9x2=18 (1+8 =9)
9x3=27 (2+7 =9) and so on right through the 9 times table.
2006-09-15 07:59:16 · 10 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
it is an interesting property of number 9
we can write x*9 = x(10-1) = 10x - x
as you can see, the two terms would be equal if the digits of each are added... (720 - 72 -> 9 - 9)
hence the effect of x is cancelled, leaving only 9 in the result...
2006-09-15 08:32:17 · answer #1 · answered by m s 3 · 0⤊ 0⤋
the sum of the digits of any real integer multiplied by 9 equals 9 can be proven as so...
9*x :given
little work we get the following
10x - x
10x - x - 10 + 10
(x - 1)10 + 10 - x
from here you can see that the (x-1) preceeding the first 10 (the multiplied 10) the going to the be the digit in the 10's spot in the product.
The 10 - x will represent the one's spot
so if we take the sum of the two digits (x-1 and 10-x) we get the equation:
(x - 1) + (10 - x)
Drop the parantheses
x - 1 + 10 - x
Simplify and cancel x's we get
10 - 1
which becomes
9
2006-09-15 09:49:42 · answer #2 · answered by Mike B 1 · 0⤊ 0⤋
Its really easy
for instance, if you have to do a 4 x 9
think of it this way, 4-1 = 3
how many more do i need from 3 to 9 = 6
so 36
9x8
8-1=7 ------------ 7 to 9 =2
so 72
just substract 1 from the number you are multiplying by 9 and see how much its mising to be a 9
thats why they all add to be a 9, because they come from that calculation
2006-09-15 08:05:40 · answer #3 · answered by Christian D 4 · 0⤊ 0⤋
In any multiple of 9, the sum of the decimal digits is a multiple of 9. It works no matter how many digits the number has. You would need to understand modular arithmetic to follow the proof.
If you write a number down in octal, it is divisible by 7 if the sum of the digits is divisible by 7. So the general rule is about "one less than the base you write the number in".
2006-09-15 08:06:46 · answer #4 · answered by Anonymous · 0⤊ 0⤋
it is just what happens when you keep adding 9 each time. basically you increase the last result by 9, which makes the first digit of the resulting number, 1 bigger and the second digit 1 smaller. This keeps the sum 9
2006-09-15 08:05:41 · answer #5 · answered by godmike 2 · 0⤊ 0⤋
Because everytime you add 9 the first one's digit goes down one and the ten's digit goes up one. So they always add up to 9 until you reach 11 where the one's goes up 9 and the ten's stays the same.
PS.
Have you ever used the hand trick to multiply by nine (from 1 to 10)? Hold your two hands up side by side. If you want to multiply by one, put your left pinky down. You have 9 fingers up so the answer is 9. Times 2 put your second finger down and it makes 1,8 or 18. Third fiinger down 2,7 or 27..etc. Neat trick to teach kids.
2006-09-15 09:46:27 · answer #6 · answered by Anonymous · 0⤊ 0⤋
Related to base 10 ?
hum mmmmm
If i had $1,111,111 and divided equally among 9 people, how much would each person receive?
2006-09-15 08:11:17 · answer #7 · answered by Roy G. Biv 3 · 0⤊ 0⤋
I think it has something to do with the multiples of 3 . I think.
2006-09-15 08:03:30 · answer #8 · answered by Mann 2 · 0⤊ 0⤋
it depends on modular arithmetic.
2006-09-15 08:30:23 · answer #9 · answered by iyiogrenci 6 · 0⤊ 0⤋
well its better if u go and ask the person who made it all out....
P.S:u made me confused.
2006-09-15 08:04:09 · answer #10 · answered by tonima 4 · 0⤊ 0⤋