..The Number Line Wasn't Going to Move for Me, So...
.. As I've learned arithmetic and other math I found that there are some ways to make it considerably easier to learn, allowing the possibility that I will speed up and suddenly, oomph! As I find more and more of these motifs that simplify and speed up a seemingly complex math it becomes more and more as if I just learn enough of these motifs and all Math will be mine, even a cheese sandwich!
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Here are some tips and types I've invented or used that may much speed up your foundations of math.
ADDITION & SUBTRACTION
To add columns of many large numbers a good trick that makes it so you can add large numbers without error is to write them on paper then add the numbers say in the first column on the right and after perhaps five numbers draw a line from the fifth number on the right to the right away from the column and sub total the column. Repeat this for the next five numbers down, draw the line and the sub total, continue doing this to reach the bottom of the right column, all you have to do then is just add your sub total numbers, authorize your #at the bottom of the big column as you usually do and carry your 10 or other number to the next column, then repeat the same with this second column from the right, subtotaling each four or five numbers and so on with your numbers sub total on the right with different length of your sub total lines for each column so you can add your sub totals well. All the lines of each column from the big list of numbers that are the same length for that column in the line also reach inward to find the exact number that's underneath the last number you've sub totaled. For more subtotal columns the lines can also reach subtotal columns on both the left and right. This method improves your ability to add large numbers about 50 million billion % with a margin for error of just +or -0. This is of worth on paper because if you missed just one number when you type with the machine your whole love's labor is often in cyberspace, but with this method you have a way to prove your labor more reliably by just reading over the sub totals.
-Another good way to learn addition and subtraction of smaller numbers is to take a number say like 99 and start subtracting say 7's. 99-7 is 92 because 7 and 2 make 9. 92 - 7 in turn is 85 because 7 is 5 + 2, and just by subtracting the two from 92 only five more is needed is to subtract to find the answer. So a more unpredictable pattern of seven is simplified to the more predictable motif of 5 + 2, and this is easy to visualize for memory by picturing the two part above the 90 of 92 and the five below it being half of the distance between 80 and the 90 which is also easy to remember so the subtraction of 92-7 is easy to visualize and remember. To then subtract the next seven on the list that is 85-7, since the 85 also has a five and five is a major part of seven once the five is subtracted from 85 to make the total subtracted just subtracting two more from 80 is the answer, 78 and this is also easy to visualize by the same trick.
This is also a good way to practice with all the addition and subtraction, because you're learning a regular pattern always associated to your number like 99 you started with. This is better than say just learning 7, 14, 21, 28. . . for adding sevens up because you're only learning how to add sevens that end on seven and not like the first number seven + one or eight which you would then add sevens to (8, 15, 22, 29 is a good way to achieve it) and most importantly because you're doing it systematically. If you start with of the same number all the time whether it's 99 or eight that you make a regular motif you build on with each go round. If you don't have regular motif you can't know what your getting as well, a dumb math devil you know is better than a math devil you know!
-Another good reason this method of learning subtraction and addition by use of an anchor number and then always adding or subtracting the same amount from this number this number + 1, this number + 2... and so on, is that instead of saying 99-7 is 92 and 92-7 is 85, you just say 99, 92, 85, and so on sort of like learning multiplication tables but with the addition or subtraction, and it's the most fast simple and reliable way by memory to learn addition and subtraction I've found. This is used with methods like visualizations or wild memory motifs (Click Here For More Solid Gold Memories/My Comedy Machine) you repeat while you build up your math foundation. Like with math, a cup a cheeze in your RV helps ants have a balanced marathon of fitness if when visits with our great antdoors, a spelling bee is ant-ernational!
Just as a road is not disproven by a Mazda, a method like the above for addition is more of value than a machine for the worth of common to common sense, and books are not on the way out because the web causes overuse and this has been linked to depression, for a simple way solve the web overuse delimma Click Here.
...As I say there are many things the web can't do, this site is about much more than math, higher learning has many complex realms that only proffs would achieve without this site, which is of worth for many other great truths in life, like if you choose My Comedy Machine, a related site method to brilliant conversation I've invented. Uncommon sense has value too. Typing in the web in moderation is good and indeed This Is A Web Machine, so thanks for making this site number one in the math list of the web.
This is why goats are with math, they ate the memos! .
Multiply Up Your Power Boost
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In order to learn multiplication tables the fastest it's important to remember about the last number of each multiplication number. To learn multiples of 14 for example if you look in the Bot you see what looks like the somewhat daunting numbers 14, 28, 42, 56, 70, 84, 98, and 112 and so on. The reason this is easy to learn with a bit of what and know-how is because you're always at the last numbers the same, that is to say when you add the 4 of the first 14 to the 4 of the second 14 to make 28, and then 14 to that 28 to make 42, the last numbers of the digits, the 4, 8 and 2 of 14, 28 and 42 are consistent no matter what the first digits are you're adding if you also start with the same number. So if you were adding multiples of 5 it goes in cycles of ending in 5 or 0 or if you're learning higher multiples of 14, the last digits go in cycles five or 10 numbers round so the cycle repeats when it reaches zero. This simplifies learning the numbers because mostly all the complexity is replaced by just repeating cycles and some more numbers, the tens and hundreds that change more slowly, by memorizing these motifs you learn them and other ways of math faster. Since it's good to break the multiples up into groups of fives to memorize them while you count them on your hand , the tens are easy to remember, just add 0. To find the fives fast just half the number and add 0, 14 5's are 14 times 1/2 with 0 added (who says you can't add 0!) or 70. So instead of all the numbers of the multiples, your 10's and fives are simple, 15's are just the 10 plus the 5, and the 20s are just 10 times 2 plus 0. If you go say five to 10 or 10 to 15 all you have to learn more deeply is the 6,7,8,9 multiples and the 11, 12 13, 14 multiples, the 5, 10 and 15 are easy and this reduces the amount of memorizing needed to learn it by about a third. Of course learning the end numbers helps a lot too. The only numbers that don't repeat and reboot at 0 after 5 multiples are 3, 7 and 9. Thus it's important to spend the most time memorizing threes 7's and 9s first by the methods on this site. 7's in particular need the most memorizing because unlike 3's they are more distance to the next 7 so they're more achievable by memory, it's easier to add three to find the 3's but seven is both odd and not near. This is why 3's are themselves are a bit tough, they need practice too. A good way to do threes is to add twos plus one, like to know the days of the week it's good ro add in twos or twos and the one. For dates like with my opthomologist she says she loves my handwriting she's so great to see! To memorize sevens it's good to memorize them based on what you already know. 7 4's are 28, because 7 2's are 14, which you know well, and 14' 2's are 28, so if you learn these two motifs at the same time where you read and write them, both by comic methods and by the Letter Method, LM, see below for how. Another good way to learn 7's is by 5 + 2, 4+3 and so on. It's important to realize you already know a lot of math, so going over the basic stuff like this you already know will help you learn fast. For example 15 4's are 60 and so are 12 times 5. When you see the same or = results like this with other causes be sure to take note in your AZ book, and memorize this more deeply too.
