MULTIPLICATION OF ANY TWO NUMBERS, LIES BETWEEN 11 AND 19
Let me explain this rule by taking examples 13*19 = (13+9)*10 + (3*9) = 220 + 27 = 247 Means add first number and last digit of the second number take zero in the third place of this number then add product of last digit of the two numbers in it.
EXAMPLE.
18*14 = (18+4)*10 + (8*4) = 220 + 32 = 252
MULTIPLICATION OF 11 WITH ANY NUMBER OF 3 DIGITS.
Let me explain this rule by taking examples 1. 352*11 = 3---(3+5)---(5+2)---2 = 3872 Means insert the sum of first and second digits, then sum of second and third digits between the two terminal digits of the number 2. 213*11 = 2---(2+1)---(1+3)---3 = 2343
EXAMPLE.
Here an extra case arises
Consider the following examples for that
1) 329*11 = 3--- (3+2) +1--- (2+9-10) ---9 = 3619
Means, if sum of two digits of the number is greater than 10, then add 1 to previous digit and subtract 10 to the associated digit.
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MAGICAL DIVISION RULE FOR 2
If a number is divisible by two it will end in an even number or a 0.
EXAMPLE.
For example
28964
given number end with 2 then it will be divisible by 2.
and
89450
given number end with 0 it will also be divisible by 2.
GOLDEN DIVISION RULE FOR 3
If a number is divisible by three the sum of its digits will be divisible by 3.
EXAMPLE.
372 = 3 + 7 + 2 = 12
A corollary of this is that any number made by rearranging the digits of a number divisible by 3 will also be divisible by 3.
EXCEPTIONAL DIVISION RULE FOR 4
If a number is divisible by four the last two digit are divisible by 4 (or are zeros).
EXAMPLE.
45624
last two digit is 24
24 is divisible by 4 then 45624 is divisible by 4.
INCREDIBLE DIVISION RULE FOR 5
If a number is divisible by five the last digit will be 5 or 0.
EXAMPLE.
48905
last digit is 5 then 48905 is divisible by 5
and
56890
last digit is 0 then 56890 is also divisible by 5
PHENOMENAL DIVISION RULE FOR 6
If a number is divisible by six the last digit will be even and the sum of the digit divisible by 3.
EXAMPLE.
46536
last digit is 6 (even) and
sum of digit
4+6+5+3+6 = 24
24 is divisible by 3
then 46536 is divisible by 6.
EXCLUSIVE DIVISION RULE FOR 8
If a number is divisible by eight the last three digits are divisible by 8
EXAMPLE.
4857248
last three digits are 248
248/8 = 31
Then 4857248 is divisible by 8
ASTONISHING DIVISION RULE FOR 9
If a number is divisible by nine the sum of its digits is divisible by 9.
EXAMPLE.
8916345
Sum of the digit
8+9+1+6+3+4+5 = 36
36/9 = 4
number 8916345 is divisible by 9
STUPENDOUS DIVISION RULE FOR 10
If a number is divisible by ten it ends with a 0.
EXAMPLE.
45683750
last digit is 0
then number 45683750 is divisible by 10.
AWESOME DIVISION RULE FOR 11
If a number is divisible by eleven the difference between the sum of the digits in the even places and the sum of the digits in the odd places is 11 or 0.
EXAMPLE.
23485 is shown to be divisible by 11 because
2 + 4 + 5 = 11
3 + 8 = 11
11 - 11 = 0
and
and 60852 is shown to be divisible by 11 because
6 + 8 + 2 = 16
0 + 5 = 5
16 - 5 = 11
LARGEST CALCULATION (9^9)^9
Ninth power of the ninth power of nine is the largest in the world of number that can be expressed with just 3 digit. No one has been able to compute this yet. The very task is staggering to the mind
EXAMPLE.
The answer to this number will contain 369 million digits. And to read it normally it would take more than a year. To write down the answer, you would require 1164 miles of paper.
WHY 1 IS NOT PRIME NO ?
If one is allowed as a prime, then any number could be written as a product of primes in many ways.
EXAMPLE.
