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

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

Multiplication is the process of finding the product of two quantities which are called the multiplicand and the multiplier. Multiplication is  denoted by the multiplication sign X, or by a dot. Usually, students who study in secondary schools master multiplication tables.

 If you know little multiplication and 2 times table, you can do multiplication of numbers above 10 and 100 easily, without using pen and paper. Bill Handley, Trachtenberg and few others have tried these methods.

We begin multiplying numbers up to ten. 

Suppose you want to know 8 X 6.

Write as below:

8 X 6

0    0

The first number to be multiplied is 8. To make it you have to add 2. Write 2 in the circle below 8. Similarly write 4 in the circle below 6 as number 4 is needed to make it 10.

Now it would be

8 X 6

2    4

Subtract diagonally

8 – 4 = 4 or 6 – 2 = 4. This is the first digit of the answer. Multiply the numbers in the circles. Two times 4 is 8. This is the second digit of the answer.

So, the answer is 48.

Let us see some more examples:

a)4 x 9 ; b) 9 x 6; c)8 x 9; d) 8 x 7; e) 7 x 9; f) 5 x 9

a) 4 x 9

    6    1

4 – 1 = 3 = 9 -6 multiply the numbers 6 x 1 = 6. So, the answer is 3 6.

b) 9 x 6

    1    4

9 – 4 = 5 = 6 – 1. Multiply the numbers 1 x 4 = 4. So, the answer is 5 4.

c) 8 X 9

    2    1

8 – 1 = 7 = 9 – 2. Multiply the numbers 2 x 1 = 2. So, the answer is 7 2.

d) 8 X 7

     2    3

8 – 3 = 5 = 7 – 2. Multiply the numbers 2 x 3 = 6. So, the answer is 5 6.

e) 7 X 9

    3     1

7 – 1 = 6 = 9 – 3. Multiply the numbers 3 X 1 = 3. So, the answer is 6 3.

f) 5 X 9

   5     1

5 – 1 = 4 = 9 – 4. Multiply the numbers 5 X 1 = 5. So, the answer is 4 5.

Those who know tables, learning this method is an added advantage. Otherwise, a little practice helps to learn the method.

Now we will see how to multiply numbers above 10 (Ten.)

Suppose we need to multiply 95 by 98. {i.e., 95 X 98 =?}

5 is needed to make 95 to 100 and 2 is needed to make 98 to 100. Write the numbers in brackets as below.

95 X 98

(5)    (2)

Take away these numbers diagonally. (95 – 2 or 98 – 5 = 93.)

Multiply the numbers in the brackets. (5 X 2 = 10)

The answer is 9310.

Try these multiplications: 1) 97 X 94; 2) 96 X 98; 3) 99 X 98; 4)91 X 92

1) 97 X 94 the answer is 9118.

   (3)    (6)

2) 96 X 98 the answer is 9408.

   (4)    (2)

3) 99 X 98 the answer is 9702.

   (1)    (2)

1) 91 X 92 the answer is 8372.

   (9)    (8)

In the above problems 10 and 100 are used as reference numbers respectively. Using these reference numbers multiplying numbers in the Teens such as 13, 21 etc;

Let us multiply 12 X 18.

12 and 18 are above reference number 10. So let us use (+) sign and write as below. (+2)  (+8); 12 X 18; work diagonally i.e., 12 + 8 = 20. Multiply 20 by the reference number 100. It is 200. It is a part of the answer. Multiplying the numbers in the brackets we get 16. So, the answer is 200 + 16 = 216.

If the number to be multiplied is below reference number put the brackets as below. Example: 6 X 9 =? (-4) and (-1). Take away diagonally. 6 – 1 = 5 or 9 – 4 = 5. So, five times 10 are 50. Multiply the numbers in the brackets. (-4) X (-1) = 4. So, the answer is 50 + 4 = 54.

Try another example:

13 X 32: (+3) (+22), the reference number is 10.

13 X 32 =? Add diagonally 13 + 22 = 35 = 32 + 3. Multiply 35 by the reference number 10, i.e. 35 x 10 = 350. Multiply the numbers in the brackets and add with 350. 3 x 22 = 66 + 350 = 416. So the answer is 416.

Try another example:

102 X 108. These numbers are above 100. The reference number is then 100.

Write 2 and 8 in the brackets as the numbers are above 100.

                                 (+2)   (+8)

Reference 100…. 102 X 108 = 110 00 (subtotal)

                                                             16

                             Answer……….110 16

 Try another example:

108X 125. These numbers are above 100. The reference number is then 100.

Write 2 and 8 in the brackets as the numbers are above 100.

108 + 25 = 133 = 125 + 8: multiply 133 with the reference number 100.

i.e. 133 X 100 = 133 00. This is a part of the answer. Multiply the numbers in the brackets. 8 X 25 = 200. Add with 13300.

                                 (+8)  (+25)

Reference 100…. 108 X 125 = 133 00 (subtotal)

                                                          2 00

                             Answer……....135 00

So, the answer for 108 X 125 = 13500.

A REFERENCE NUMBER IS ALWAYS NECESSARY.

அடுத்தப் பதிவில் இரு வேறு ரெபரன்ஸ் எண்களைக் கொண்டு பெருக்கும் முறைதனைக் காண்போமே!!

அன்புடன் 

AND.கிருஷ்ணமூர்த்தி / tnsfchromepet.