This quote has evolved over time into the quote you see above. The orginal Shakespeare Quote is:
"Though this be madness, yet there is method in 't."
--From Hamlet (II, ii, 206)
Friday, September 28, 2007
MCDL 2.1
Questions and Comments:
The Real Number Line
14 comments:
Anonymous
said...
J.B.
What i am having trouble with in this chapter is with factions(adding,dividing,mulitpying, and subtractiong stuff like that.) The problem i do not understand is problem #91 on the mixed review. It is on page 70. Te problem is:
A.H So, I understand that real numbers are any numbers that can easily be plotted on a number line, but what truly is a real number? Even though pi is a non repeating, non terminating number, it can't be plotted on a number line. Does this mean that pi isn't a real number? If you take a number like infinity or the square root of -1, these things are real, but they have no definite value. This doesn't make them fake does it? If all of these are real numbers, how do they fit into a number line, and if they aren't, what are they???
what is the differance between real numbers and like... fake numbers? we were talking about real numbers in class and they are posative and negative and zero. they can also have decimals so what would be a "fake number"?
VB to JB what you have to do in this problem is to find the common denomminator. ok. so lets use the problem that u gave in ur comment.
Ex. 5/8+1/3 so the common denominator for each of these fractions is 24. so what you do is 5/8*3/3. you have to do this becuz that's how u'll get the denominator to 24. so the answer is 15/24. now with 1/3...u do the same thing execpt u multiply it by 8 becuase 3*8 equals. so the new fration is 8/24. then u just add straight across.
15/24+8/24=23/24
the denominator will always stay the same only when ur adding fractions.
problem #91 all you have to do is find least comon denominator for the two fractions. ok so the smalest number 3 and 8(the denominators) are both a factor of is 24. 8x3=24 and 3x8=24. now you would have to multiply the numerator by the same number you multiplyed the denominator to get 24. 5x3=15 and 1x8=8. the new fractions you will have to add are now 15/24 and 8/24. 15/24+8/24= 23/24. wow! that was long and kind of confusing but i solved the problem =]
C.T. to J.B. Ok. First, you would have to find the lowest common denominator. (lcd) To find this,you would keep adding 8 to itself and 3 to itself, until you find a commmon number between those two numbers. Once you do that, you need to find how many times you added 8 to a number to get the lcd. That is the same for 3. Here is the example.
8+8=16+8=24 3+3=6+3=9+3=12+3=15+3=18+3=21+3=24
You should have added 8, three times to get 24 and you should have add 3, 8 times to get 24. After you find the lcd, and find how many times you multiplied or added 8 and 3 to itself, you multiply the number of times you added to get the lcd by the numernator. When you did this, you should get two fractions that have the same denominator. Your new fractions should have been 15/24+ 8/24. Now, all you have to do is add 15+8 and you get you answer. You should simplified after you get you answer also. I hope this helps!
8 * 3 = 24 3 *8 = 24… Now don’t get confused, when you take a glance at the problem, don’t think there aren’t any multiples, and don’t think that the lowest multiple will always be the denominators multiplied by each other…
BACK TO THE PROBLEM: Ok, do we found out that the lowest common multiple is 24. To get the numerators: You have to multiply 5 by 3. Which equals 15. So the new fraction is: 15/24
The next fraction: Since we multiplied the denominator by eight, we have to do the same with the numerator: 8 * 1 = 8 So the fraction becomes: 8/24
After you do all that you add them because that’s what the problem says to do: 15/24 + 8/24 = 23/24
And you can’t simplify that so that is your answer.
Reminder: What ever you do to the denominator, you have to do the same thing to the numerator!!!
with adding fractions, first you have to find a common denominator of both fractions. A common denominator of 5/8 and 1/3, the common denominators is 24. You then make both of the fractions equivilent but have the denominators of 24. 1/3 would then be 8/24 and 5/8 would be 15/24. You can then add the two fractions. 8/24+15/24=23/24 the answer is 23/24
this is for 2.1 for C.K. and A.H. I think that numbers that you would call "fake numbers" would be numbers that are non terminating numbers that are evergoing. This is because they are evergoing and there is no actual way of knowing what their actual value is. However, I don't think they'd be fake numbers, because they have a value, but just not a value that could be put on a real number line. I hope this helps.-A.L.
there are no "fake numbers" that i know of. however i think that there are names for the numbers that aren't possible like negative zero. i hope this helps.
J.B. to M.G. i think that i can help you with the problem 5/8+1/3=?. The first thing you have to do is find the lowest common deniomenators that 8 and 3 both go into. That would be 24 so if you do 8x3 you get 24 and what you do to the denominators you have to do to the numerator so 5x3=15. So your new fraction would be 15/24 now you have to do 1/3 so 3x8=24 and what you do to the denominator you have to do to the numerator so 1x8=8 so your new fraction would be 8/24. so now you have to actually add the fractions 15/24+8/24=23/24 now that you have the answer you have to simplify 23/24 which is 1 and 1/24.
I no there are not fake numbers but I do not understand what you would call a number that is not real, and can you give me some examples of numbers that are not considered real?
first of all, a real number is a number that can be graphed on a number line, there are not really, fake numbers but there are numbers like pi where the decimals go on forever, which is inposible to graph on a number line.
14 comments:
J.B.
