The top of page 130 of Chapter 8 in Number Properties Guide-
It shows the number line, upper-lower/# of intervals.
Why is 3 listed as the # of intervals? And then is changed to 5?
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- jlo4451
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- tommywallach
- Manhattan Prep Staff
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Re: Number Properties, pg.130
Hey Jen,
I think you're confusing terms here. There are tick marks (the lines), and intervals (The spaces between lines). Then there are the actual values of the tick marks. In this case, the top tick mark is labeled 5 and the bottom is labeled 3. This is irrespective of the number of the intervals. In this case, there are three intervals and also 3 numbers between 2 and 5. That's a coincidence.
Imagine the same picture, but instead of saying 2, the first tick mark said 10, while the second tick mark said 20. Now, there would still be three intervals between them, but each interval would not be equal to 1, it would be equal to 10/3.
So the 5 you're talking about is not an interval, it is the actual value of the top boundary (the highest tick mark is labeled 5).
Does that make more sense?
-t
I think you're confusing terms here. There are tick marks (the lines), and intervals (The spaces between lines). Then there are the actual values of the tick marks. In this case, the top tick mark is labeled 5 and the bottom is labeled 3. This is irrespective of the number of the intervals. In this case, there are three intervals and also 3 numbers between 2 and 5. That's a coincidence.
Imagine the same picture, but instead of saying 2, the first tick mark said 10, while the second tick mark said 20. Now, there would still be three intervals between them, but each interval would not be equal to 1, it would be equal to 10/3.
So the 5 you're talking about is not an interval, it is the actual value of the top boundary (the highest tick mark is labeled 5).
Does that make more sense?
-t
- jlo4451
- Students
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Re: Number Properties, pg.130
I'm not sure we are talking about the same problem. The problem I'm referring to starts with 3/5 and ends with 7/5 on the bottom of page 129 and continues onto the top of page 130, stating 6 tick marks and 5 intervals. Directly below that is the formula, and the denominator says 3.
(7/5 -(-3/5))/3
Then the equation becomes
(10/5/(5))
Where the denominator is 3 and then 5.
I'm trying to establish why the first equation has 3 in the denominator.
(7/5 -(-3/5))/3
Then the equation becomes
(10/5/(5))
Where the denominator is 3 and then 5.
I'm trying to establish why the first equation has 3 in the denominator.
- tommywallach
- Manhattan Prep Staff
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Re: Number Properties, pg.130
Aha! I understand now. Sorry, the e-document version of the book that I use is paginated differently, so it's sometimes tough to find the right question.
Yes, it should be a 5 in both cases. It's a typo! But pretty clear, right? The numerator hasn't changed (if it had, then it could have been some kind of simplification). Sorry!
-t
Yes, it should be a 5 in both cases. It's a typo! But pretty clear, right? The numerator hasn't changed (if it had, then it could have been some kind of simplification). Sorry!
-t
- jlo4451
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Re: Number Properties, pg.130
Thanks for your help! I was racking my brain about that 3. I thought it was a typo, but it wasn't listed in the errata.
Thanks again!
Jen
Thanks again!
Jen
- tommywallach
- Manhattan Prep Staff
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Re: Number Properties, pg.130
It has hopefully been added to the errata now. Thanks for catching it!
-t
-t
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