# Techniques

## Multiplication tables

Almost every child in school is told to memorize multiplication tables from 1 to 20. Once these are memorized, one can easily extend by learning very quickly and be able to recite 52 of all tables from 1 to 100. Let us see how.

Consider this. Having memorized 20 tables means you can recite 20 tables. Add to that tables of 30, 40, 50, 60, 70, 80, 90 and 100, which simply are tables of 2 to 10 with 0 appended at the end. That means you already can recite 8 more (total 28) tables.

Tables of 21, 31, 41, 51, 61, 71, 81 and 91 are as simple as reciting tables of 2 to 9 respectively with 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 appended to the unit's place.

For example,

Table of 71 is as follows

7 1 71

14 2 142

21 3 213

28 4 284

35 5 355

42 6 426

49 7 497

56 8 568

63 9 639

70 0 700

With little practice you can now recite 8 more (total 36) tables.

For tables of 29, 39, 49, 59, 69, 79, 89 and 99, since the unit's place is 9 the unit's place of table of all these numbers will go as 9, 8, 7, 6, 5, 4, 3, 2, 1 and 0. For the ten's place and above in the table, if we consider the table with ten's place value is 'n', then just add (n+1) for next value in the table. This can be easily understood by taking an example.

Let consider example of table of 69 for explaining this. Here the ten's place value is n=6. So the table of 69 will go as follows,

(n+1) = 7

Ten's One's Table

6 9 69

(6+7) 13 8 138

(13+7) 20 7 207

(20+7) 27 6 276

(27+7) 34 5 345

(34+7) 41 4 414

(41+7) 48 3 483

(48+7) 53 2 532

(53+7) 60 1 601

(60+7) 67 0 670

Some more practice and that will take the total to 44.

Even tables of numbers ending with 5 are easy to learn. The unit's place for these number alternate between 5 and 0. And, similar to tables of numbers ending with 9, the ten's place values need to be added, but alternatively by (n+1) and n.

Consider as an example multiplication table of 45. It goes as follows.

n = 4

(n+1) = 5

Ten's One's Table

4 5 45

(4+5) 9 0 90

(9+4) 13 5 135

(13+5) 18 0 180

(18+4) 22 5 225

(22+5) 27 0 270

(27+4) 31 5 315

(31+5) 36 0 360

(36+4) 40 5 405

(40+5) 45 0 450

That means you now know total 52 tables.