Kit
-
Posts
44 -
Joined
-
Last visited
Content Type
Profiles
Forums
Events
Blogs
Classifieds
Store
Posts posted by Kit
-
-
36 minutes ago, Roadrunner said:
What is your goal with AoPS? There are other prealgebra programs that will teach you the material if you are looking at passing certain tests.
AoPS is great for kids who want to pursue math/physics degrees, but is an overkill for the majority of children both in terms of difficulty and the time commitment that is invariably reducing time spent on other subjects they might be more interested in. I am not sure how it’s going to serve you. Are you doing it just for fun?
I have always been interested in maths. I am almost 60 and my own education was patchy and truncated. I have read a lot, but not maths or science.
I would love to understand maths, how it works, how to use it. Could you track viruses, predict earthquakes? And just the sheer fun of finally tracking down that x! I may never get there, but that’s no reason not to try. In fact if I was honest I would love to give myself a classical education, but I probably don’t have time normally (lockdown hopefully being an exception). So I decided to concentrate on maths. And I chose AoPS after much research as I want to understand the stuff rather than just learning how to do stuff.I am also doing maths reading. I just got a book out of the library called “Alex’s adventures in number land”, and a friend gave me a book she used with her kids called The History of Mathematics. I will be reading those too.
-
Hello again, from lockdown. I will be locked down for the next 4 weeks at least, so I am having a ‘maths camp’ in my house!
However AoPS Pre Algebra is not going well. I am doing each chapter twice and still getting at least 50% of the exercises wrong at the first attempt. I usually understand the answer when I read it, but I don’t get there by myself.
so.....I have taken advantage of AoPS offering beast academy Online for free for one month and have just started BA level 4. This is, sadly, not too easy! I do get everything right, but I do have to learn it first. Once I know what they are talking about, I can normally do it. But there is so much that is new to me. I may not get through the lot in a month....I have decided to work through EVERYTHING.....but it’s only $15 for a second month, so I will see how I go.
As to how I do it, I don’t like the cartoon books, so I read the instructions for the lesson, watch Richard if the lesson has a video, read the instructions again, and go for it. You normally get 2 attempts at a question, and only once have I not been able to get it by the 2nd attempt. I’m doing every lesson in every chapter because I don’t know where the gaps are in my knowledge, and I don’t want to skip something that later turns out to be important.
I hope you are all keeping well in these weird and unprecedented times. Take care and look after yourselves.
-
I got it! Thank you for the tip off.
i wallowed a bit 2^n =1/8 2*2*2=8 gotta go fractions....so negative? 2^-3?Tested it 2^-3 =1/2^3 =1/8
The I realised, after a bit, looking at the above, what we actually needed was 2^12=8^n and then simply negate the answer.
so this is my working
2^12 = 2^n*2^n*2^n (negated)
= 2^n+n+n (what 3 numbers added make 12?)
Thus 2^12=2^4*2^4*2^4 =8^4(negated)
And 8^4 negated is 1/8^-4. One eighth to the power of negative 4
phew!
Thank you for the tip off, I appreciate it.
-
1 minute ago, Caroline said:
Think of how to express 1/8 as a power of 2. 2^what=1/8
Thank you. I’m off to the sofa with my notebook and a cuppa to consider this.
-
Just now, Caroline said:
3^(-3) is 1/27 not 1/3. 3^(-1) is 1/3.
Seriously! An arithmetic mistake! Opps! Thank you so much.
while you are here, you couldn’t please give me a hint on where to start with
Express 2^12 as a power of 1/8
Not the answer, just an angle of attack please.
Thank you.
-
Hello mathy people. I have a little “why am I wrong” puzzle for you.
Find k.
3^3+3^3+3^3=243*3^k
my working
27+27+27=81. 243/3=81 3^-3=1/3
thus 81= 243*3^-3
Their working.
3^3+3^3+3^3=3^1*3^3=3^4 243=3^4*3^1 We need to get rid of the 3^1 thus k= -1
As usual I can see why their way works, but not what I have done wrong with mine....
Thank you.....
-
Im into chapter 2 and I’m enjoying squares, and I just thought I would tell you all that the next perfect square year will be 2025 which is 45^2!
And I worked that out all by myself by counting on perfect squares from the easy one of 40^2 (1600...easy) and then each one more iswhen a is the year
a^2 + 2a + 1
thus counting on from sixteen hundred in perfect square years we get
1681 (41^2)
1764 (42^2)
1849 (43^2)
1936 (44^2)
2025 (45^2)!!!!
Can you believe I just spent about an hour working that out just for fun! 😅😅😅😅😅
I never thought I would do sums for fun! Thank you @square_25 and others who are helping me on this journey.
