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Maths Addition, Subtraction and Multiplication

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If you look back at the 'Person 0 to 9' article, you see that I used letters of the alphabet to mean digits from 0 to 9.

I believe that mathematics is easier for some people if they speak maths rather than picture it. Let us say that:

B is 0

Ch is 1

Sh is 2

G is 3

D is 4

N is 5

S is 6

Z is 7

X is 8

F is 9


Let us say that one of those digits needs adding to another digit; and let that other digit be expressed as:

0. O (sounds like o in 'pot')

1. I (sounds like ee in 'peep')

2. A (sounds like a in 'pat')

3. E (sounds like e in 'pet')

4. U (sounds like oo in 'hoot')

5. W is oo (eg. the Ue sound in 'tune')

6. X is ie (eg. the Ie sound in 'pie')

7. K is i (eg. the i sound in 'pip')

8. Y is ah (eg. the sound in 'park')

9. V is u (eg. the sound in 'pun')

What I want to develop is a way of expressing 37 + 89 in a way that automatically solves the question. If the 7 and 9 have no carrier to deal with then I would use the 'o' sound between the Z of 7 and the F of 9: ZoF. But I would have a rote table where Z and F are listed as ZeeF: the 'ee' means that the sum is more than 10 and so a carrier is involved. In fact the look up table would state: ZeeFie because the 'ie' is the sound for 6 which is the right side answer of the question. I could write a 6 on paper at this point.

Now I want to look at the 3 and 8 of the tens part of the question. Normally, that would be GeeX: the G is the 3, the 'ee' is the fact there is a carrier, and the X is the 8; but I already have the 'ee' from the 'ZeeF' I just did; so GeeX is expressed as 'GaX'. A rote lookup table would say 'GaXeeSh' where the eeSh is the 12 to put at the start of the answer. So the answer is 126.

Note: GeeX of 3+7 would have a rote table answer of GeeXeeCh.

I wonder if this approach would work better for some people than ordinary maths. If so then a similar rote syste could be developed for subtractions maybe.


I have other ideas about calculations. I like the idea of counting in 50s. So, if you add 45 and 47 (=92), you would note that the answer is at least 50 or higher; and you would know from memory the remainder of 92-50: learn the 42.

You could tot up a lot of 2 column numbers, noting the 50s being passed, and then re-introduce all the 50s when presenting the final answer. Or maybe 25 is the upper limit before the reset (I am playing with ideas.)


Another idea is two digit multiplication: there would be 5000 person images numbered from 0000 to 4999.

The hair or hat and the colour has an encrypted 3 digit meaning; and the outfit and colour has encrypted 3 digit meaning too.

If you need to calculate 47 x 49, person 4749 would have 3 digits of the answer encrypted as one of the hat or hair styles; and its colour.

If you need to calculate 97 x 49, you subtract 50 from the 97 to get 47; and then look up person 4749 who would have 3 digits of the answer encrypted as an outfit and outfit colour.

Each of these people has a first name based on two syllables of the Town 100 syllables; and

Each of these people (with a 0 to 49 x 0 to 49 aspect) has a surname which is a syllable representing the remainder when a 50s addition is done. Eg. 45 + 47 has a carrier and the appropriate 42 syllable represented in the surname [see the Person 00-99 article]. The suffix 'Ch' could indicate the carrier. 45 = MO, 47 = MA. So person with number code 4547 (so the first name is MOMA) would need a surname meaning "42 and add 1 to the count of 50s": LACh.

So about 2500 results would need memorising to make use of the approach. In modern times, with the wide availability of calculators, there is probably little appeal for this facility.


The 1000 Women and 1000 Male cartoon images of people involve logarithm data. Logarithms were very important before computers made difficult calculations easy. They are very weird. For instance, multiplication is achieved by a process only slightly more complicated than a basic addition calculation. Int this way, approximate answers can be calculated that are of sufficient accuracy to be useful to navigators or engineers.


Adding Syllables

Another way of thinking about summing differently is to apply the syllables form the People 00-99 article:

Left Part of Syllable Add This
Left Vowel Right Vowel Add This
B 0
O O 0
CH 5
O I 1
D 10
O A 2
F 15
O E 3
G 20
O U 4
H 25
I O 1
J 30
I I 2
K 35
I A 3
L 40
I E 4
M 45
I U 5
N 50
A O 2
P 55
A I 3
R 60
A A 4
S 65
A E 5
SH 70
A U 5+1
T 75
E O 3
V 80
E I 4
W 85
E A 5
Y 90
E E 5+1
Z 95
E U 5+2



U O 4



U I 5



U A 5+1



U E 5+2



U U 5+3

Let's express 37+39 as a pair of syllables from that article: 37 is KA and 39 is KU; so the word I make is KAKU. If i have memorised the table above then the K and the K mean 35 and 35 which is 70; this is easy to calculate because numbers ending in 5 are easy to add together. The A and U can be looked up in the second table above and, rote, mean 6. It is easy to add the 6 to the 70. The answer is 76.

So a small amount of rote learning can make a sum be expressed in a way that is easier to solve; and the syllable pair is also an alternative way of holding an intermediate result in your short term memory if the 37+39 is just a part of a bigger calculation.

I think there is less chance of number errors when syllables are used.

