Hello
I didn't know about this hint. Usually, I simply develop .
In the case of , where 9 and 7 are close to 10, I'd rather do which avoids manipulating too large numbers. (yes, I consider 63 as large )
Hello,
1.*1.
This has nothing to do with extraordinary technique, but you gotta think about it (I'm confident that some of you know about it)..
So multiplying two such numbers is equivalent to :
 sum one of the numbers with the unit digit of the other one
 multiply it by 10
 add the product of the two unit digits.




I hope this would help at least one person in the future
Enjoy calculations !
Well, this goes too for 12x15 for example, which involves smaller numbers
I only gave an example with random numbers... Sometimes, there are easier ways of calculating
When I'm talking about mental calculations, I consider it as being without any paper & pen... Unfortunately, (201)(203) for some people needs some writing :)
Another thing :
The square of a number whose unit digit is 5.
If you're looking for the square of a number N=X5 (with X representating all the digits of the number, meaning that actually, ), don't worry, this can be shortened ^^
First of all, calculate
will simply be
For example :
Hence
Another example :
Hence
Using binomial to avoid long calculations...
If you're asked to multiply two numbers, you can rapidly go through this checking.
See if the numbers are symmetric with respect to a number N.
If so, the numbers a and b can be written as : and
The product will be :
By using a binomial formula, you get :
Which can sometimes be more sympathical to calculate..
For example :
Notice that these numbers are symmetric with respect to 50.
I know that these methods look elementary, but it sometimes helps when you are in a hurry and not allowed to use any calculators
Check for the unit digits (and cubic roots of numbers)
In general cases, when you gotta check rapidly if your calculation seems correct, look at the digit number.
Let and
Hence the unit digit of XY will be the unit digit of ab, which is easier to get.
For example :
Here, and . So
Hence the unit digit of is
If you find a result whose digit number is not 8, you can directly calculate again.
Here is only a beginning for cubic roots... And shall be known
Notice that each number appears once in the unit digit.
This means that if, for example, you're looking for the cubic root of a number whose unit digit is 6, its cubic root necessarily ends with a 6.