more tricks

Square 2 Digit Number: UP-DOWN Method

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.



Multiply By 4

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


Multiply By 5
To quickly multiply by 5, divide the number in two and then multiply it by 10. Often this can be done quickly 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

Practice it on paper first!