SPEED MATHEMATICS!!! SUBTRACTION-கழித்தல் - வேகம் & விவேகம்!

SPEED  MATHEMATICS!!! கணிதத்தில் வேகமா???
ஆம் கணிதத்தில் வேகம் கூட்டுவோமே !!!
 
http://tnsfchrompet.blogspot.in/2012/09/speed-mathematics.html
கடந்த பதிவில்  எளிய முறையில், அதி விரைவில் ஒன்று, இரண்டு மற்றும் அதிக இலக்க எண்களைக் கையாண்டு  ADDITION எனப்படும் கூட்டல்  முறையில் கணிதத் தீர்வுகளைக் அதிவிரைவாகக் காணும் முறைதனை நாம் கண்டோம்.  தற்போது நாம் காணவிருப்பது; ஒன்று, இரண்டு மற்றும் அதிக இலக்க எண்களைக் கையாண்டு  SUBTRACTION எனப்படும் கழித்தல்  முறையில் கணிதத் தீர்வுகளைக் அதிவிரைவாக காணும் முறைதனை காண்போமே !!!

LESSON: II   -   SUBTRACTION:
Subtraction is an essential function. Suppose I take loan of Rs.15,000/- from my friend. I return Rs.12,450 after 2 months.Then what is the balance that I have to pay to my friend. Then the function "SUBTRACTION" comes to our help.
 
15,000 (-) 12450 = 2550.  I have to pay Rs. 2550/- to my friend. But how to do it mentally and quickly? Speed mathematics is to be used.


METHOD: 1
For example you have to subtract 8 from 63.
To take Eight from 63 in your mine, the fastest method is to subtract 10 and add 2
i.e., 53+2 = 55 is the answer.
To take 6 from 84, take 10, (74) and add 4. (78).
Suppose you have to subtract 67 from 456.
Take 100 to 356. Add 33, to get 389.
Remember here 67+33 + 100)
i.e., 456 - 67 + 389.
               (33)
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METHOD; 2
Say the number you are subtracting is below 100 and the number you are subtracting from is >100 and <20.
For Example:  154 - 86 is required.
154-86 = 
(54)(14)
Here 86 is 14 less than 100.
so also 154 is 54 higher than 100.
So simply add 14 and 54. It is 68. You can do it mentally.
To be sure, try another example.
198 - 35
        (65)
98 + 65 = 163.
Another example: 123 - 70
                               (23) (30) 
 23 + 30 = 53.
Suppose you have a number to subtract and the number is below ten.
say 18 - 5 =
          +(5)
         8+5 = 13. ( 18 - 5 = 13) 

Suppose you have three digits

Eg :  861 - 376 =
here 376 is 24 less 400. So, 861 - 400 = 461 than add 24
i.e., 461 + 24 = 485. (Here addition function becomes necessary)
541 - 87 =  Here 13 less of 100. So, subtract 100 from 541 which results = 441 and than add 13. So, the result is 454.
541 - 87 = (541-100)+13 = 454.
Subtracting large number from another large number needs writing. 

But the mental subtraction is quite easy. Usually such subtraction is done by carrying and borrowing.

Eg :    85
        8963
(-)    3896
        5067

Here subtract 6 from 3. It is not possible. So, you have to borrow 1 from the tens column. So, in the upper line 6 becomes 5. In easy method, we say instead 6 from 13 and 6 from 10 = 4. Then add the above (37 to get 7, i.e ., the first digit answer.

It is clear that with this method we do not subtract any number greater than 10. Next, we do addition. So, 9 from 5 won't go. So borrow again. 9 from 10 is 1, plus 5 in 6 which is next digit answer.

Then 8 from 8 is possible. The 3rd digit is 0.

Then 3 from 8 is 5, the final digit of the answer.

For subtraction from a power of ten, a simple rule is followed.

Eg : 1000

(-)      875

You have to start from left or right.  Subtract the units digit from 10, then each successive digit from 9, then subtract 1 from the digit on the left.
Now subtract the units digit from 10.
i.e., 10 - 5 = 5. It is the right hand digit of the answer. Then take the other digits away from 9. Take 1 from the first digit.
i.e., 5 from 10 is 5
       7 from 9 is 2
       8 from 9 is 1
and 1 from 1 is 0

So, the answer is 125. This is from right to left. Suppose we try from Left to right.

1 from 1 is 0
8 from 9 is 1
7 from 9 is 2
5 from 10 is 5.......The answer is 125.

Example No: 2

      80000

(-)    6478

Take 1 from the left hand digit (8) to get 7. It is the first digit or the answer. 6 from 9 is 3, 4 from 9 is 5, 7 from 9 is 2 and 8 from 10 is 2.

The answer is 73522.

When the number you are subtracting has only two digits or few digits than the one you are subtracting from, then add zeros before the number subtracting to complete the calculation. Zeros can be added mentally.

For example: you have to subtract 47 from 62000, then write it as

     62000

(-)   0047

    61953

Extend the zeros in front of the number being subtracted as far as the first digit that is not a zero.  Subtract 1 from this digit. 2 - 1 = 1.
Subtract each successive digit from 9 till you reach the final digit which you subtract from 10.
(9-0=9), (9-4=5),10-7=3).

VERIFICATION:

Checking the answer is similar to that used for addition, that is by casting out nines.

Example 1: 9 5 3 8..........7
               (-) 3 4 9 6......... -4
                    6 0 4 2........   3    .. So the answer is correct.

Example 2: 5 6 7 2 ..........2
               (-) 2 5 9 6......... -4
                    3 0 7 6........  7    .. Here 2 minus 4 equals 7.  Is it possible?

It is true - All that you have to do, you add 9 to the number you are subtracting from 2 + 9 = 11. Then the problem would be 11 - 4 = 7. So, the answer is correct.

KNOW THESE TERMS:

ADDEND: ONE OF TWO MORE NUMBERS TO BE ADDED.

SUM: THE ANSWER WE GET BY ADDING TWO NUMBERS. (THE RESULT OF ADDING TWO OR MORE NUMBERS.)

ADDEND  ....... 18

ADDEND + ..... 28

SUM.................. 46

NUMBER: A number may be a single digit such zs 9, 6 etc., or an entire numerical expression of any combination of digits such as 9 4 2 5  or 1 1 4 2 5 etc..,

PLACE VALUE:

The value given to a digit because of its position in a number.

Example: 8 5 is a two digit number.

Here Eight, 8 is the tens digit. Therefore its place value is 8 tens, 5 is the unit digit. So its place value is 5 units.

DIFFERENCE:

The answer to a subtraction problem is called the difference.

Example: The difference of 10 and 6 is 4.

SUBTRAHEND:

A number from which another number is to be subtracted.

MINUEND:

A number from which another number is to be subtracted.

682 – 242 = 440. Here Minuend is 682. Subtrahend is 242.

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In lesson III we will see the MULTIPLICATION.

மேலும் பயணிப்போம் 
இனிய நண்பர்களே !! 

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AND .கிருஷ்ணமூர்த்தி / tnsfchromepet