bindibadgi
Flashlight Enthusiast
3+4*2-1=7*2 has me stumped. /ubbthreads/images/graemlins/grin.gif
CPF University - EE Course - Class in session!
- Thread starter MrAl
- Start date
Negeltu
Enlightened
3+4*2-1<>7*2 ? /ubbthreads/images/graemlins/smile.gif I'm a tad confused too. Both sides are clearly not equal.
Darell
Flashaholic
Hey. The question was "how many terms?" not "does this make sense?" (!)
/ubbthreads/images/graemlins/grin.gif
/ubbthreads/images/graemlins/grin.gif
Darell
Flashaholic
[ QUOTE ]
McGizmo said:
You idiots! in this example, 2 is a sanscript letter and represnts a variable! If you solve for 2, I believe you will find that 2= 2/3 /ubbthreads/images/graemlins/blush.gif
[/ QUOTE ]
Yup. Goes to prove that there is no stupid question. Only stupid answers. /ubbthreads/images/graemlins/whoopin.gif
McGizmo said:
You idiots! in this example, 2 is a sanscript letter and represnts a variable! If you solve for 2, I believe you will find that 2= 2/3 /ubbthreads/images/graemlins/blush.gif
[/ QUOTE ]
Yup. Goes to prove that there is no stupid question. Only stupid answers. /ubbthreads/images/graemlins/whoopin.gif
bindibadgi
Flashlight Enthusiast
/ubbthreads/images/graemlins/crackup.gif
MrAl
Flashlight Enthusiast
Hello again,
Saaby:
A 'sticky'...wow thanks! I think that will help the
people who want to follow the course find the info
as fast as possible.
On behalf of myself and the 'class', THANKS MUCH!
Maybe you could point me to some info about the
'Chat Auditorium' too...i dont think i've seen this
yet?
bindibadgi:
You found an error? Extra credit for you! :-)
Thanks, and i'll correct it right away.
As you may have noticed, i blasted that first 'lesson'
out kinda quick, but im glad...i've found some people
are very awake and paying close attention and that's
really great!
Take care for now,
Al
Saaby:
A 'sticky'...wow thanks! I think that will help the
people who want to follow the course find the info
as fast as possible.
On behalf of myself and the 'class', THANKS MUCH!
Maybe you could point me to some info about the
'Chat Auditorium' too...i dont think i've seen this
yet?
bindibadgi:
You found an error? Extra credit for you! :-)
Thanks, and i'll correct it right away.
As you may have noticed, i blasted that first 'lesson'
out kinda quick, but im glad...i've found some people
are very awake and paying close attention and that's
really great!
Take care for now,
Al
MrAl
Flashlight Enthusiast
Hello again,
I'll post the next Part here. Once i have the format
of the web site set up properly i'll start posting
there and linking from here.
Serial: EE-Ch0001-p102-{A939C0B7-558E-4687-9271-AB92E4935FD0}
We need to establish some ground rules when evaluating
numerical expressions. These rules have long been set
almost since the dawn of man's desire to understand
the world numerically.
REPLACEMENT, ORDER OF OPERATIONS, OPERATOR PRECEDENCE
When calculating an expression, we proceed from left to right
once the precedence of all the operators is the same.
To calculate 1+2+3 we start with 1+2, and to calculate
2*3*4 we start with 2*3.
When we have to calculate a multi-term expression we cant do
the whole thing at once, we have to do two terms at a time
or evaluate a product first.
We can do:
1+3
right away without any problem because there are only two terms,
but when we go to do:
4+2+7
we have to do two terms first, then continue to the next term
something like this:
4+2 gives us 6, then 6+7 gives us 13.
Notice we had to do two terms first, then proceed to the next term
in order to calculate the whole expression. We cant add all three
numbers all at the same time really.