-
6
-
-
1 hour ago, EKS said:
OP, one thing that I sometimes do when I get mucked up the way you described is to substitute smaller/easier numbers. So in the case of your problem, if you substitute 10 for 37037, you get 6 x 10 = 60 and 27 x 10 = 270, and it becomes easier to see what you did wrong with the 21 (because 21 x 10 = 210 and 60 + 210 = 270).
Yes, this is a really good idea, and I need to remember to do this. 😀
-
31 minutes ago, Lucy the Valiant said:
(Threads like these make me so happy. I was convinced at a very early age that I was "just bad at math", which is why it seemed hard to me. As an adult, in an effort to truly help my own children, I have given "Dreadful Math" another chance, and . . . oh, I'm just so thankful! It's BEAUTIFUL and MYSTERIOUS and TANTALIZING, not dreadful at all! (And it has even informed my faith, too!) And there are ever so many ways to keep puzzling through and people to ask when I am stuck. I can actually say with enthusiasm that I now LOVE math, even though I am still self-educating through high school stuff. 😉 I share this just as an encouragement - so much joy in this journey. I am currently in pre-calculus and QUITE EXCELLENT at algebra. A statement that - if you knew my childhood - is truly astonishing. Here's to all the students and all the teachers out there, no matter how old or clever you are.)
Thank you for posting Lucy. It makes me very happy, and it’s very inspiring to hear another math ‘duffer’ has found her way through and to Pre Calculus no less! How exciting is that! Maybe one day I will be writing a post like this to encourage others on this mathy journey.
-
1
-
-
1 minute ago, square_25 said:
Yep, exactly :-). See, they are really not that bad. Multiplication is repeated addition of the same number, and exponentiation is repeated multiplication of the same number :-).
Exponentiation! What a brilliant word. I will be learning exponentiation next !!!
-
3 minutes ago, square_25 said:
The other thing you could do is to keep posting on the same thread... then everyone who's following the thread would get notifications. (Plus, we'd have a fun AoPS Prealgebra thread people could look through if they wanted!)
That’s a great idea if you think people would be interested.
-
Just now, square_25 said:
They ought to define them, I think! They aren't so bad. As a definition,
x^n = x * x * .... * x, n times.
(I'm using the short hand x^n to mean "x to the power of n," which mostly would be written with the n on top as a superscript. But I can't type that into here :-).)
So, for example,
4^2 = 4*4 = 16.
And what are 3^2, 2^3, and 2^4? 😄
3^2 is 3*3. (I just deleted my first reply i did 3*2 =6 🤭) so 3^2=9
2^3= 2*2*2? So 8?
and if the above is correct then 2^4 would = 2*2*2*2=16
-
2
-
-
Just now, square_25 said:
No problem at all! Happy to help :-). Feel free to tag me when you post these, if you like -- my oldest is only 7, so I'm not always on this board (although I am sometimes, since I've taught older kids before and like answering questions about it occasionally :-).)
How do I tag you?
-
Square 25, The next chapter is exponents. All I know about them is squares and that is the number doubled...time 2.....and that is it. Do you think I should bash on with AoPS or do them first with Khan academy, and then try the chapter? I like AoPS and I’m enjoying the challenge and the little grey cells working, but am I setting myself up for disaster here?
-
Just now, square_25 said:
Wait, wait, i think you're right!! You just need add on the missing bit.
Yes...got it whilst you were typing! Thank you so much for your help square. I’m feeling so much better now. We got it worked out!
-
1 minute ago, Kit said:
An easy way to do 21* 37,037?
well 10*37,037 would be easy...370,370. So double it and add another 37,037?
Lets see if it works
370370+370370= 740740 And 740740+37037=777,777 😥 wrong......back to the drawing board. I’ll be back in a moment ........
Oppps....plus the 222,222!
Now it’s 999,999!I get the rotten egg award for that one 🤣🤣🤣🤣🤣
-
Just now, square_25 said:
Right! But what’s an easy way to figure out 21*37037? 😉
An easy way to do 21* 37,037?
well 10*37,037 would be easy...370,370. So double it and add another 37,037?
Lets see if it works
370370+370370= 740740 And 740740+37037=777,777 😥 wrong......back to the drawing board. I’ll be back in a moment ........
-
Ohhhhh oho oh oh oh oh oh.....I think I have it!
I was just reading through the post to check for silly spelling mistakes etc and I think I saw the answer.
I multiplied the product of 6*37,037 by 21 not the 37,037 itself! Is that right? Is that what I did wrong?
so I should have multiplied 37,037 by 21 and then added the 222,222?
obviously their way is simpler. 🤣☺️
-
There is a question I don’t understand why my way of solving it is wrong. I can see that it is, and I even used a calculator to check it was and it wasn’t just an arithmetic mistake.