I could also develop a table to state what any two letters add up to. Eg. KN is 85 because it is 35+50 (K is 35, N is 50). If I have a two syllable word like KAKU then the KK would, by rote, give me 70 (K 35 plus K 35) and AU is +5 and +1 to give me 76. KN and NK are going to have the same table answer of 85 because of the similarity in adding 35+50 or 50+35.


Adding up 3 digits

How many 3 digits are there when faced with adding three digits together? 1+2+1 will be similar to 1+1+2; so that helps reduce the number of three digit numbers to learn rote the total of.

There are about 220 results that, if rote learned, would speed up the summing of three digits:

Ascending Order Sum
000 0
100 1
110 2
111 3
200 2
210 3
211 4
220 4
221 5
222 6
300 3
310 4
311 5
320 5
321 6
322 7
330 6
331 7
332 8
333 9
400 4
410 5
411 6
420 6
421 7
422 8
430 7
431 8
432 9
433 10
440 8
441 9
442 10
443 11
444 12
500 5
510 6
511 7
520 7
521 8
522 9
530 8
531 9
532 10
533 11
540 9
541 10
542 11
543 12
544 13
550 10
551 11
552 12
553 13
554 14
555 15
600 6
610 7
611 8
620 8
621 9
622 10
630 9
631 10
632 11
633 12
640 10
641 11
642 12
643 13
644 14
650 11
651 12
652 13
653 14
654 15
655 16
660 12
661 13
662 14
663 15
664 16
665 17
666 18
700 7
710 8
711 9
720 9
721 10
722 11
730 10
731 11
732 12
733 13
740 11
741 12
742 13
743 14
744 15
750 12
751 13
752 14
753 15
754 16
755 17
760 13
761 14
762 15
763 16
764 17
765 18
766 19
770 14
771 15
772 16
773 17
774 18
775 19
776 20
777 21
800 8
810 9
811 10
820 10
821 11
822 12
830 11
831 12
832 13
833 14
840 12
841 13
842 14
843 15
844 16
850 13
851 14
852 15
853 16
854 17
855 18
860 14
861 15
862 16
863 17
864 18
865 19
866 20
870 15
871 16
872 17
873 18
874 19
875 20
876 21
877 22
880 16
881 17
882 18
883 19
884 20
885 21
886 22
887 23
888 24
900 9
910 10
911 11
920 11
921 12
922 13
930 12
931 13
932 14
933 15
940 13
941 14
942 15
943 16
944 17
950 14
951 15
952 16
953 17
954 18
955 19
960 15
961 16
962 17
963 18
964 19
965 20
966 21
970 16
971 17
972 18
973 19
974 20
975 21
976 22
977 23
980 17
981 18
982 19
983 20
984 21
985 22
986 23
987 24
988 25
990 18
991 19
992 20
993 21
994 22
995 23
996 24
997 25
998 26
999 27

More about Multiplication

When I mentioned the big multiplication system, above, to someone in the mental maths arena, he said that the maths can be done mentally without needing mnemonics. I know that; but some people can visualise numbers better than others.

When a 2 digit number is multiplied by a 2 digit number, some people do a lot of adding digits of a column of the answer as part of their technique; I think that rote learning the result of adding any three digits helps that step.

Another rote learning idea is to learn flash cards where two digits are in the middle and a digit of the answer is written above and below the two digits. For instance, 7x8=56; so the flash card would be the number 78 but the 5 is written above it and the 6 is written below it. I think that this would be a nice way of recalling parts of a times table subcalculation while doing a multiplication of a 2 digit number by a 2 digit number. School times tables might slow down that process because perhaps there is a delay in visualising the 7x8 before mentally seeing the 56: the school lesson would present 7 x 8 = 56 but recall might be 7x8 and a short while later the 56.


Reciprocals

The Super Hero Letter Pairs article contains some of the answers to reciprocals maths; and I intend for the 100 History People (new version coming in late 2022) to contain reciprocal maths as well.


Rough Results

Sometimes, an approximate answer to a maths problem is useful. Eg. Logarithms.

Regarding division, if I know (approximately) what 5/7 is (0.714...) and what 6/7 is (0.857..) ten I can guess what 5.5/7 is because it has to be somewhere between those two answers. Or 5000/75 can be guessed at by using the 5/7 and 5/8 results and moving the decimal point a little: 5/8 is 0.625; so somewhere between 0.714 and 0.625 is the answer to 5/7.5; so let's say 0.65. 5000/75 is like 5.000 / 7.5; so the answer is close to 0.65 but with the decimal point moved twice: 65. The answer is really 66.666 recurring. So it is not too bad.

An item 57 could have a clue in its image to the answer to 'what is 5/7'.

An item 58 could have a clue in its image to the answer to 'what is 5/8'.

In the article about people from 00 to 99, I have put in surnames for the people which, using the 'Person 0 to 9' article rules, represent 3 digit numbers. This is a way to learn the three digits that come after the decimal point of a division question. Eg. 15 is 1/5 is 0.2 or or 200. So 200 is represented as surname Hoo where H = 2, O = 0, O = 0. You have to mentally work out the whole number that is to the left of the decimal point. Eg. 52 is like 5/2 and so you mentally know that 5/2 is 2 remainder something.


Conversion Tables

Another area of numbers which would be nicely represented by mnemonics is conversion tables. Eg. Converting from pounds to stones or vice versa.