b^x) The exponent x in your example equals -3/2. So, (1/2)^-3/2 = ( 1^-3/2) / (2^(-3/2) Now, use a^(-x)= 1/ (a^x) So, in the denominator (2^(-3/2) = 1/ (2^(3/2) which makes the whole expression equal to (2^(3/2) (dividing by a fraction. Alternatively, you may look at it as a product: (a*b)^x= (a^x)*(b^x) The exponent x in your example equals -3/2. So, (1/2)^-3/2 = ( 1^-3/2) * (1/2)^(-3/2) Now, use a^(-x)= 1/ (a^x) So, in the second factor (1/2)^(-3/2) = 1/ (1/2^(3/2))= 2^(3/2) Quote Link to comment Share on other sites More sharing options...
Teachin'Mine Posted January 13, 2012 Share Posted January 13, 2012 As Regentrude said. The only thing they're not showing you is that they took 1 to the -3/2 which equals 1. Quote Link to comment Share on other sites More sharing options...
Suzq Posted January 13, 2012 Author Share Posted January 13, 2012 Laws of exponents. So, in the denominator (2^(-3/2) = 1/ (2^(3/2) which makes the whole expression equal to (2^(3/2) (dividing by a fraction. Now, use a^(-x)= 1/ (a^x) So, in the second factor (1/2)^(-3/2) = 1/ (1/2^(3/2))= 2^(3/2) Thanks for typing all of this out and taking the time to respond. I think I see what you are saying ---( I like the way you set this up for this kind of typesetting) But at the end in both of your examples above, your denominator has the positive exponent and in my answer book it is still a negative exponent. Or am I not understanding? You say " So in the denominator (2^(-3/2) = 1/ (2^(3/2) " which leaves the three halves positive and not negative. But my book says it is still a negative three halves. Am I making sense? Quote Link to comment Share on other sites More sharing options...
regentrude Posted January 13, 2012 Share Posted January 13, 2012 (edited) Thanks for typing all of this out and taking the time to respond. I think I see what you are saying ---( I like the way you set this up for this kind of typesetting) But at the end in both of your examples above, your denominator has the positive exponent and in my answer book it is still a negative exponent. Or am I not understanding? You say " So in the denominator (2^(-3/2) = 1/ (2^(3/2) " which leaves the three halves positive and not negative. But my book says it is still a negative three halves. Am I making sense? No, I do not understand what you are saying. The denominator of the fraction is 2^-3/2, and that is correct. But the final answer to the whole problem is 2^(3/2)=sqrt(8)=2sqrt(2) Let me type the whole thing again for you: (1/2)^-3/2 = ( 1^-3/2) / (2^(-3/2) the denominator of this fraction is (2^(-3/2) = 1/ (2^(3/2) (this FRACTION is now in the denominator!) which makes the whole expression equal to (2^(3/2) . or: (1/2)^-3/2 = 1/ ((1/2)^(3/2)) (here I have used that a^-x=1/a^x) = 2^(3/2) as a final answer. Edited January 13, 2012 by regentrude Quote Link to comment Share on other sites More sharing options...
Suzq Posted January 13, 2012 Author Share Posted January 13, 2012 the denominator of this fraction is (2^(-3/2) = 1/ (2^(3/2) (this FRACTION is now in the denominator!) This is what I see (1/2)^(-3/2) = 1^(-3/2) / 2^(-3/2) = 1 / (2^(3/2) But in the answer book (1/2)^(-3/2) = 1 / (2^(-3/2) Do you see how the last part in your problem is positive 3/2 and the last part in the book is negative 3/2? We may be losing something in our translation since we are not face to face. Quote Link to comment Share on other sites More sharing options...
regentrude Posted January 13, 2012 Share Posted January 13, 2012 (edited) This is what I see (1/2)^(-3/2) = 1^(-3/2) / 2^(-3/2) = 1 / (2^(3/2) No, this is NOT what I wrote. I wrote (1/2)^-3/2 = ( 1^-3/2) / (2^(-3/2) the denominator of this fraction is (2^(-3/2) = 1/ (2^(3/2) so the WHOLE DOUBLE fraction is equal to (1/2)^-3/2 = 1/ ((1/2)^(3/2)) = 2^3/2 But in the answer book (1/2)^(-3/2) = 1 / (2^(-3/2) Which is exactly my answer. Edited January 13, 2012 by regentrude Quote Link to comment Share on other sites More sharing options...
Suzq Posted January 13, 2012 Author Share Posted January 13, 2012 Thank you Regentrude -- I do think I am beginning to understand. I have been writing it all out on paper to work it out. I am still not completely sure but I think if I keep looking at it, I will see what you are saying. I appreciate you taking the time to help us. I do think if we were face to face I would see it in a split second. We are saying the same thing in different ways I think. I told my son what we were doing and he only said to me there is another problem like it today. We will see if we figure that one out. :D Thanks again, Quote Link to comment Share on other sites More sharing options...
kiana Posted January 13, 2012 Share Posted January 13, 2012 This is what I see (1/2)^(-3/2) = 1^(-3/2) / 2^(-3/2) = 1 / (2^(3/2) But in the answer book (1/2)^(-3/2) = 1 / (2^(-3/2) Do you see how the last part in your problem is positive 3/2 and the last part in the book is negative 3/2? We may be losing something in our translation since we are not face to face. SuzQ, you are misreading what she's saying. What she's saying is (1/2)^(-3/2) = 1^(-3/2) / 2^(-3/2) = 1 / (2^(-3/2) Then, in her next step she's simplifying the denominator only, so 2^(-3/2) = 1/2^(3/2) Then, when you put that back into the first step, you get 1/(1/2^(3/2)), and applying the laws of reciprocals/fraction division you get 2^(3/2) Quote Link to comment Share on other sites More sharing options...
Suzq Posted January 13, 2012 Author Share Posted January 13, 2012 Ah ha -- thank- you Kiana!!! Now I do see it. OK I am going to write this all out and see how well I explain it to my son. Thank-you, thank-you, thank-you. Quote Link to comment Share on other sites More sharing options...
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