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, for this example 37:

• Look for the nearest 10 boundary
• In this case up 3 from 37 to 40.
• Since you went UP 3 to 40 go DOWN 3 from 37 to 34.
• Now mentally multiply 34x40
• The way I do it is 34x10=340;
• Double it mentally to 680
• Double it again mentally to 1360
• This 1360 is the FIRST interim answer.
• 37 is "3" away from the 10 boundary 40.
• Square this "3" distance from 10 boundary.
• 3x3=9 which is the SECOND interim answer.
• Add the two interim answers to get the final answer.
• Answer: 1360 + 9 = 1369

With practice this can easily be done in your head.

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!

Finger Math: 9X Rule

To multiply by 9,try this:
(1) Spread your two hands out and place them on a desk or table in front of you.
(2) To multiply by 3, fold down the 3rd finger from the left. To multiply by 4, it would be the 4th finger and so on.
(3) the answer is 27 ... READ it from the two fingers on the left of the folded down finger and the 7 fingers on the right of it.

This works for anything up to 9x10!

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!