Multiplying a 2 digit number by 11

There are a lot of Mathematical Principles out there, some more useful than others and I haven’t quite worked out how to involve this one into a trick yet…but I’m working on it.

We all know how to multiply by 10, we simply add a 0 to the number we are multiplying, but is there a rule for multiplying by 11? As it happens there is for a 2 digit number.

We will use 52 as our first example

52 x 11

To work this out almost straight away take the digits and add them together, in this example 5+2 =7, this 7 is then placed between the original 2 numbers and you have your answer, 52 x 11 = 572

33 x 11 = 363

17 x 11 = 187

61 x 11 = 671

But what happens if your 2 digits add up to a number greater than 10? The same rule still applies but we have to make one extra addition in the tens column.

Example 79 x 11, 7+9 =16

We can’t simply insert the 16 between the 79 to make 7169, but we can insert the 6 and then add the single 10 to the 7 in the tens column.

79 x 11 = 869

65 x 11 = 715

46 x 11 = 506

One of the most interesting aspects of Maths Magic is coming up with the routines, on its own this is a cool principle to know but it isn’t magic, not yet. This is one of the ideas I have in my notebooks to work on, possibly combined with another principle or used as a prediction, possibly as a presentation as a human calculator or something a little further reaching like a presentation on Apophenia, the perceptual phenomenon of people looking for patterns in randomness. A little advanced for a Primary Magic Maths Day maybe but everything has a beginning somewhere.