multiplication with 11

multiplication with 11

To multiply a single digit number with 11:

1*11 = 11
2*11 = 22
3*11 = 33
4*11 = 44
5*11 = 55
etc.
easy!

There is also a shortcut to multiplying bigger numbers with 11. You write the number that you want to multiply with 11 and leave a gap between the 2 digits of that number. To find what digit you need to write in the gap you just add the 2 other digits together and voila, you have your result.
Let's look at 2 digit numbers first:

10*11 : 1 __0 with __=1+0=1 --> 10*11 = 110

11*11 : 1 __1 with __=1+1=2 --> 11*11 = 121

12*11 : 1 __2 with __=1+2=3 --> 12*11 = 132

13*11 : 1 __3 with __=1+3=4 --> 13*11 = 143

14*11 : 1 __4 with __=1+4=5 --> 14*11 = 154

67 *11: 6__7 with _ = 6+7 = 13 carry-over!!! --> 67 *11 = 737

89*11: 8__9 with _= 8+9 = 17 carry-over!!! --> 979

93*11 : 9_3 with _= 9+3=12 carry-over!!! ---> 1023

You can do it in a similar way when the numbers get bigger. Just now you need to add neighbouring digits and you need to do several additions. Let's have a look:

74352 * 11

write 2
next add 5 + 2 = 7
write 72
add 5+3=8
write 872
add 3+4=7
write 7872
add 4+7=11
write 17872 remember 1 for carry over
now 7 + 1 (the carry over)=8
final result: 817872
74352 * 11 = 817872

52438 * 11

write 8
add 3 + 8 = 11
write 18 remember 1 for carry over
add 3+4=7 , 7+1 (carry over) =8
write 818
add 2+4=6
write 6818
add 2+5=7
write 76818
final result 576818
52438 * 11 = 576818

To get an idea why you can do this you have to look at long multiplication (like with the conjuring up of the numbers by magic).
example:

52438 * 11 =

		5	2	4	3	8
+	5	2	4	3	8	0
carry over	-	-	-	1	-	-
	-	-	-	-	-	-
	5	7	6	8	1	8

You can see that you are really doing the same thing when you do long multiplication. It's just that long multiplication is usually done with pen and paper while you can try to do the above method in your head.