Since the higher faster arithmetic is built out of the basic 1-9 digits like a brilliant guitarist who never stops playing scales and other exercises, many good math geniuses never completely stop with the basic 1 to 9 motifs, and I certainly recommend alternation here and with and higher math motifs on a regular basis, especially with the always right answers of the math machine like a calculator, see below. Another good way with the machine is to reverse all your operations with each step both to see if you're right and to see the same problem in another light. If you have more than one way to remember and learn an idea it stays with you, just as cleaning a room is much more sure if you look at it from close up and at a zoom. When you have the machine in hand try to think of the solution before you read it out. Take notes in your book about what needs labor, and spend more of your math time with the improvements. When you're without the machine 1/4 of the time you're using your memory more so skip the guess and just do your best. As I say about my comedy machine you can make words out of letters for the numbers 1-9 and just say the word when you want to remember or subtotal it while you're doing a problem. In amazing memory feats there are those who can remember say a 60,000 digit number, even so the geniuses with words (like vocabulary) have done even far more amazing than this, and the authors of the comics say they almost always go by words to make the action not the other way around with the actions to make the words. Thus having a word to remember the number like a subtotal with while you're in the middle of a problem is a good memory aid for the genius bit and comic words with the math machine are even better, especially if you use the more dug in wild words to remember your foundations for longer term reliable buildup. It's not so much wild moves that win, it's wild moves used most efficiently.
14 and 7 are 21 but 14 times seven are 98 even though they both start out sounding the same which can give you a wrong answer otherwise, be sure to always note distinctions about sound alike motifs with different results while you practice, and multiply up the abount of time you spend on these motifs because like when you learn an instrument, some of the tune may take more labor to learn than the rest, so you must make more labor to learn these, thus in real time you aren't learning fast and then have to slow down for 10 minutes because you goofed. Remember with each go round of practice that you're not just trying new numbers, they're important too, but mostly the ones you're most familiar with and add more to these by way of the machine and other ways like absurd words while you learn new stuff. Don't try to be a math hero genius especially at first, be strong, slower but surer. Always keep the machine handy so you can easily see and remember the numbers well, this is a good memory aid, be a genius when you can only after you're more than 3/4th sure you are savvy for the given type of problem. Once you can do well without the machine, don't stop using it. Instead find a somewhat tougher and or higher speed problem and learn it till you know it 3/4 well and repeat this cycle. This is also good to continually refresh your memory for arithmetic maintenance because they say memory like in the memory Olympics is more like a muscle you flex than like where you either know it or you don't. Obviously you can't just spend all our time at the machine to learn math, but it's fun to achieve more when you're already using this method so with each go round your math depth is at higher and higher resolution and broadens!
This is good for math basics and can be used for higher math with the Programmed Math series of books, e.g Programmed Algebra by Robert H Alwin and Robert D Hackworth.
These Programmed Books have all the right answers for more complex math, in gradual steps of many questions and answers right on the memo, complete with exams where you must pass more than 3/4 with each level. While it's not true that all we learn is self taught as some have said much of what's called brilliant is just by way of finding both deeper and slower learning and outside sources that are more robust, and then with higher speed and more. Certainly you can't learn as well in any subject like math or television! without learning the basics well and what errors not to make and this is often not possible in a busy math class where you can't even follow what the math lady is saying. It seems especially true with math that you're own your own and this is how to buy a ticket to the world and return with more! The best way to learn this is at your own speed, you read it like a book except going over and over it at higher and higher speed from the start in repeating loops after first making sure you're right by writing down the error if you make a mistake while you read the memo, going over this seperately like with mnemonics or on audio with reps and with reps of the Comedy Machine COMICS..
A good way to do this is to pick a page in the book and read that page watching for errors (like in your number motifs) and write your errors with the page number in a booklet of blank paper taped in the front of the book. If you have a book like my Programmed Algebra book that's paperback and not well bound, just write a one word name about the page and the page numbers where you'll look up in the front of the book and then write your notes in the top of each page "in" the book for longer life of the book which may cost 20 or 30 new, used you may find it for 5. Take these motifs to boost and after you save up a batch and read over them with the right answer, then record them with a voice recorder in question and answer form and also rearranged in other ways e.g. first with the answer than the question or with numbers and words to fill in. Try to use the optimum number of reps. You'll remember much faster and better with this method (by recording song improvs block by block and then asking myself question and answer like science causology and evidence my memory for music was boosted 3 to 5 X.). All you have to do to improve reliably is read and listen to the audio while you do your other labors. If you go in loops of like this of error and improvement, with time and watching, then listening more indepth, your speed will speed up and finally you'll triumph at math. (For a morale boost put higher math memos from whatever site you want to learn on your audio memo or other stuff like comics or prayer with the number motifs.).
About half the answers in the Programmed algebra books are of the marms alarm, to find them, just use the adding machine or the web, and no doubt reverse the operations. One good thing is if you have questions look in the Programmed (math volume's) index, turn to the page where the solution is and continue your edits to improve, truly as they say in the Programmed book it's more like reading any other book to learn math. With the programmed method you'll be given many ways to look at the same idea so you'll be able to learn your more basic math well while learning higher math even if you learned it wrong in the old days, moms so wise in 2009! If you're unsavvy about the Programmed answer in the book Berlitz language says audio has been found to be much more memorable (As memorable as TV? No when you rewind and repeat something more brilliant you remember it better than TV while you're asleep, Real sleep learning, sort of like how a hen rents out feather beds filled with air!)..How To keep Track of Your Audio Memos While You Save a Boucoup of Hens!
It's good to memorize the truths about math, and going at your own speed if you learn it right has been found to be most conducive to learning. Many people say they couldn't do math well at all without the Programmed Method books and these have won many top prizes and awards no other method I've heard of can match for more complex math like Algebra and calculus. Actually polymaths who speak 20 business signs say algebra is much tougher than calculus once you've learned the basics so cheer up if you have math with tears, the math boss may be you if you love to revv up your opera pumps up the superhighway!
No doubt while taking a course is good, learning at your own level is often more of value, these methods are cheap and research shows that learning is improved the best when you learn for like a week and come back a few weeks or months later. When you take a course due to the cost, you often have to study so much so fast you learn it wrong. This is often not true with other courses like history. With an unintuitive subject like math that's complex and abstract the problem is you may well learn it the wrong way without using another method like the Algebra Programmed so first you have some general idea what the marm is saying and you won't be left behind. I often wonder how marms in math couldn't be amazing without us! Why not just take a course online? Online the answer is not always easy to find. With the Programmed Method you're always sure, so first the general way and if you have real nonwimpy questions may be the Programmed method, you can always find it in the book, outdoing even the web. Once your foundation is solid, then take the course so you can reinforce your knowlege, or perhaps not if like for most it's actually not viable to learn math well from a course.
...I recommend using ridiculous memory associations (as On This Site, MY COMEDY MACHINE.) to learn numbers like multiples for the reasons on This Link and writing them down. The best way to write them down is to use an index, make or buy a blank book of paper and the number the pages 1 to 100 or higher, then to remember the Memory methods for 27 or VHS you've thought up, you just look in the book under 27. While no doubt all these motifs are of worth in combination and seperately, there are no seperate combinations in elevator math!