This becomes even more apparent when we try to add many terms:
1+2+3+4+5+6-7+9
We have to start somewhere, and the rule is we have to start at the
leftmost term and proceed to the right (once we reduce the expression
to all additions and subtractions or the operators have all the
same precedence).
If you want to keep track of intermediate results the following helps:
We start with the full expression:
1+2+3+4+5+6-7+9
Then, we start with the left most terms,
1+2
We do the operation, then replace the two terms with the
result. Since 1+2 equals 3 we replace these two terms with
the number 3, and we get:
3+3+4+5+6-7+9
Next we do '3+3' and get 6, and replace '3+3' with '6':
6+4+5+6-7+9
Next, 6+4 and replace that:
10+5+6-7+9
Likewise 10+5:
15+6-7+9
15+6:
21-7+9
21-7:
14+9
Now we are down to our last two terms, so we do the operation and
we are done...
14+9 equals 23:
23
And we have the result!
1+2+3+4+5+6-7+9=23
In each case i simply copied the remaining expression and pasted it
to the next line, then replaced the left two terms with the result
from doing the operation between those two terms.
Notice each time we do this we reduce the expression by one term.
Eventually we get all the terms combined into one single term,
which is of course the answer.
It's very important to do the left two terms before anything else,
because we MUST proceed from left to right in order to evaluate
expressions when all the operators are of the same precedence.
Now so far we've only done expressions with addition and subtraction.
When we do addition and subtraction with multiplication and division,
we have to take into account the precedence of the operators.
Precedence simply means operators with higher precedence get
calculated first. Of course we have to know the precedence of
operators in order to know which ones are higher, so here's a list:
addition 1
subtraction 1
multiplication 2
division 2
Notice some are higher then others.
Now let us see how this affects our calculations...
Calculate 1+2*3=? (the question mark indicates a number we dont know yet)
Because multiplication is higher than addition, we have to start with
that...
We start with the original expression:
1+2*3=?
calculate 2*3 and replace it with it's result, 6:
1+6=?
Now we do the last two terms and get 7, so we have the answer:
1+2*3=7
Notice that if we do the '1+2' first we would get the wrong answer:
1+2=3, and 3*3=9, and '9' is not the correct answer...
1+2*3<>9
This should show how important operator precedence is.
Self test exercises
1. compute the answer to: 3+4*5+7-2*2 = ?
2. compute the answer to: 3+4*3*8 = ?
3. compute the answer to: 2+3*5+1 = ?
4. compute the answer to: 8-3*2+3*2*3 = ?
5. compute the answer to: 8-3*2+3*2+3 = ?
6. compute the answer to: ? = 8/2+3*2+3*2-3
See ya next time,
Al
I'll post the next Part here. Once i have the format
of the web site set up properly i'll start posting
there and linking from here.
Serial: EE-Ch0001-p102-{A939C0B7-558E-4687-9271-AB92E4935FD0}
We need to establish some ground rules when evaluating
numerical expressions. These rules have long been set
almost since the dawn of man's desire to understand
the world numerically.
REPLACEMENT, ORDER OF OPERATIONS, OPERATOR PRECEDENCE
When calculating an expression, we proceed from left to right
once the precedence of all the operators is the same.
To calculate 1+2+3 we start with 1+2, and to calculate
2*3*4 we start with 2*3.
When we have to calculate a multi-term expression we cant do
the whole thing at once, we have to do two terms at a time
or evaluate a product first.
We can do:
1+3
right away without any problem because there are only two terms,
but when we go to do:
4+2+7
we have to do two terms first, then continue to the next term
something like this:
4+2 gives us 6, then 6+7 gives us 13.
Notice we had to do two terms first, then proceed to the next term
in order to calculate the whole expression. We cant add all three
numbers all at the same time really.
This becomes even more apparent when we try to add many terms:
1+2+3+4+5+6-7+9
We have to start somewhere, and the rule is we have to start at the
leftmost term and proceed to the right (once we reduce the expression
to all additions and subtractions or the operators have all the
same precedence).
