If you had 343, you would double the last digit to get six, and subtract that from 34 to get 28.
If you get an answer divisible by 7 (including zero), then the original number is divisible by
seven. If you don't know the new number's divisibility, you can apply the rule again
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.
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.
2) 758*11 = 7+1---(7+5-10)+1---(5+8-10)---8 = 8338
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
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.
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.
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.
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
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.
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