..How do you know if you have the right answer if you multiply divide add or subtract a number or large number? A simple "cheap" way I use for multiplication is to just multiply the two numbers on the right side and see if the last number of the answer is the same, for example to multiply 99 by 27, this is easy by the general to specific motif; 100 times 27 or 2700, minus the one extra 27 (the number you add or subtract is always the one that's unchanged [27]) or 2673. Here's how to see if this is alright in any sense of the word number line! In 99 times 27, the last two digits of 7 times 9 when multiplied are 63, and the last digit of the answer, 2673 is also a three, so the chance is only one in 10 or perhaps one in five with the other numbers of 2673 that the answer is wrong, this is a method that's cheap and fast to know if your answer is at least not wrong especially if you know it in general, or for use if for example you're in a hurry or you know the answer has to be exact, or you're mostly sure already that you have the right answer. The general to specific method is a good use for multiplying, dividing, addition and subtraction. It's one of the easiest ways to go from general and then zero in with each go round (like science with the scientific method).
People say I'm somewhat amazin to know the answers in math or etymology. While I realize I must labor in math and life, may they be blessed with rest like realtors when they count roofs above not sheep if the roof holds more moss..If people eat no more than real hotdish in the RV, this is like in millions of years in evolution, actually I use representative math to be good here, not when I'm out west since I can't be out west here!
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CASTING OUT 9's ANOTHER WAY TO PROVE YOU ALREADY WERE SO WEBWISE
A more complex but more reliable way when used in combination to proof your work is by what's called casting out 9's. If for example when you're multiplying 32 times 74=2368, in casting out 9's adding the 3 and 2 of the 32 gives you 5, and the 7 and 4 are 11. If you then multiply these two numbers 5 and 11 =55 and divide by 9 you have a remainder of + one . To see if the answer is right you also also add the digits of the answer, adding digits of the answer give you 19 which also when divided by nine leaves a reminder of + one. Adding the digits of all three numbers, 32, 74, and 2368 is a way to see if it's the right answer by way of the same remainder when divided by 9. It's possible this is the wrong result by this method but the probability of is it is not large. Casting out 9 's is of worth for seeing any of the four operations of multiplication division addition and subtraction are correct. For example to know if to subtracted numbers was the right answer you add the digits of the numbers to be subtracted, and the answer, subtract the residues of the numbers you subtracted and divide both sides by nine. If the remainder is the same, it's probably the right answer.
How To Use The Web To Learn Math If You Don't Have Much Time For Math But Still Would Like To Wind Your Way Up To Higher Math With Multipliers and A Winch
....If you're like me and just never had time for math and taking a course seems too high priced and boring a good compromise may be to find problems of the sort you've been most interested in, then type in the search for "that math~ problems and solutions" so you can at least see if you are savvy and find the general drift and even get good at solving the problems as you improve. Be on the lookout for underlying motifs that may be the key to the entire solution in general.. For example percents seemed a problem for me till I realized to find say 27% of 200 just find 1% which is 2 and multiply by 27 so the answer is 54, this simple motif gives you many types of percents and makes it easy to do much here.
To become a genius at anything the first step is just to be interested in it they say. This is why I recommend vocabulary and learning rote by rote like from a websters of math. To learn the basics of a field of math you know nothing about but may want to learn, look at the words in the definitions and see if they remind you of the meaning, an easy way to remember them. For example the word derivative is much like "divide" and this is what a derivative is a ratio of two changing motifs at a given moment. Likewise "integral" means whole and so to remember that integral means the summation of many derivatives, it's "the integral as the overall more general opposite of the derivative". This brings up another important observation. In all of math the most important thing ever seen is how one motif changes relative to another, a "function", so what you learn about functions like ratios improve a lot more faster than anything else you may learn in math. The basic function motif is simple, you have knowns and unknowns, the knowns are numbers like 2 or three, the unknowns are numbers you fill in like x and y. To graph an equation, often you just pick random numbers for one of the variables and plug in one of these, do the operation, and see what your answer is, then plot all the answers, say x and y in the book the first number relative to the second number, rather like with music where you have the general tune and there are ways to improvise that are allowed or not, or like a cyber machine where you put in some numbers to find other numbers, the solution. Often no doubt there are shortcuts to knowing what random numbers to plug in, but it's still the same motif of balance, like energy conservation, what changes and stays the same. If you already know algebra the pros say higher math than this is usually easier. Most higher mathematicians use no numbers higher than 5, and no words like *&$)**&%@$# when in frustration!
The Letter Method For Memory, LM
To learn vocabulary or general knowlege of many types I just buy a Webster's with a strong binder and make a booklet of memos between the outside of the final page and find the words of worth or write them where they would go between the lines if it's a cheap (and easier to carry) volume. I number the words on the outside of the page to find them and then go to the memo field and write the page number of the word (like to learn definitions, or anything with words you want to memorize deep and well not the same as just KNOWING) and the number or then write the word and then the first letter of each word, this is about 5 times as fast as copying the words you want to learn and the definitions, then you can just read the letters like they were words to remind you of the words. For example to memorize 5+8=13, I write this in its list of numbered numbers at the bottom of the page and upward, and the letters for these words in a list from the top of the page going downward both toward the middle. The letters for five plus eight are thirteen are f p e a t, and this has the same number on the list at the top as its numbers in the list at the bottom, the access numbers are on the outside of edge the page to reduce confusion. You can use blanks for more advanced memorization, e.g. 5 and three are 8 can also be F a _ a e or f a e a ? or / a/ a e, with right or left slants to save room. Mostly just the letters seems to work best, and it takes longer with the slants especially with math, even so if you're real serious and ambitious about math you can use the slants for more exercise. A caution is if you do this in ink it will be permanently in your book and it's not all that much better overall. (If you're a genius at math you are excused to earn 75,000!) The Letter Method is useful and easy to learn anything you want to memorize, numbers or letters by alternation between the numbers and letters, with words like vocabulary in websters not so necesary in a while after you know the words well. Math being abstract takes more special "mapping" so alternation between the letters and numbers for each to learn is especially important, like a question and answer, and-AHA! You win more than the brats with their own store, Toys or Else! They don't labor, they celebrate months! (For saving room, I write the letters for words in the margain of the page (like an Americana encyclopedia) with the same numbers for both page memo (words, or numbers like historic dates in my volumes, and so on) to learn and letters, or you can write the letters between the lines where the words on the page you want to memorise are using a bic (the best cheap writing utensil by far, they always write) and the letters to read are about the same size as the print, this is most readable you'll find, perhaps with the slanted letters for the words, and so on.) And by making related or absurd words (As I say how on My Comedy Machine or see more herein) out of the letters for words and repeating these in alternation between the letters, words and acronyms it's faster to memorize. If you have trouble with some word for the letter, slow down the loop with the general acronym word and say, A is for Alice, B is for Betty, or other words you may hope to learn. The reason to use word letters is because it's not only easy to copy the words to learn, it's also a good bit of effort to read the letter words and by making the effort but not too much and where you have it where you are reading these letter-word definitions like a good book, you're familiar with the words even if you know nothing about the field, and you can learn a lot without knowing about math! When you combine this with absurd associations and then write letter memos for these, you can also make easy exercises using the letters like reading them in reverse, going forward and the return and then forward and return more or the opposite, It's an easy way to make effort and exercises to achieve your goals. If in doubt, just rep the word or words in the sentence, sort of a zoom lense of memorization. Your knowledge augments not so fast but more surely which has more worth in the long run (EVEN SO FOR HOW TO SPEED UP THE LM THE MOST SEE BELOW, TRICKS TO SPEED UP THE LM.)