24 = 1*2*2*2*3
or 24 = 1*1*2*2*2*3
or 24 = 1*1*1*1*1*2*2*2*3
The fact that factoring into primes can only be done in one way is important in mathematics.
FAMILIARITY WITH CARDINAL AND ORDINAL NO
An ordinal number given us the rank or order of a particular object and the cardinal number states how many objects are in the group of collection.
EXAMPLE.
Fourth - an ordinal number
Four - a cardinal number
EVOLUTION OF + AND - SIGN
The + symbol came from Latin word et meaning and. The two symbols were used in the fifteenth century to show that boxes of merchandise were overweight or underweight.
EXAMPLE.
For overweight they used the sign + and for underweight the sign -.
Within about 40 years accountants and mathematicians started using them.
FASCINATING NUMBER 3
There are a couple of strange things about the first few prime numbers,
153 = 1^3 + 3^3 + 5^3
And 3 and 5 can also both be expressed as the difference between two square
3 = 2^2 - 1^2 5 = 3^3 - 2^2
EXAMPLE.
The secret steps in the 3-times table are very simple
3*1 = 3 ---------------- 3
3*2 = 6 ---------------- 6
3*3 = 9 ---------------- 9
3*4 = 12 --------- 1+2 = 3
3*5 = 15 --------- 1+5 = 6
3*6 = 18 --------- 1+8 = 9
3*7 = 21 --------- 2+1 = 3
3*8 = 24 --------- 2+4 = 6
3*9 = 27 --------- 2+7 = 9
3*10 = 30 -------- 3+0 = 3
3*11 = 33 -------- 3+3 = 6
3*12 = 36 -------- 3+6 = 9
Again the pattern of the secret steps recurs whatever stage you carry the table up to - try it and check for yourself.
AMAZING NUMBER 4
With number 4 the secret steps in the multiplication tables become a little more intricate.
At first the sums of the digits look like a jumble of figure, but choose at random any sequence of numbers and multiply them by 4 and you will see the pattern emerge of two interlinked columns of digits in descending order.
That it is easier to add round numbers like 40 or 50 than numbers ending in 7, 8, or 9. If you round these awkward numbers up by adding 3, 2 or 1 the calculation is not much longer, and is easier. Instead of 49+52 = 101 think of it as 50 (that is 49+1) + 52 = 102-1 = 101
Other example If you are adding 215 426 513 112 328 ----
First add the figure in the hundreds column and hold the total, 1500, in your head. Now add the total of the tens column, 70, to it. To this total 1570 add the sum of the units column, 24, to arrive at the final total of 1594
EXAMPLE.
Even when you use pencil and paper carrying error can occur. Here is a method of working which makes them much less likely.
----9845674
----7465387
----8236472
----4578348
----3847568
----3569841
----------------
----4200960
---3334233
--37543290
Another method of avoiding carrying also involves adding each column separately. the column totals are set out in a staggered line, the units figure of the second column below the tens figure of the first, the units figure of the third column below the tens figure of the second ans so on. the column totals are then added to given the final answer. Here is an example
----962853 ----------- 19
----524861 ---------- 22
----212346 --------- 24
----401258 -------- 13
----864321 ------- 28
-------------------------------------
------------------2965639
INTERESTING SUM
Another method of avoiding carrying also involves adding each column separately. the column totals are set out in a staggered line, the units figure of the second column below the tens figure of the first, the units figure of the third column below the tens figure of the second ans so on. the column totals are then added to given the final answer.
EXAMPLE.
Here is an example
----962853 ----------- 19
----524861 ---------- 22
----212346 --------- 24
----401258 -------- 13
----864321 ------- 28
-------------------------------------
------------------2965639
PERCENTAGE COMPUTATION
Calculate 65% of 460: 50% of 460 = 230 10% of 460 = 46 5% of 460 = 23 (half 46) ------------------------------ 65% of 460 = 299 (sum)
EXAMPLE.
Calculate 67.5% of 460:
50% of 460 = 230
10% of 460 = 46
5% of 460 = 23 (half 46)
2.5% of 460 =11.5 (half 23)
------------------------------
67.5% of 460 = 310.5 (sum )
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