SPEED MATHEMATICS!!! MULTIPLICATION-பெருக்கல்-வேகம்&விவேகம்! - பதிவு-II

SPEED  MATHEMATICS!!! கணிதத்தில் வேகமா???
ஆம் கணிதத்தில் வேகம் கூட்டுவோமே !!!

http://tnsfchrompet.blogspot.in/2012/09/speed-mathematics-subtraction.html
கடந்த பதிவில் எளிய முறையில், அதி விரைவில் ஒன்று, இரண்டு மற்றும் அதிக இலக்க எண்களைக் கையாண்டு  SUBTRACTION எனப்படும் கழித்தல்  முறையில் கணிதத் தீர்வுகளைக் அதிவிரைவாகக் காணும் முறைதனை நாம் கண்டோம்.  தற்போது நாம் காணவிருப்பது; ஒன்று, இரண்டு மற்றும் அதிக இலக்க எண்களைக் கையாண்டு  MULTIPLICATION  எனப்படும்  பெருக்கல்  முறையில் கணிதத் தீர்வுகளைக் அதிவிரைவாக, எளிய முறையில் தீர்வுகளைக் காணும் முறைதனை இரண்டு பதிவுகளில் காண்போமே !!!

LESSON THREE :: MULTIPLICATION..continued

We have seen: A REFERENCE NUMBER IS ALWAYS NECESSARY in the previous post. (http://tnsfchrompet.blogspot.in/2012/09/speed-mathematics-multiplication-i.html ).

Multiply:   94 X 96:

Here reference number may be taken as 100.  Write in brackets the numbers by which the given numbers which are below 100.

     94 X 96 = 9000

    (-6)   (-4)    +   24

                        9024 the answer is: 9024.

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Try another problem:

87 x 87:

Here also reference number may be taken as 100.  Write in brackets the numbers by which the given numbers which are below 100.

     87 X 87  =  7400

    (-13) (-13) +  169

                        7569 the answer is: 7569.

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Try another problem:

91 x 91:

Here also reference number may be taken as 100.  Write in brackets the numbers by which the given numbers which are below 100.

     91 X 91  =  8200

    (-9) (-9)     +    81

                        8281 the answer is: 8281.

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Suppose you have two numbers, of which one number is below the reference number and the other above reference number and the reference number is 100.

Example: 97 X 142 then write as below.

                         (+42)

                  97 X 142

                  (-3)

(+) sign is put in front of 42 because 142 is 100 + 42.  (-) sign is put in front of 3 because 97 is below 100 is 100 minus 3. Then work diagonally.  Take either 97 +42 or 142 – 3. Both are same. It is 139. Here reference number is 100. So multiply with reference number. You will get part of the answer which is

139 X 100 = 139 00

Then multiply the numbers in the brackets. (+42) X (-3) = (-126)

                         (+42)

                  97 X 142….. = 139 00 – 126 = 13774 is the answer.

                  (-3)

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Try another problem: 99 X 146

Here also the reference number is 100.

99 + 46 or 146 – 1 = 145. And the multiplication of the numbers in the brackets is (-46).

Then write as below.

                         (+46)

                  99 X 146….. = 145 00 – 46 = 144 54 is the answer.

                  (-1)

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Try another problem: 252 X 242

 Here also the reference number is 100.

Then write as below.  252  X  242

                                   (+152)  (+142)

Take either 252 + 142 or 242 +152 = 394. Multiply with the reference number 100.
We will get a part of the answer, which is = 394 00.…(1)

Here (152 X 142) has to be done mentally.

So write as below:

                             (+52)   (+42)

Reference 100…. 152 X 142 = 194 00 (subtotal)

Take either 152 + 42 or 142 +52 = 194. Multiply with the reference number 100.   

We will get a part of the answer, which is = 194 00….(2)

Again here (52 X 42) has to be done mentally.

So write as below:

                           (+2)

Reference 50…. 52 X 42 = 194 00 (subtotal)

                                    (-8)

Take either 52 -8 or 42 +2 = 44. Multiply with the reference number 50. We will get a part of the answer, which is = 2200. By multiplying the numbers in the brackets (+2) X (-8) = -16. So adding (-16) to 2200 we will get: 2200 – 16 = 2184

2184 which is a part of the answer ….3.

By adding the results 1, 2 & 3:

Result no: 1…….. 394 00

Result no: 2…….. 194 00

Result no: 3…….. 021 84

                             609 84

Here the answer can be checked by “casting out nines”

Example:  13  X

                 14

      =       182

Here in 13 : 1 + 3 = 4…(substitute for 13)

         in 14 : 1 + 4 = 5…(substitute for 14)

       in 182 : 1 + 8 + 2 = 11 = 1 + 1 = 2…(substitute for 182)

Multiply 4 X 5 = 20.  i.e. 2 + 0 = 2.

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Again we can check the sum:  252 X 242

                 252  …. 2 + 5 + 2 = 9

           X   242  …. 2 + 4 + 2  = 8

              60984 …6 + 0 + 9 + 8 + 4 = 27 = 2 + 7 =9.

Multiply the above numbers 9 x 8 = 72 = 7 + 2 = 9.

So the answer is correct.

YOU MAY TRY ANY NUMBER OF PROBLEMS AND ADOPT SIMPLE METHODS TO CARRY OUT CALCULATIONS.

அடுத்தப் பதிவில் LESSON FOUR – MULTIPLICATION BY FACTORS – MULTIPLYING DECIMAL காண்போமே!!

அன்புடன் 

AND.கிருஷ்ணமூர்த்தி / tnsfchromepet.