Example;
Say I'm memorizing down the page to memo number 12 and 13;
(12) (listed at the bottom of the page, which is, say) 3=12 over 4 and 4 =12 over 3;
(13) therefore 1/5 of 4 is 4 fifths; the number after "of" in a/b of blank is blank is the dividend ("divide into")
To remember and memorize this better than by any other method I've found, I use the LM;
(12) T E T O F A F E T O T (LM for 3=12 .... and)
(13) T O F O F I F F; T N A "O" I A O B O B I B I T D (D I)..
first to memorize this better I use the number to letter methods seen here to help make a more memorable general mnemonic (sometimes too many T's and F's to make it more memorable, samo old same old, though still of worth (see second post below). For better or best results even so the first number I convert to letters by the method on the link (the others aren't converted to more than the letters for words naming the numbers because, this would be too different to recognize as well, a combination and convention of the two here works best;
Thus for the number (12) I Use the words "a ton (12, one tine has 1, n has two tines) to eat of fat is hoot" for (12) T E T O F A F E T O T; and I repeat the memo "Feed your faith, and your doubts won't starve to death" (an elf (12) is short and not fat!)
And for (13) T O F O F I F F; Time of tofu for Fifi; Mnemonic; Feed your tummy tofu, so Fi Fi will stop growling, more a veggie won't bark!
And
A "O" I A O B O B I B (after "of" in a over b....) might be An Ahh of a blond is a boo boo, if she draws a blank (a/b of blank is blank) but when she draws a great picture, Ohh and Ahh.
And
B I T D (D I).. And old biddy is a devine diva when she dives in (dividend is dividend)
With reps of memnonics like these, it's much more memorable; you don't need to write the mnemonics themselves, just the letters, the reps and the content make them memorable enough, nor is it necessary to use these mnemonics for all you want to memorize, just the ones you have trouble with and perhaps some more for depth, speed, and celebration, often hysterical math. It's easy to make the comics by reading what they remind you of, because comedy and creative memory has a major random element to it like the Letters, and if you know what you're looking for (in the example here I use contradictions on the good side of life, and puns, these are three of the best ways to make mnemonics.). The reason I use the example above was because I was having trouble with remembering about the word Dividend, and for more general familiarity at higher speed. Though the example is to learn a simple math truth, about the dividend, this method can be used to learn anything like math and especially where memorizing is important. I've used it to learn chemistry, foreign and english words, history, physics, stuff "otherwise like math impossible" to learn, especially math, though only some of the time (1/3 of my life I'm asleep or awake!). I've found with a bit of time I can learn about one memo a day via this "indepth" way to learn math, the best I've found in math for the basic memorys. There are 400 items to learn in multiplication up to 20 times 20, and of these you may already know half with the ones fives 10's and 20s trimming another third (see above) and each of these is also to memorize in inverse, and so you only need to learn 150 for multiplication, leaving only about 200 here to learn. In two years of about 600 days this leaves you with 400 more basic number elements you can learn for a lifelong foundation in math, then you can keep repeating the LM on up. This will save you time if you want to learn math because often it takes years to unlearn errors and while you may spend the same amount of hours learning math someone who knows it moderately well may, you learn it with much more depth. Some who author great books when asked how, would say, with all the books to read, the trick is knowing what books to read. So too with math, it's mostly knowing how to learn, at least if you have enough time each month to read the LM beyond a certain level.
For a solid math foundation, don't forget to memorize fractions, negative numbers, hundreds (e.g 12=7+5 "is also" 120=70+50) and practical math like thursday plus 3 is sunday (=4 plus 3 is 7) and axioms too on your wish list of math as you may find you're unaware in common practice and so on. The idea is to first build up solid components with all the elements well powered in memory like a machine to then reach the higher math..
LM To combine with AZ MEMORY
Another good way to learn the basic and more advanced math vocabulary is something you may discover about this. Like a crystal shining on the inside, each angle or word reflects on the rest just so, to change one you change them all. For example one definition often will contain four or five more words, and each of those definitions five more, and these definition words themselves are usually abstract and seemingly nonintuiuitive. With a book like a math dictionary or an AtoZ index where you can ask what the definition is and get the answer in a second instead of having to look it up and print out 50 pages you can't find in a month, and alternate between say the 20 most important definitions, the eureka moment about this is the number of definitions are limited! And sooner or later you reach a concrete definition most based on evidence. This is like meditation with the number machine except for words you can edit. Even if like a complex crystal or a solid that has to have each facet just so in perfection, once all the facets are well learned, you find your savvy is indeed strong like a diamond! How I or others even do well in math without this method I don't even know, even if a lot of the math course with the marm is about arithmatic alone, to get in the general area of definitions how to learn it needs a boost. It's believed by some you can't even think a thought without some vocabulary of some sort to have some idea about what goes on, obviously this would be of worth to carry on a technical discussion with the teacher. Even if she's real nice without some way to somehow wonder well what she's saying, obviously there are at the least going to be moments when knowing the definitions is of real worth sometimes a lot of worth. And no doubt it will help you a lot with reading so you are more and more fluent in the language beyond when the crystal is more flowing. Once you know all the definitions well by the simple meditation method of the A-Z or other high speed access definition motif, you may find more in the higher branches of arithmetic, geometry and math, about definitions. Of course the Toolbox can be used for definitions and formulas, or for solving any other type of problem or improvement, but since you can always find stuff in and out of order by making two copies of each memo with and ABC, one in the index with date and another shorter overview copy synopses in order at the top, you can find all your questions and answers too, so you have it both in and out of order important in order as your ToolBox increases so you can find the most recent memos at the top. You can ask a question about a memo and not know the answer and then build up your savvy the same way a marm does to tell you the answer when you ask her, except you may have a way of finding out on your own years later. Often the teacher may not know and like Edison you may end up with better results because you ask questions like about physics formulas nobody has asked before and found the answer because of your own perspective. In essence this invention of the Toolbox is the same as a person who was good at math who just bought a good Webster's for math in the old days and just written in the margains, but with a machine this has more room for edits and search (good if you have a lot of memos and are good at math) and is more customizable, you can cut and paste the definitions in fast from the web so it's more good for upgrades, like practicing problems right on the memo, so you can read. I've had a lot of trouble with having to erase my errors till would find a solution, with this it's always readable when finished years later.
