Example 1: Multiply 7 by 8. : base number as 10. HTML clipboard Here we compare this multiplication with the formula N1 = 7 , N2 = 8 and Deviation D1 = -3 & D2 = -2
95 -05
(75+(-05)) or (95+(-25)) / 25x05 = 70/125
Compare multiplication with the formula N1 = 786 , N2 = 998 & Deviation D1 = -214 & D2 = -002
786 -214
998 -002
(786+(-002)) or (998+(-214)) / 214x002 = 784/428 = 784428
HTML clipboard D- Multiplication whose first figure are same And whose last figure add up to 10, 100 ,1000 etc.
Example.1 : Find 43 X 47
Check for R.H.S : 3 + 7 = 10, L.H.S. portion remains the same i.e.,, 4.
HTML clipboard HTML clipboard E. Numbers of which the last 2 or 3 or 4 digits added up gives 100, 1000, 10000 etc.
HTML clipboard The same rule works when the sum of the last 2, last 3, last 4 digits added respectively equal to 100, 1000, 10000
HTML clipboard Example.1 : Find 292 X 208
HTML clipboard Here 92 + 08 = 100, L.H.S portion is same i.e. 2
HTML clipboard Example.3 : Find 693 X 607 HTML clipboard Check for : 93 + 07 = 100, L.H.S. portion remains the same i.e., 6HTML clipboard HTML clipboard 6 93HTML clipboard 420651HTML clipboard Now R.H.S product 93 X 07 can be obtained mentally. 693 x 607 = 6 x 7 / 93 x 07 = 420 / 651 (for 100 raise the L.H.S. product by 0 i.e. 42X10) = 420651. HTML clipboard Assignments : Q1. 393 X 307 Q2. 696 X 604 Q3. 873 X 827 Q4. 188 X 112HTML clipboard HTML clipboard Example.1 : Find 213 X 203 [Base is 200 ]HTML clipboard Complement of 213 is 13 Complement of 203 is 03. HTML clipboard 213 / 13HTML clipboard 203 / 03 HTML clipboard 213+3 / 39 = 216 x 2 / 39 HTML clipboard G- Numbers are close to different bases 10,000, 100 etc..HTML clipboard Example.6 : Find 9998 X 94HTML clipboard 94 / - 06[Base 100] HTML clipboard 9398 / 12 = 939812HTML clipboard Note that 6 is not subtracted from 8, but from the 9 above the 4 in 94 Second column from left. So 9998 becomes 9398.Right hand side will as lower base 100
998 -002
(786+(-002)) or (998+(-214)) / 214x002 = 784/428 = 784428
Example.1 : Find 43 X 47
Check for R.H.S : 3 + 7 = 10, L.H.S. portion remains the same i.e.,, 4.
Multiply 4 ( the same figure in both the numbers ) by the next number up 5. This gives 4 X 5 = 20 as the first part of the answer and the last part is 3 X 7 = 21 so the answer is 2021
4 3
4 7
4X5 / 3X7 = 2021
Example.3 : Find 127 X 123
Check for : 7 + 3 = 10, L.H.S. portion remains the same
12 7
12 3
12X13 / 7X3 = 15621
Assignments : Q1. 23 X 27 Q2. 34 X 36 Q3. 62 X 68 Q4. 136 X 134
2 92
2 08
2X3 / 92X08 = 60/736
6 07
F- Multiplication by using other base
since the base is 200 i e 2X100. The numbers are close to 200 which is 100X 2 we multiply only the left hand part of the answer by 2 to get 43239.HTML clipboard
Numbers are close to different bases 10,000 and 100
9998 / 02 [Base 10000]