The 11 Rule

Selvaganesh_i

The 11 Rule

You likely all know the 10 rule (to multiply by 10, just add a 0 behind the number) but do you know the 11 rule? It is as easy! You should be able to do this one in you head for any two digit number. Practice it on paper first!

To multiply any two digit number by 11:

For this example we will use 54.
Separate the two digits in you mind (5__4).
Notice the hole between them!
Add the 5 and the 4 together (5+4=9)
Put the resulting 9 in the hole 594. That's it! 11 x 54=594

The only thing tricky to remember is that if the result of the addition is greater than 9, you only put the "ones" digit in the hole and carry the "tens" digit from the addition. For example 11 x 57 ... 5__7 ... 5+7=12 ... put the 2 in the hole and add the 1 from the 12 to the 5 in to get 6 for a result of 627 ... 11 x 57 = 627
Practice it on paper first!

Multiply By 4

To quickly multiply by four, double the number and then double it again.
Often this can be done in your head.

The 11 Rule Expanded

You can directly write down the answer to any number multiplied by 11.

Take for example the number 51236 X 11.
First, write down the number with a zero in front of it.
051236
The zero is necessary so that the rules are simpler.
Draw a line under the number.
Bear with me on this one. It is simple if you work through it slowly. To do this, all you have to do this is "Add the neighbor". Look at the 6 in the "units" position of the number. Since there is no number to the right of it, you can't add to its "neighbor" so just write down 6 below the 6 in the units col.
For the "tens" place, add the 3 to the its "neighbor" (the 6). Write the answer: 9 below the 3.
For the "hundreds" place, add the 2 to the its "neighbor" (the 3). Write the answer: 5 below the 2.
For the "thousands" place, add the 1 to the its "neighbor" (the 2). Write the answer: 3 below the 1.
For the "ten-thousands" place, add the 5 to the its "neighbor" (the 1). Write the answer: 6 below the 5.
For the "hundred-thousands" place, add the 0 to the its "neighbor" (the 5). Write the answer: 5 below the 0.
That's it ... 11 X 051236 = 563596

Square a 2 Digit Number Ending in 5

For this example we will use 25

Take the "tens" part of the number (the 2 and add 1)=3
Multiply the original "tens" part of the number by the new number (2x3)
Take the result (2x3=6) and put 25 behind it. Result the answer 625.

Try a few more 75 squared ... = 7x8=56 ... put 25 behind it is 5625.
55 squared = 5x6=30 ... put 25 behind it ... is 3025. Another easy one! Practice it on paper first!

Community Contributions - Articles by goIITians

The 11 Rule

Multiply By 4

The 11 Rule Expanded

Square a 2 Digit Number Ending in 5