..About how I've learned I've tried the promises of the memory whizzes and had no dramatic acceleration of my math, so I dug in deeper to where I can learn even math but this combined with the letter for word memo is the best I've found. Absurd living is a real life, couldn't live without it, but life needs a stronger foundation than just guffaws, actually it's good to go in conversation in cycles of evidence, joke and, rhetoric, as on the Comedy Machine link. The good thing about vocabulary and other rote by rote learning, e.g. definitions is it's like learning a foreign language, you learn the building blocks and then you can put the puzzle together, much of what you learn is definitions. So for learning on your own you need to find a reliable source of the classic truth about math, basic building blocks you can learn like by the letter word method so eventualy like my el sis who was learning to be an interpreter, one day she just said, "AHA, I el finally know whata they're ah saying!" For a realiable source of general knowledge you might want to try a math encyclopedia or other reference book, I use Encyclopedia Americana. Other encyclopedias I've owned had authors like professors who would use a third of the words we didn't know and many other useless words. With Americana the words are all common but they aren't dumb and you know this because when they say something like in math that I don't yet know, it either makes general sense or it's like something I already know and because they are an author I trust I know it's worthwhile to write down the motif even if I don't know it yet to memorize it. Because of the way all that I know in them is logical, I have confidence that other knowlege will be of worth to the puzzle when I finally can put it together, even if years or months later, or for more immediate savvy. If there's a goat in an elevator, a 3rd power box of math, he likes The Nanny most on the station! She always cleans up, she charges more because she's worth more. Math and science are more uncommon so I write the numbers and topic to find them at the hoof clop inside the cover of each volume and the general stuff at the higher up to say hay to the neighbors with. This way I don't have to look through all the numbers to find the math and science alone. Americanas are the best by far and they're durable, not so heavy like Britannicas (so more light reading!) and they're more beautious. The Americanas have the whole math course outlined in the index so you can go all the way through learning all the general stuff that's known about math in outline from start to finish, often better explained than teachers or websites, because the Americanas were written and edited by professionals over many years and websites are often written by amateurs. This way by the Americanas you have all you learn in outline and highlighter the rest of your Litelife and by using audio to remember well and deep and faster by reps in question and answer form what you've highlighted in the book from more than one angle. Audio is much more easy to remember (and write) so you can learn it in half hour blocks complete with memory methods, e.g. in relativity proper time is defined as the time near a single clock, To Remember on the audio ask what a boot has to do with a sock, If you put on shoes and socks to stay cozy, but socks before shoes in the heat! Even though the Americanas will give you the general outline I recommend learning the basics well first by using mnemonics and audio like this from a book like Programmed Algebra. The fastest and easiest way to learn is to write mnemonics (and other motifs since familiarity is of real worth to learning too, e.g. if a mnenonic isn't needed or if you don't yet have a mnemonic) record the audio in question and answer form (more than two reps each and in reverse order with the questio now the answer for the second set works best) and then go over the half hour for say five times till you've learned it completely and without error, then go on to the next half hour and do the same. If you have problems or want more depth you can always go back to your earlier audio to refresh, you may find a great morale math boost compared to other methods. See my post below How to Remember the More basic ABC's of Math... And the post following with a more advanced method I've more recently innovated, and for why and how I use more than one method to remember math. Once you've learned all the basics then you can go online and deepen your knowledge and no doubt you can ask questions about what's in the book as you learn and put this on the audio too. Americanas are indeed just the general outline of all the math even if they have authors like Carl Sagan or others who are often bestselling authors about the subject they write about. You may be able to find a set online like Amazon second hand, hope they're often cheaper than a memory marathon for you when you jog.
About the idea that functions are the foundation of math and the two general types of function are the derivative and the integral, one is much like DI-vision, DE-rivative; and the other INtegration is rather like addIN addition or multiplication or summing up. This is important because as they say there's nothing new under the sun. There are often two types of math involved in solving a problem, the function which is often of the form a=b/c or it's equivalent (like b=a times c or c=b/a ect.) and the number facts like arithmatic that fit in general operations like this of the problem. The a=b/c and the equivalent expressions are quite important and will carry through to the higher math no doubt. These expressions involve all four of the basic operations My Dear Aunt Sally, M, D, A, S, Multiplication, Division, Add Subtract (all in this order if you don't know what to do with a complex motif to solve or in general, they say except if in brackets and so on which you do first). Since this is one of the most important basic motifs of math because it involves the basic idea of functions and many other types of math it's important to memorize it well. If you still have trouble with the general logic of a problem, to find out what to do, a good way is to plug in numbers you already know so you can see if the general math is right before you do it the more elaborate way. Since this general equation a=b/c is so important and so general, it's good to use standardized numbers to try it out. I always use 3=12/4, if you use many nonstandard numbers your math reflexes for this important motif are slower in general, and if you have a math exam where you value speed and your math reflexes, it's most optimal to use the same numbers at any rate for this so when in doubt you can plug in fast without having to solve for other nonstandard numbers. It's important to memorize both the general idea and some examples too when you memorize by the LM on you math wish list. For instance to memorize 3x -2x=x, plug in numbers like 3x-2x=x because 3 5's -2 5's are 5 and 3 8's -2 8's are 8, this way you know how the idea applies to the use, by memorizing both the formula and the numbers it uses, you understand well and you also know the more general use.
If you're like me you may have learned the basics either not deeply or in error. To solve this no doubt it's good to write all the motifs to learn right and well in your A/Z with the letter Method to remember. Even so you won't know what you need to improve without a bit of troubleshooting. No doubt you'll find many of the errors to weed out with the LM just in common use of your math, and in reading books like Programmed Algebra. Like me you may have needed more complete cleansing and a good way to do this is by picking random numbers, say 293 times 27 and trying it mentally and seeing if you have errors by checking it step by step with the machine. Any problems you can just write in your AZ LM and add them to your list to memorize, sooner or later you'll have all your errors relearned well and your speed and depth will improve. Don't be afraid to learn numbers like multiples of 3, 7's or even twos or negative numbers like -5 + 2. You often don't know them because you never will till you go over them by a method like the LM, no one can teach you like other types of exercises. General familiarity for me at any rate wasn't good enough, for math. It's important to be on the lookout for motifs of general use and memorize them More Exactly while you're learning if you're positive you definitely know and know it's of general worth. Learn the basic axioms first or if like me you already know a lot of math but the basic definitions were just sort of implied by the "way I learned them" and you want to deepen your memory before you build your math higher, much or most of learning especially like math or music is about familiarity. To learn the axioms well go to the A Z of the authors in the Programmed (or other math book perhaps) and look up Commutative, Associatiave, Distributive, Simplify Expressions, and so on. I find the page and write the letters for the words at the top of it and it's number on the page, and write the name of the axiom and number of that page in the blank in the front of the volume to find where I am now in my progress when I learn as usual. When learning the definitions and axioms it's good to know them well and to note what they disprove and memorize this too. You see in the book where the Commutative Law holds for addition and subtraction. Try to ask yourself questions aboyt the general axioms, like, does the Commutative Law also hold for subtraction and division? That the answer is no is implied by the book, but you're are on more solid ground more by defining the implied uses of the basic definitions so you're more in focus. If you memorize these well, they can be used as a future building block of your math, solid memory is like a Wool of the Wisp at Xmas, cozy to have more heat! Write this about the Commutative Law being of worth for addition and multiplication, and not for subtraction or division and memorize it too by the exercises. It's good to both write and memorise the basic definition, an example or two, and also use the first letters of the words to memorise it better yet and the make a letter for word exercise for this memory aid. For example Commutative Order Reversed, Addtion and Multiplication Not Subtraction oR Division this has it's own letter for word method at the top of the memo. The next number down on the page has, GO wheRe All MoNey iS RaDio! CO=Commutative Order=biz, (Radio waves are the most high priced real estate on earth, like to buy an Fm station, lend me your aurora!). Also make letter for words for this number it and memorize this too. For memorizing where it's somewhat uncommon and tougher to learn at first like this, letters for the syllables instead of words may be better with blanks for some of the syllables to make it the right level of exercise to improve resolution. To make puns fast so the memory words fit the letters of the definition, you can just use your own puns like from websters, better is to use the pun lists as in the COMEDY MACHINE so you're building up in general for conversation and all the other uses, general health of your words as on the link, better memory in general to learn other fields of college, and so on.
