In the last article of this series we read how some of the math operations can be made very interesting. Nobody is dull in mathematics. The problem is that when a student start lacking in a particular topic of math, he loses confidence. If such things are repeated in his school life, a strong conception develops in him/her that math is not his/her cup of tea or it is impossible for him/her. Math then becomes a stranger for the student. With the passage of time, the student dishearten about this subject that he could not get rid of the phobia for math. QMaths is such an effort so that the basic operations of arithmetic can be made easy to understand as well as interesting.
Let’s try to understand easy short cuts for multiplying or dividing a number by ‘5’.
To multiply a number by ‘5’, we should make the number as half or we can say that divide the number by ‘2’. Then we should see whether the last number is ‘Even’ or ‘Odd’. If even put ‘0’ at the last and if odd then put ‘5’ at the last. The following examples can help to understand the shortcut:
286402 X 5
= 1432010
(Half of 2 is 1, 8 is 4, 6 is 3, 4 is 2, 0 is 0, 2 is 1 and last digit ‘2’ is ‘Even’, so ‘0’ is put at the last of the answer)
4163287 X 5
= 20816435
To understand in a better way, treat it as 4,16,32,8,7.
(Half of 4 is 2, 16 is 08, 32 is 16, 8 is 4 and 7 is 3 with 1 as remainder. The last digit ‘7’ is odd, so ‘5’ has been put at the last of the answer.
5460123 X 5
= 27300615
To understand in a better way, treat it as 54,6,0,12,3.
(Half of 54 is 27, 6 is 3, 0 is 0, 12 is 06, 3 is 1 with ‘1’ as remainder. The last digit ‘3’ is ‘odd’, so ‘5’ has been put at the last of the answer.
Let’s try:
642,082,246,288,640,866,244,826,884,260,024,846,282,864 X 5
Is this multiply sum still difficult for you?
Now we would try to understand the division of a number by ‘5’:
To divide a given number by ‘5’, the easiest way is to double the given number or we can say that multiply the number by ‘5’. Then put a decimal (.) leaving the last digit of the answer. The following examples can help to understand the shortcut:
142032 ‹ 5 =
28406.4
(Double of 1 is 2, 4 is 8, 2 is 4, 0 is 0, 3 is 6 and 2 is 4. A decimal has been placed before the last digit 4.
174232625 ‹ 5 =
34846525.0 or 34846525
To understand in a better way, treat it as 17,4,2,3,26,25.
(Double of 17 is 34, 4 is 8, 2 is 4, 3 is 6, 26 is 52, 25 is 50. A decimal has been placed before the last digit ‘0’ or we can write the number without ‘0’.
1262741835 ‹ 5 =
252548367.0 or 252548367
To understand in a better way, treat it as 1, 26, 27, 4, 18, 35
(Double of 1 is 2, 26 is 52, 27 is 54, 4 is 8, 18 is 36, 35 is 70. A decimal has been placed before the last digit ‘0’ or we can write the answer without decimal.
4230,1134,2314,0021,2113,2442,1423,4012,2331,2132,1230,4112,4001 ‹ 5
Is this division sum still difficult for you?
Let’s try to understand another short cut of multiply. If a figure is to multiplied by ‘11’, then the following shortcut can be used:
35 X 11 = 3 (3+5) 5 = 385
52 X 11 = 5 (5+2) 2 = 572
Go ahead a step more:
234536 X 11
= 2(2+3)(3+4)(4+5)(5+3)(3+6)6
= 2579896
417235180345127 X 11
= 4(4+1)(1+7)(7+2)(2+3)(3+5)(5+1)(1+8)(8+0)(0+3)(3+4)(4+5)(5+1)(1+2)(2+7)7
= 45895869837963971
Try this yourself:
235416317 X 11
Similarly it is very easy to multiply a figure by 25 or 125 if we use the basic concept of multiplication and use the easy short cuts available with Qmaths.
Are you interested to multiply 99999995 to 99999992 within 10 seconds? If so please wait for our coming articles. It may be possible for you to solve it in less than 10 seonds.
We shall also discuss methods to find the divisibility of a number not only by 2,3,4,5,6,8,9,10,11,12,15 but also the prime number like 7,13,17,23,29,31,37,41 etc. with very easy and non-conventional methods.
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Surinder Bharti Tiwari
QMaths Center of Learning
www.qmaths.com
email : info@qmaths.com
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