There are few Math Problem Solving Strategies. In stead of taking up the lengthy method to solve a math problem, we can adopt the short method which will save our time and energy.


Strategy : 1 >>> Multiplication by breaking up numbers :


Let us take an example of multiplication of two big numbers.


8142 x 131 = what?


131 can be restructured into 100 + 10 + 10 + 11


8142 x 131 = (8141) x (100 + 10 + 10 + 11)


(8141) x (100 + 10 + 10 + 11) =


8141 x 100 = 814100


8141 x 10 = 81410


Add these numbers.


8141 x 110 = 814100 + 81410 = 895510


(8141 x 11) = (8141 x 110)/10 = 895510/10 = 89551


Add this to 895510.


895510 + 89551 = 985061


8141 x (100 + 10 + 11) = 985061


8141 x 10 = 81410


8141 x (100 + 10 + 11 + 10) = 985061 + 81410 = 1066471


8141 x 131 = 985061 + 81410 = 1066471


Strategy : 2 >>> To multiply a number by 1001 :


256 x 1001 = what?


In this write 256 two times continuously. That is the answer.


256 x 1001 = 256256


453 x 1001 = 453453


108 x 1001 = 108108


800 x 1001 = 800800


669 x 1001 = 669669


123 x 1001 = 123123


963 x 1001 = 963963


Strategy : 3 >>> To multiply by 11 :


132 x 11 = what?


Step 1 : Prefix zero and suffix zero to the multiplicand.


Step 2 : Write down the answer from right to left.


The digits of the answer are got by adding two successive digits of the multiplicand, its right neighbour.


In case you come across any two digit number in the step of addition, put down only the right digit and carry the left digit.


132 x 11 =


Prefix zero and suffix zero to the multiplicand (132).


132 >>> 01320


0 + 1 = 1


1 + 3 = 4


3 + 2 = 5


2 + 0 = 2


132 x 11 = 1452


Strategy : 4 >>> To multiply by 12 :


This is same as the previous one (Strategy : 3) except that you have to double each number before you add the right neighbour.


132 x 12 = what?


Prefix zero and suffix zero to the multiplicand (132).


132 >>> 01320


(0 x 2) + 1 = 0 + 1 = 1


(1 x 2) + 3 = 2 + 3 = 5


(3 x 2) + 3 = 6 + 2 = 8


(2 x 2) + 0 = 4 + 0 = 4


132 x 12 = 1584


Strategy : 5 >>> Square of a number :


To find out the square of a 2-digit number, take the nearest multiple of 10. Rewrite the 2-digit number ad addition and subtraction of the nearest multiple of 10.


Then the calculation is done as following.


43² = 43 x 43


The nearest multiples of 10 for 43 are 40 and 50.


43 = 43 x 43 = (40 + 3) x (46 - 3)


= (40 + 3) x (50 - 7)


= (40 x 46) – (3 x -7)


= (1840) – (-9)


= 1840 + 9


= 1849


43² = 1849





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