So I'm building up this large volume of math comics where I can find just the right comic of many types in My Comedy Machine after someone mentions about it, but how to remember and make the most of them? One of the better ways to read the letters is to set them to sound. This makes an otherwise large and more tedious labor fun and more memorable as had been found about the worth of music in research. You remember at higher speed and with more depth. I think of some good sounds and instead of listing the tune by the memo and so on I list the songs all on one page with codes like SC (=Song Code) WIRTW and on the Song Code memo I list the name of the song the code is for (WIRTW= When I Ruled The World, And How You Will Perhaps!) By using song codes you save room in the Comedy Machine and it's fast to write, and you don't have so many songs you forget and you learn them at the right rate of worth, if you learned too many you would forget them, too few and it's like singing a one memo song all year, you use the optimal amount and reuse them more than once. For the important words or memos, I combine absurd creative memories with letters and other meaning or puns and then list two songs with the Code, one to sing it forward and the other in reverse if it's a list of most worth to remember. If you're not boring like mom and want the real memory she's always active when aware !
For like number mnemonics like to learn 13 5's are 65, the menomics I use for more 13's (65, 78, 91, 104, 117, and 130) are "jewel, coffee, boat, to see her, the doxology and the most" (Click here for easy way to convert letters to numbers, and so on) I imagine a lady in church with a sparkling (jewel=65) (coffee boat=78 91) hat, (to see her=104) sing (the dox=117) ology is (the mos=130)t. Church is not over till the fat lady Sanka's! This fits the five numbers of your handheld Palm Pilot type machine, but to make it more solid at first I break it up into sets of 3. E.g.for these 13's I sing "13's, 5, 6, 7" and then "jewel coffee boat" while counting the same on my hand in alternation, this makes it so I know what and where each number is in the memo I want to remember. For 13's, 8, 9, 10, I just sing this and then, "to see her, the doxology, the most, ect." in alternation. This is both higher speed and your perception will be deeper, perhaps twice as good. I tend to also alternate between the memory song for creativity and just the numbers on my hand without the song for more serious memory, both are of worth, even so singing is often more of worth than a out of tune RV at christmas! The best method yet I've found to remember multiples like this is to first find the words for the numbers, go over them counting on my fingers, repeating the words, and once I generally know them in order mostly, I use the lower number multiples to learn the higher ones. For instance, once I know , 13's 8, 9 and 10, (to see her=104) sing (the dox=117) ology is (the mos=130)t
I practice them in and out of order. For instance to find 9 13's, what are 9 3's? 27. "The doxology" (117) ends in 7, so 9 13's are 117. 13's 1 to 5 are (tame 13) (noah's shower 26, first words) with a (mop 39) and you('ll (be) a anjel 52, 65) what Mom knows on November 25th! To find 4 13's 4 3's are 12, 12 ends in 2 and so is 52 or 4 13's. By doing them this way by picking a number out of order for say 13 7's 13 4's and so on, learning is more gradual while definite, as in learning them without having to look them up. Once I know the multiples, as time goes on and I use them for learning say my grocery cost or other use, I learn them well without so much practice.
To the ancients it was a sine or cosine of brilliance to count on your hands, numbers were tougher to count than the Arabs till they invented 0 to be cool in the desert! It's also good to count each word for say the multiple of 14 on your fingers, one to 4 on the fingers and then five is the thumb, then moving your thumb to your fingers is 5 plus 1 or 6, 5 =2 or 7 and 5 = 3 or 8 and 5 =4 or the ninth multiple, this is good for many tipes of counting. By the usual method of sites you find where you can count and have a hundred fingers, the left hand stores 10's so the tenth word to learn would be the index of your left hand held down while you count through the 10s + the other nine numbers of your right ahnd again as in 10 plus the 1 to four on the right are stored as 10 to 14, the thumb is used as the five for 10 plus 5 or 15 on through to 19, storing each number by raising or lowering each digit to count higher or lowering each bit to subtract. The method (in a book I once counted, where else!) is to store each bit by tapping on the shelf top. If you find you need the option to count higher on your hand with more ease, a more portable motif of mine I've devised like most of these tricks that also gives you 50 fingers on just the right hand alone is to store the 5's 10's,15's and higher by just moving the thumb to first the top of the index finger for five and moving your bits together for each following bit of your number crunch, with use of just relative motion of the bits to store the numbers. To store the first 4 the fingers are moved to clamp in turn, say lower or higher in return, then five is stored as the thumb to the nail of the index finger and the fingers are then moved to store 5+1, 5+2 and so on up to 9, then for 10 move the thumb between the tip and the line where the line of your finger is, with the other 4 up to 14 stored the same way, than to 15 stored by your thumb on the line of your digit, and so on, this will give you 25 fingers on one hand and you can even count in the shade, unlike the books I've read, and at higher speed it's easier to enter or "read out" the number you stored or counted. If you use both the thumb on the top of the digit and alternate with the thumb also under the index finger at the right time of the number, this will give you 50 fingers on your right hand and if you use the left hand for the 10's and 150s and so on you can labor this up to 50,000 bits, like 50,000 bits with an easy readout. An elaborate method was used in the hand math book, with elaborate skips they memorize from number to number to multiply and divide. This more portable method of 50,000 bits at higher speed may also be developed into a more complete system for multiplication and division, this is a whole new realm of math, if you like math like for college, you have my copyright's word to improve it. Books have been written about this and this improvement may be another wordsworth. For the counting of pun words like the Machine, having 50 bits is good enough for me, just to know where I am in a list of the best comedy words as I say on the Comedy Machine link, math seems to know more than lots.
About Conversions Like Oz. To Royal Pounds
To find out for conversion of 100 kilometers to miles, a kilometer is 5/8 of a mile. (My rediculous memory here is a koala has faith in 8 fuzzy arms when she smiles=a kilometer is 5/8 of a mile. Australian airline hostess are luxury sweet!) You know a kilometer is smaller than a mile, it takes more than one kilometer to fit into the mile if it's 5/8. You know one of the numbers will be smaller than the other. How do you know whether to multiply the 100 kilometers by 8/5 making it larger to convert or by 5/8th to make it smaller? If a kilometer is smaller than a mile the answer would be smaller in miles because there are more kilometers that fit in a mile, so to go to miles they will be fewer in number, the distance of kilometers is smaller than a mile so the number of kilometers is larger, and vice versa for miles. The 100 kilometers is the number. To find a fraction that converts a larger number to small, by the above about 3=12/4, to convert the three to a smaller number, or 1/3, invert the other side to 4/12. This tells us that to convert a number to a smaller number, you multiply it by a fraction with the smaller numerator. So to convert 100 kilometers to miles you multiply the conversion number with the smaller numerator, 5/8 by the 100 kilometers, or 500/8 or 62.5 miles.
You'll find about math you often won't know this without practice and just 1 mnemonic however. Thus the best way to learn is to first find the general idea, like the above. Using kilometers to miles is often useful, and it's good to learn more gradually, the more unfamiliar is often the best. To achieve this, first I just memorized the mnemonic above, and then later with the next kilometer to mile conversion like when I read in a magazine, it's still not intuitive.
To improve the reflex with each go round of use of the math, if the least unsure, I type in the problem on the web, find the answer, and compare it with the mnemonic, like learning both the theory and experiment and memorizing examples of both, this is the general method to learn math well.
