Take for instance multiplication of 2847. Build the answer in three steps. First, 27=14. 14 , 87=56 => add 5 to 14 and stick the 6 on the end, i. e 196 196, 74=28=>add 2 to 196 and stick the 8 on the end, i. e 1988 .
Suppose you want to calculate (108109) where the base is 100. Add 108 and 9 to get 117. Add to the end 98, or 72, to get your answer: 11772. Therefore, 108109=117||72=11772 Another example: (115106). Add 115 + 6 = 121, and then stick 90(156=90) on the end. 115106=121||90=12190. Another example: 108113=121||104 =12204. 121 is 113+8, and 104 is 813. Add the 1 from 104 to the last digit of 121 to get an answer with the right number of digits, 12204. When base is 1000 : Consider 10241008. Just write 1032 (1024+8=1032). Suffix it with 192 (0248=192) to get 1032192.
If you want to calculate (9889) where base is 100, just write 22 [from (100-98=2)(100-89=11)=22] and prefix it with 87 [from 98-11=87 or 89-2=87]. When base is 1000: Consider 998568. Now just write 864 [from (1000-998=2)(1000-568=432)]. Prefix it with 566 [from 568-2=566 or 998-432=566].
Consider the example 32 x 38 = 1216. Both numbers here start with 3 and the last digits (2 and 8) add up to 10. Multiply 3 (the first digit of both numbers) by 4 [from (3 + 1)] to get 12 for the first part of the answer. And multiply the last figures: 2 x 8 = 16 to get the last part of the answer. Similarly: 4248=20||16=2016 5357=30||21=3021 99*91=90||09=9009
Consider the example 2525. The last two digits of the answer are 25. The first part of the answer is the product of the first digit of the number being squared and its successor. In this example, the first digit of 25 is 2, and its successor is 3 (2+1=3). 2 * 3 = 6, so the solution is 625. Similarly: 3535=(34)||25=1225 4545=(45)||25=2025 9595=(9*10)||25=9025
To multiply any 2-figure number by 11 we just put the total of the two digits between the 2 figures. For example, 26 x 11 = 286. Notice that the outer digits in 286 are the 2 and 6 from 26. The middle figure is the sum of 2 and 6. 4511=495 6511=715. This involves a carry: 6+5 = 11, which is now added to the 6 to get 71 for the first two digits. For 3 digits, 13211=1||(1+3=4)||(3+2=5)||2=1452 14811= 1 || (1+4=5 5+1(carry)= 6 ) || (4+8=12 =>2 carry 1)||8 =1628
23 / 9 = 2 remainder 5 . The first figure of 23 is 2, and this is the answer. The remainder is just 2 and 3 summed up. Similarly: 34/9=3 remainder 7 71/9=7 remainder 8