I also understand what they did and why it works, but I don’t understand why my solution doesn’t also work.
The question. The number 222,222 is equal to the product 37,037*6. What is the product of 37,037 and 27?
AoPS solution is as follows: Because 6 times 37,037 is 222,222, we know that 3 times 37,037 is 111,111. So we have
27*37,037=9*3*37,037=9*111,111=999,999
I understand this and can see why it is correct BUT I don’t know why my different solution didn’t work.
My solution. The difference between 6 and 27 is 21 so the product will be 21 times bigger than 222,222.
so. 222,222*20 plus another 37,037 making 27 times 37,037. But I was really really wrong! Why?
Thank you. 😀
-
adult learner AoPS pre algebra. Chapter 1, Second attempt. I thought I would let you all know how I am getting on.
So.....I started the book again. I read every word. I did the learning questions one at a time and then checked my answer before moving on. I did this because the learning questions are progressive, and if I misunderstood one then it throws the next one off. If I didn’t understand I went over it working through the steps until I did.
I also started a note book and noted down the rules we proved, plus anything else I thought I ought to remember. I gave myself permission to check this notebook whenever I wanted. And....I tidied up my work, instead of scribbling on sheets of scrap paper and the backs of used envelopes, I brought myself a maths book (actually next time I won’t use squared paper, a lined workbook will be fine) and I wrote all my working neatly. If the AoPS working was different I laid theirs out beside mine and compared the two.
the result this time has been much better. I made it through the review questions....even 123,123/1001.....and I have started the challenge questions. I have done the first 3 and got them right (apart from a silly arithmetic mistake in one), and I am going to try the rest tomorrow. I may be back...by the look of them some of them are a bit gnarly!
Thank you for your help and support and encouragement after my last post. It may be that I have to work through each chapter twice! We will see how it goes. Thank goodness I don’t have to work to a timetable or get credits for a year or get to Calculus in however many years. I rather think it may take the rest of my life to get to calculus 😅.
-
9
-
-
3 minutes ago, square_25 said:
Hahahaha, perfect!!! And yes, uhmm, let's use apples or something, so we can split them evenly if need be.
OK, so you were asking a couple of questions.
1) Why is 1000*123 + 123 = 1001*123. Do you see why that is now, if we think in apples?
2) Why is 1001*123/1001 = 123. Do you see how that works out, if we're splitting 1001*123 between 1001 people?
In my opinion, getting this kind of visual for the operations, and getting used to thinking of them this way, is precisely what takes you from fumbling about and using whatever the teacher tells you and actually understanding things. And I'm really impressed you're doing this!! I hope that one day I get the energy to do this for the stuff I didn't learn well in school...
Light bulbs are pinging on all over the place. Thank you, and Regentrude as well for explaining all this. Just wait until we get to the challenge questions 🤣🤣🤣
it seems you had a great education, in maths at any rate. I am nearly 60, and semi retired. I thought learning maths would be a nice little hobby, 😉
-
3
-
-
7 minutes ago, square_25 said:
Perfect :-). And what does dividing by 1001 mean?
Well.....now we have those 123,000 bottles in a big heap and we have to divvy them up into 1001 crates. And if they don’t fit exactly some crates will be short if we put the extras in some crates, leaving others with one less, or..............we have to start smashing bottles and spreading the shards around evenly 🤣🤣🤣🤣🤣
This doesn’t sound like a very mathematical explanation......nor very useful if you want to use the bottles........
-
1 minute ago, square_25 said:
Don’t apologize, please :-). However, I’d like to make sure. What does 1000*123 mean to you, in words?
Ummm......in words!
1000 lots of one hundred and twenty three. Is that what you mean? So if I had 123 bottles in a crate it would mean I had one thousand crates.....and 123,000 bottles altogether........?
-
1
-
-
7 minutes ago, regentrude said:
You're not stupid. You just had an inadequate math education. Do not apologize. It's awesome that you are working through this.
123(1000+1)/1001 = 123x1001/1001 = 123 x (1001/1001)= 123 x 1=123
So yes, basically we can cancel the 1001 because it's both in the denominator and the numerator
So 1001/1001 is 1.....of course it is!!!!! Because 2/2 is 1. Ha! 🌞🌞🌞🌞🌞🌞🌞🌞🌞
-
1
-
AoPS Adult learner. Failed with Pre Algebra.
in High School and Self-Education Board
Posted
Sadly, no I can’t. I know there is a method, and I am not really supposed to do all those huge calculations, but my mind just doesn’t seem to retain it. With BA, I am learning different ways of doing things. I learnt yesterday about the ‘area method’ for long multiplication. Cool!
and I am regaining my confidence, which the first 2 chapters of pre algebra had really knocked!