For example, reading about the distances of the snow and ice fountains on a moon of the solar system, I read it's 6 Kilometers, so I think, times 5/8 or 8/5ths, find the answer, it's, How many miles are in 6 kilometers? 6 kilometers = 3.72822715 miles. Then I see if it fits the mnemonic well, 6 times 5/8ths is a smaller number for the answer, so 6 Km=3.7 Miles, yes. Then to make sure I type in another site for 1000 kilometers equal how many miles? 621 miles. This confirms that to convert kilometers to miles, multiply by the 5/8ths not 8/5ths But if one mnemonic is not enough another will add to my depth of perception, thus
Kilometers to Miles Multiply Miles by 5/8, the smaller number of the mnemonic (K to M= CoMe (T(Times) M=TM) by Life (=5/8) M You Come=KM to TM With Life) You will (Smile=Small) when the anesthelogist makes you Number (=Smaller number).
And to generalize for Miles to Kilometers You MaKe Time with FoiL (=8/5ths) like an aluminum space hat "in the year 2000!" Click here for the link about how to easily convert numbers to letters for the 5/8=FoiL and 8/5ths LiFe, this is a second way to look at your memory from other perspectives, this is important in memory, like cleaning a wall in more than one light or angle when the landlady is about to show up, so no "loose ends", so in general in learning math you want to both try a good number of problems after first memorizing the general idea, then more problems with the right answer on the web, or marm, confirm to see if the mnemonic is right, and then generalizing and perhaps using another mnemonic to see it from another perspective. This is why I say you don't know it without more refinement. And no doubt, be sure to save all your progress in the Toolbox (See above AZ MEMORY). I list these mnemonics under "Conversion" C2 or Cn.
..I read just a bit of math each day or two or three days, it's a lifelong goal, by memorizing the letters for words. Though first it was slower (see below for how to speed up here) I find a slow but sure way combined with the mnemonics and a sure way to remember these too is the best. I learned about science when I was about 5, words when I was 8, inventions ways to paint, more science and comedy methods like the mnemonics when I was 22, languages rhetoric and more of the rest when I was about 35, music when I was about about 40, and math only when I reached 45, math has arrived later for me and this seems not coincidence because it's abstract, complex and and unlike say, science, there are few teachers who can teach it well. They all seem to expect us to learn without their influence, or in the brain outdoors! I've found these math methods by long buildup, especially like the programmed book and the Letter Method and the AZ, even so like with music which is abstract and uses memory more which was also later in my life so far, the slower but surer methods seem the best where deeper memory is involved. I don't use computers like software so much because common sense rules the web, if this were not so, it would already be done by the web, and we would have no labor. They may be too much too soon. My plan is not to be ambitious about math because I assume math which is also like computers and music is abstract and complex, but rather my plan is to be efficient in view of more time and compound rates of interest. I saw this 25 cent held to the sidewalk with superbond and I think it's not a waste, in 10, billion years with interest it will be worth a listing on the Dow Jones! If you spend much time on math people will chide you, and it's not of great value to talk about, so a more inspirational method like to learn how to paint or be a comic won't work for math. Math like music takes a more gradual roundabout method of first improving memory in an abstract way, and a slower but surer method is needed especially. Unlike music, with math there is no proof that can be trotted forth I'm unwasting my time, or math would be more general. This is why it's arrived the slowest for me, but as they say evolution is speeding up and it's a way to be great if this is indeed the golden age of math.
..In truth this method to learn by the letter method and comics to learn anything and math too is actually not slow, it's the fastest overall. If I read the letters enough to learn the words for the letters, I speed up, and I know I'm automatically learning it right because the letters always are reliable to know I'm learning well and deep. I start out with the rediculous words (Click Here or see post below for how ) for the basic motifs like multiplication or addition in the AZ, then I write them with other LM's for other things I want to remember like algebra or other higher learning (morale boost) on the same page in the algebra book. Then in general I list them there too (for lack of room in the AZ and for speed and convience) in the LM number to letter form with a cross ref (stop the umpire!) to where the comic words are too for the LM for the numbers, so I find the comic memory words first and then the higher speed LM for the numbers and if I fail on the numbers sometimes, I just revise to the memo of creative memorising .
TRICKS TO SPEED UP THE LM...
A gyro to stabilize an airplane on landing or takeoff has been devised, this is where most of the crashes are, if there was swimwear which absorbed moisture in the cloth for in the desert and then the fan inside would cool in the shade, they could live years in the desert or outdoors people in the heat would sigh in relief, these are creative methods so they must more about math!
Even so here are special tricks to speed up the LM
To not be unfamiliar at the start of the cycle of the letters to words to memory, a good trick is to keep the word near the letter memos above and below on the same page high and low with the same number sets of 2 one above for the letter method and one set below numbered upside down for the words. First you can read the words in twos or threes with reps in different linear combinations and the more of the words of the sentence written out, then by comparing the letters to words in sets of two or three till familiar makes it much easier to read the letter words in other linear batches of twos or threes, then you're reading just the LM's above. Even so it's good to refresh your memory by reading the words too from time to time by reps for more boost yet especially if you alternate between the words and LM here also.
To start with the LM like for vocabulary, I would make up the mnemonic and it was a bit confusing, and this wouldn't seem to allow for edits. To greatly reduce confusion, like beginners luck, it's bad! I learned to first write the words if copying from a source, or write the numbers or whatever to learn. Then I divide off the words in say batches of four or five each, and the letters with the same batches of letters, first letters of the words and so on. Next, use small numbers say in red ink for each like batch of words and letters. With this you can more easily go back and forth between the words and letters, reducing confusion and my speed and depth are improved about a third here. This makes it fast and simple to go between numbers and letters right away, and indefinitely. If I'm even a bit unsure with the letters, I go back to the words of the same number and do reps repeating the first letters of each word as I see them and then go back to the letters then, in cycles also of letters to words. Once you know the letters well, there are often a few words you don't know, so here I read the letters up to that point and then read the just the words to improve, then continue the letters for the words below, improving only as needed to both be comfortable with familiarity, and also solving and perfecting any less improved realms I may want to learn reliably.
Example;
\135 and 6\25 are 100;
\1tfas\2faoh;
the left slashes used so I have room on the page (of paper, right, wheelwright!) to write the link numbers between the letters and those words, right slash has no room above to write there.
Another trick to speed me with each cycle from when I write the LM to higher speed deep memory reading the whole sentence fast, is with reps of the first letters of these words and then the rest of the word pronounced with each rep to link my general memory of where the letters are for what words exactly in the sentence, a letter is a letter otherwise.
Another good ruse of use to combine with this is to do reps mostly of the meaning words in the LM , not words like a or and. Even while depth, then speed is the goal, speed is what life is about, I invented a small helicopter to zoom around and catch bits of my lunch if I drop it, my rooms are clean at the speed of celebration, if the bib whirls rolls up and around with all the hotdish inside to wash, moreso!
