Multiplying by Eleven
Just some ideas of ways to play around with
multiplying by 11. Memorizing the "tricks" is not the important thing - it is
the underlying understanding of why the tricks work that will
last.
It's easy to figure out
11 times any number up to 9 -- 11X2=22, 11X3=33, 11X4=44, up to 11X9=99.
For 11 times 10 or higher,
here's a handy trick:
For 11
times a two-digit number take the first digit, place it to the left and then
place the second digit on the right. Insert the sum of those two digits in the
center. It works from 11x10 = 110 and up as long as the sum of the two digits
is less than 10:
Examples:
11 x 11 = 1 2 1 (1 + 1 =
2)
11 x 12 = 1 3 2 (1 + 2 = 3)
11 x 13 = 1 4 3 (1 + 3 =
4)
11 x 14 = 1 5 4 (1 + 4 =
5)
and so
on.
If the sum of the 2 digits
is 10 or up, there is an extra step. You still put the left digit on the left
and the right digit on the right and then find the sum. If it is 10 or more then
just put the right number (of the sum) in the center. Increase the left digit by
one.
Examples:
11
X 19 --- put the 1 on the left, the 9 on the right. The sum of 1 and 9 is 10, so
put the 0 in the middle and then increase the left digit by 1 to get
209.
11 X 29 -- put the 2 on
the left, the 9 on the right. The sum of 2 and 9 is 11, so put a 1 in the center
and increase the left digit by 1 to get
319.
11 X 48 -- put the 4 on
the left, the 8 on the right. The sum of 4 plus 8 is 12, so put the 2 in the
center and increase the 4 to a 5 to get
528.
Some people might find it
is fun to figure out why these little "tricks"
work.
11 times anything is
really 1 times it plus 10 times it (11 is 1 plus
10).
1 times something is easy
- it is that thing.
10 times
something is easy - it is that thing with a zero on the
right.
So = 11 times 4 is 1x4
plus 10x4 or 4+40=44.
11 X 9
is 1x9 plus 10x9 or 9 + 90 =
99.
Two-digit numbers work the
same way:
11 x 41 is 1x41 plus
10x41 or 41 + 410 = 451.
11 x
39 is 1x39 plus 10x39 or 39 + 390. Notice how when you line these up like
this:
39
+
390
429
then when you add you're really just
putting the 9 on the right, adding the 3 and the 9 and getting 12 and then
putting the 2 in the middle and adding the 1 to 3 to get 4 on the left. This is
the "trick."
Posted: Sun - June 13, 2004 at 10:17 PM