If you want to keep track of intermediate results the following helps:
We start with the full expression:
1+2+3+4+5+6-7+9
Then, we start with the left most terms,
1+2
We do the operation, then replace the two terms with the
result. Since 1+2 equals 3 we replace these two terms with
the number 3, and we get:
3+3+4+5+6-7+9
Next we do '3+3' and get 6, and replace '3+3' with '6':
6+4+5+6-7+9
Next, 6+4 and replace that:
10+5+6-7+9
Likewise 10+5:
15+6-7+9
15+6:
21-7+9
21-7:
14+9
Now we are down to our last two terms, so we do the operation and
we are done...
14+9 equals 23:
23
And we have the result!
1+2+3+4+5+6-7+9=23
In each case i simply copied the remaining expression and pasted it
to the next line, then replaced the left two terms with the result
from doing the operation between those two terms.
Notice each time we do this we reduce the expression by one term.
Eventually we get all the terms combined into one single term,
which is of course the answer.
It's very important to do the left two terms before anything else,
because we MUST proceed from left to right in order to evaluate
expressions when all the operators are of the same precedence.
Now so far we've only done expressions with addition and subtraction.
When we do addition and subtraction with multiplication and division,
we have to take into account the precedence of the operators.
Precedence simply means operators with higher precedence get
calculated first. Of course we have to know the precedence of
operators in order to know which ones are higher, so here's a list:
addition 1
subtraction 1
multiplication 2
division 2
Notice some are higher then others.
Now let us see how this affects our calculations...
Calculate 1+2*3=? (the question mark indicates a number we dont know yet)
Because multiplication is higher than addition, we have to start with
that...
We start with the original expression:
1+2*3=?
calculate 2*3 and replace it with it's result, 6:
1+6=?
Now we do the last two terms and get 7, so we have the answer:
1+2*3=7
Notice that if we do the '1+2' first we would get the wrong answer:
1+2=3, and 3*3=9, and '9' is not the correct answer...
1+2*3<>9
This should show how important operator precedence is.
Self test exercises
1. compute the answer to: 3+4*5+7-2*2 = ?
2. compute the answer to: 3+4*3*8 = ?
3. compute the answer to: 2+3*5+1 = ?
4. compute the answer to: 8-3*2+3*2*3 = ?
5. compute the answer to: 8-3*2+3*2+3 = ?
6. compute the answer to: ? = 8/2+3*2+3*2-3
See ya next time,
Al
LEDmodMan
Flashaholic*
Oh man, a pop quiz! /ubbthreads/images/graemlins/icon15.gif Time to wake up! /ubbthreads/images/graemlins/drool.gif
26
99
18
20
11
13
Winning lotto numbers? Hmmm... /ubbthreads/images/graemlins/thinking.gif
/ubbthreads/images/graemlins/crackup.gif
26
99
18
20
11
13
Winning lotto numbers? Hmmm... /ubbthreads/images/graemlins/thinking.gif
/ubbthreads/images/graemlins/crackup.gif
Bullzeyebill
Flashaholic
Where are answers located?
Bill
Bill
What is that serial thing? Dang - already missed something. /ubbthreads/images/graemlins/thinking.gif
What about having a thread as a sticky where only each chapter is published, nobody will post there - but people could put that thread in their favourites and always receive the newest stuff via email. This way even if you cannot access CPF at one time you'll at least receive the newest stuff via email. /ubbthreads/images/graemlins/wink.gif
What about having a thread as a sticky where only each chapter is published, nobody will post there - but people could put that thread in their favourites and always receive the newest stuff via email. This way even if you cannot access CPF at one time you'll at least receive the newest stuff via email. /ubbthreads/images/graemlins/wink.gif
Darell
Flashaholic
I like K-T's idea LOTS. Make it sticky in place of the sticky links thread. Stand by - I'll see what I can do. Here we go: Chapters Stickie
If this makes no sense, please let me know. I really think that this will be the best approach, but I've been wrong before™
BTW, I'm thrilled to see that at lesson two, we're already in a place where an RPN calculator rules. /ubbthreads/images/graemlins/smile.gif
If this makes no sense, please let me know. I really think that this will be the best approach, but I've been wrong before™
BTW, I'm thrilled to see that at lesson two, we're already in a place where an RPN calculator rules. /ubbthreads/images/graemlins/smile.gif
MrAl
Flashlight Enthusiast
Hi again,
Jody:
You were looking at LEDmodMan's answers; shame! :-) hee hee
McGizmo:
Yeah something like that :-)
Im hoping to get going quick...