For any type of more indepth words to remember by the Letter Method, e.g. math or historical dates or where you're learning foreign words or other words you don't know well, and when combining these with comics it's important to go back and forth between the words and the letters, say 3 letters and 3 words at a time, and just do reps of these, this will speed you up even for the most technical of motifs, then once you know the basic sentence by reading the general motif, I start with 2 or three letters reps at a time to zero in including if an error, just rewind get a running start, then more reps for the first or second letter before the goof to correct errors and the most reps where you want to improve when you are at the start of the loop, then when the errors are gone, you just do deeper and deeper and faster reps from there, at higher speed correcting when needed, by rewinding a bit and then accentuating the right way to learn it where the error was in loops here. Another good exercise if you don't use connecting numbers for both letters and words or ect to remember is to do reps of three letter words then the next two then the first two letter words than the following three, of the same five letter words, for the loop. Your brain refines the sensation more reliably by changing the image in a moderate reliable way like this, like in evolution with large numbers of moderate changes, not small numbers of large changes. If you have problems, it's good to just reduce the loop and do more reps, then just restart and plug into the rest of the LM, no doubt in general to go numerically from start to finish on the page is higher speed than a web MCI saving binge, and from the start to finish of each set of words to remember, digesting more and more and with the comics on the same page copied from the AZ twice with the cross reference to always find the comic about that number combination to memorize when you want it without two books as with the rest of the session to reinforce your memory as you go.
The basic idea of the loop is to first find content you're sure of, either a comic you're sure you must learn, or math that's definitely to remember, if you want to, write the LM and start the loops while always making sure the loops are short enough and with enough reps and exercises to win more than you lose in a reliable way. Say if your discomfort is amount a, if you always stay like a fourth below this level by staying inside the loop, with labor you'll always overpower it sooner or later, at least for memory where you can know it definitely. Another confidence builder is to memorize related motifs, for instance to learn 8 and 3 are 11, 3 and 8 are 11, 11 -3 is 8, 30 and 80 are 110 and so on, by the LM if you must, that is if you're doing some simple calculation and you don't yet know it fast and well, you write this in your LM wish list at the end of the memo, and you want to learn by the LM. The psychics out west on the FM are with the ads saying that they have definite tests so they have board certified brain readers. Wow if we could ask them how they learn math! The Psychic in the W are most aware with the spin of the math. Due to audio volability, and cost, I've generally opted out of the audio method, actually with improvements of my written math, and it's basic accessability I've not been involved with audio. As far as I can tell, written by these methods is better than audio because the written in the A2Z with the LM is at no cost, no meltdown, easy to always find and reliability outdoes the problem of the codes changing in a few years, a written document never will fail, handwriting is good for your brain too no doubt.
If you have trouble plugging in a word you already know in the sentence, a good method is to spell out the word when you reach the first letter, if it's just a habit about the sentence about a word you know well you want to derail, just spell the first letters of the word when you reach that point in the reps, saving having to spell the entire word to remember it. For spelling foreign words or words I don't know how to spell in English, a good trick I use is to break the word down into familiar spellings in english, and then memorize those words, works great to remember passwords in reverse, i.e. to make a good password I find words familiar to me alone and then make up uncommon spellings and then do reps of the spelling with each go round. To spell problem words in English like the word "evidence" it's good to use the sound spelling, think of ev-ee-dayn-ce when you type in, ar an-gee is an angel with her weightloss in orbit and her amazin' gee force marathon! If I'm major to a mac at Macdonalds maj not mac if I'm a Phd in dish love at first bite. Or like an opthomitrists, love at first site, the opthomotrist will see you in an hour, she looks so rich!
.. I know about lots of words I read, and I read Encyclopedia Americanas and Popular Science and Popsci and Sciamer. I find most are inspirational for both comic and serious inventions. Americanas have much better explanations than like Colliers or other encyclopedias, I found about Americanas by reading at the library, if you try them you may like them (and no 5 dollar words on 3/4ths of the pages instead of content like other encylopedias had). You may like a set of real Americanas like me you can buy secondhand cheap on the web. Reading the comics the words remind me of and remembering what's of worth for years and the insights they allow has been a great enrichment in my life (And sometimes lifesaving like for health. I searched the web for five years for a herb and then I remembered where I had read Science News 15 years before about a power herb by memorizing the Letters, and it was better than the entire web, for 5 years. The web is isn't as good as it may seem because it's got gimmicks and not the most important information like Americanas or other more reliable authors too.). My mom's a PHd and she got me a perscription of science magazines, Dr. MOM!
..While this may sound complex, the method to learn math (or anything) has just 4 elements, the words, comic or serious, the letters for the words, the exercises that are easy to make by just combinations of the letters right on the memo without rewriting, and the index numbers (like general page number plus memo number on the page, to find it fast), these 4 are about how to create or read the memos to remember on the page like in Webster's, how to find them and how to remember them when you find them, especially in order so e.g. you always have a new comic to share. To find the words and the exercises on that page like in a magazine, I just write a word or two and the page and memo number on a sticker outside or inside the blank cover of the volume or magazine, this way reading goes where interest leads. This is of value for any important volume where you have to search to find your current state of your knowlege.
If you have your wish list of all the math you know you want to remember by the LM (mines 15 pages now) it's good to write the most important or related motifs in an index i.e. 1 - - - 5 - - - - 10 - - - - 15... down the page inside the start of the book and then say you've written some 8 exercises , 80, 160, 240, on the 15th page. You look on the 5 to the 7th notch where your index is and here are all the important exercises to achieve, and related exercises so you don't have to write them too much and so your definition is focused. And as you go through your general motifs you also write all the exercises by number you've already learned, so your progress is more linear and if like me you just wrote your list in delight of math! Finally! A way to reliably win more than I lose at math! I had a moment like this about music (going over and over the song with reps and words of the rep "found by theory and experiment" trial and error. The reps of the words help your memory in power and by this method I was then sure I would at least be able to remember and edit music in a reliable way.) If you have a moment like this, it's memorable, and, you're optimi sing on up! I searched for years for this and it's yours thanks for rememberizing me.
This is a deeper method to remember, and I find that it takes about two weeks to learn the LM for 25 math memories on one page well enough to read them fast without error and with confidence, that will last for a lifetime. While no doubt it's best to continue reading and deepening the reflex, at 25 in two weeks, this is about 625 a year and about 1200 number building blocks you can learn in two years, with just 5 or 10 minutes of reading a day. I already know about say 400 of them well, so if you're like me, in just a year or so you can mostly overpower your basic math block. But you can use this for all your higher math beyond, or to learn anything verbal or numerical, by repeating the loops, you can even give visuals names and learn them well too!
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These tricks will speed you for all uses of the LM for any use say languages or science. This is great for vocabulary and to learn comics because I found I didn't have to even learn that much to open a larger world of language, just to learn a moderate amount well beyond a certain level is better than to learn a lot without so much depth (if you're learning what's important, like say the axioms in math first, even so just making the labor is of most important, like in fitness and the marathon). Though math is the toughest to learn of all my talents, and it takes the most LM reps of labor, anything important you learn here about learning you can use for any other type of learning, if you can learn math, you can learn all there is!
If you want to be good at math, it's good to be able to edit up with a word processor and go over your own math memos so you can often find a deeper truth if you know an equation 3/4 or higher because it often takes many edits if you're not in the Programmed realm and if the teacher doesn't have time to help. Once you've reached your 3/4 or more level of excellence repeat the result like on an audio document and the LM too, you searched for your conclusion so you deserve to be able to hold on to your precious insights. Hope this site is of worth to you to achieve and be good at math. Einstein had no licence to drive and wore no CPR machine when out sailing so he must know as much math as us!
..In closing I want to say thanks for remembering me on the web, a good mother or father realize it's not that grandma always remembers, its how she's kind that means she cares and always remembers us, and I like what's good about you grandma would always say, shoot for the moon, even if you zoom by, you'll be an All Star!