What i am having trouble with in this chapter is with factions(adding,dividing,mulitpying, and subtractiong stuff like that.) The problem i do not understand is problem #91 on the mixed review. It is on page 70. Te problem is:
5/8+1/3
A.H
So, I understand that real numbers are any numbers that can easily be plotted on a number line, but what truly is a real number? Even though pi is a non repeating, non terminating number, it can't be plotted on a number line. Does this mean that pi isn't a real number? If you take a number like infinity or the square root of -1, these things are real, but they have no definite value. This doesn't make them fake does it? If all of these are real numbers, how do they fit into a number line, and if they aren't, what are they???
C.K.
what is the differance between real numbers and like... fake numbers? we were talking about real numbers in class and they are posative and negative and zero. they can also have decimals so what would be a "fake number"?
VB to JB
what you have to do in this problem is to find the common denomminator. ok. so lets use the problem that u gave in ur comment.
Ex.
5/8+1/3
so the common denominator for each of these fractions is 24.
so what you do is 5/8*3/3. you have to do this becuz that's how u'll get the denominator to 24. so the answer is 15/24.
now with 1/3...u do the same thing execpt u multiply it by 8 becuase 3*8 equals. so the new fration is 8/24.
then u just add straight across.
15/24+8/24=23/24
the denominator will always stay the same only when ur adding fractions.
=]
C.k- THERE IS NO SUCH THING AS FAKE #S!!!! real #s cover all the #s so there are no fake #s!
C.K. to J.B.
problem #91 all you have to do is find least comon denominator for the two fractions. ok so the smalest number 3 and 8(the denominators) are both a factor of is 24. 8x3=24 and 3x8=24. now you would have to multiply the numerator by the same number you multiplyed the denominator to get 24. 5x3=15 and 1x8=8. the new fractions you will have to add are now 15/24 and 8/24. 15/24+8/24= 23/24. wow! that was long and kind of confusing but i solved the problem =]
C.T. to J.B.
Ok. First, you would have to find the lowest common denominator. (lcd) To find this,you would keep adding 8 to itself and 3 to itself, until you find a commmon number between those two numbers. Once you do that, you need to find how many times you added 8 to a number to get the lcd. That is the same for 3. Here is the example.
8+8=16+8=24
3+3=6+3=9+3=12+3=15+3=18+3=21+3=24
You should have added 8, three times to get 24 and you should have add 3, 8 times to get 24.
After you find the lcd, and find how many times you multiplied or added 8 and 3 to itself, you multiply the number of times you added to get the lcd by the numernator.
When you did this, you should get two fractions that have the same denominator. Your new fractions should have been 15/24+ 8/24. Now, all you have to do is add 15+8 and you get you answer. You should simplified after you get you answer also.
I hope this helps!
JS to JB:
With the problem:
5/8+1/3
You have to find the lowest common multiple:
The lowest common multiple in this case is:
24.
8 * 3 = 24
3 *8 = 24…
Now don’t get confused, when you take a glance at the problem, don’t think there aren’t any multiples, and don’t think that the lowest multiple will always be the denominators multiplied by each other…
BACK TO THE PROBLEM:
Ok, do we found out that the lowest common multiple is 24.
To get the numerators:
You have to multiply 5 by 3.
Which equals 15.
So the new fraction is:
15/24
The next fraction:
Since we multiplied the denominator by eight, we have to do the same with the numerator:
8 * 1 = 8
So the fraction becomes:
8/24
After you do all that you add them because that’s what the problem says to do:
15/24 + 8/24 = 23/24
And you can’t simplify that so that is your answer.
Reminder:
What ever you do to the denominator, you have to do the same thing to the numerator!!!
E. Mu. to J. B.
with adding fractions, first you have to find a common denominator of both fractions.
A common denominator of 5/8 and 1/3, the common denominators is 24. You then make both of the fractions equivilent but have the denominators of 24. 1/3 would then be 8/24 and 5/8 would be 15/24. You can then add the two fractions.
8/24+15/24=23/24 the answer is 23/24
this is for 2.1 for C.K. and A.H.
I think that numbers that you would call "fake numbers" would be numbers that are non terminating numbers that are evergoing. This is because they are evergoing and there is no actual way of knowing what their actual value is. However, I don't think they'd be fake numbers, because they have a value, but just not a value that could be put on a real number line. I hope this helps.-A.L.
CVDV to CK
there are no "fake numbers" that i know of. however i think that there are names for the numbers that aren't possible like negative zero. i hope this helps.
J.B. to M.G.
i think that i can help you with the problem 5/8+1/3=?. The first thing you have to do is find the lowest common deniomenators that 8 and 3 both go into. That would be 24 so if you do 8x3 you get 24 and what you do to the denominators you have to do to the numerator so 5x3=15. So your new fraction would be 15/24 now you have to do 1/3 so 3x8=24 and what you do to the denominator you have to do to the numerator so 1x8=8 so your new fraction would be 8/24. so now you have to actually add the fractions 15/24+8/24=23/24 now that you have the answer you have to simplify 23/24 which is 1 and 1/24.
C.K. to R.S.
I no there are not fake numbers but I do not understand what you would call a number that is not real, and can you give me some examples of numbers that are not considered real?
E.H. to C.K.
first of all, a real number is a number that can be graphed on a number line, there are not really, fake numbers but there are numbers like pi where the decimals go on forever, which is inposible to graph on a number line.
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