Bill:
I was going to post the answers, but i wanted to give
anyone a chance to try the questions out first.
K-T:
The serial number marks the post as a unique GUID,
so anyone asking about a particular subject in the
future can find it using the CPF search engine.
It's very likely that no one else will use a number
like that in their post, so it will turn up only
one post which contains the information they are
(hopefully) looking for.
If you would like to try it now, enter
EE-Ch0001-p102-{A939C0B7-558E-4687-9271-AB92E4935FD0}
in the search engine and see what comes up.
Of course if someone copies the thread to another
location it will show up in the search too.
Darell:
Thanks, i think that will work nicely.
Do you think it's possible we can get all the info
copied to the new thread when possible?
Thanks again...
Take care for now,
Al
Jody:
You were looking at LEDmodMan's answers; shame! :-) hee hee
McGizmo:
Yeah something like that :-)
Im hoping to get going quick...
Bill:
I was going to post the answers, but i wanted to give
anyone a chance to try the questions out first.
K-T:
The serial number marks the post as a unique GUID,
so anyone asking about a particular subject in the
future can find it using the CPF search engine.
It's very likely that no one else will use a number
like that in their post, so it will turn up only
one post which contains the information they are
(hopefully) looking for.
If you would like to try it now, enter
EE-Ch0001-p102-{A939C0B7-558E-4687-9271-AB92E4935FD0}
in the search engine and see what comes up.
Of course if someone copies the thread to another
location it will show up in the search too.
Darell:
Thanks, i think that will work nicely.
Do you think it's possible we can get all the info
copied to the new thread when possible?
Thanks again...
Take care for now,
Al
Darell
Flashaholic
[ QUOTE ]
MrAl said:
Darell:
Thanks, i think that will work nicely.
Do you think it's possible we can get all the info
copied to the new thread when possible?
Thanks again...
[/ QUOTE ]
It is all there, as far as I know. I think I will simply stick the links from Ryan's post in that one thread, and zap his. NO need for two stickies with the same info. I'm sure Ryan won't mind - and to be doubly sure of that, I won't even ask him. /ubbthreads/images/graemlins/smile.gif
MrAl said:
Darell:
Thanks, i think that will work nicely.
Do you think it's possible we can get all the info
copied to the new thread when possible?
Thanks again...
[/ QUOTE ]
It is all there, as far as I know. I think I will simply stick the links from Ryan's post in that one thread, and zap his. NO need for two stickies with the same info. I'm sure Ryan won't mind - and to be doubly sure of that, I won't even ask him. /ubbthreads/images/graemlins/smile.gif
Yeah, suck the links out and place them in your fist post in the other thread. That way you have all the content, but you can easily jump to the first post and link to the discussion. Does that make sense?
PS--I think that as we start new chapters we need new discussion threads, that way the discussion in any given thread is more focused, know what I mean? I suppose it causes some redundancy (Because we have the information in both the content and discussion thread) but that's fine by me. Even all that text won't add up to much bandwidth at all...
PS--I think that as we start new chapters we need new discussion threads, that way the discussion in any given thread is more focused, know what I mean? I suppose it causes some redundancy (Because we have the information in both the content and discussion thread) but that's fine by me. Even all that text won't add up to much bandwidth at all...
