Trik Perkalian dan Pembagian Cepat

Perhatikan contoh-contoh berikut ini :

1. 13 x 17 = 1x2|3x7 = 221

2. 23 x 27 = 2x3|3x7 = 621

3. 33 x 37 = 3x4|3x7 = 1221

4. 43 x 47 = 4x5|3x7 = 2021

5. 53 x 57 = 5x6|3x7 = 3021, dst.

Contoh lain :

1. 32 x 25 = 8 x 4 x 25 = 8 x 100 = 800

2. 64 x 12,5 = 8 x 8 x 12,5 = 8 x 100 = 800

3. 125 x 800 = 125 x 8 x 100 = 1000 x 100 = 100.000

Dengan pendekatan 10, 100, ... :

(100 + a)(100 + b) = 10000 + (a+b)100 + ab

Contoh :

1. 104 x 105 = (100 + 4)(100 + 5) = 10000 + 900 + 20 = 10920

2. 106 x 103 = (100 + 6)(100 + 3) = 10000 + 900 + 18 = 10918

(100 - a)(100 - b) = 10000 - (a+b)100 + ab

Contoh :

1. 97 x 96 = (100 – 3)(100 – 4) = 10.000 – 700 +12 = 9312

2. 96 x 95 = (100 – 4)(100 – 5) = 10.000 – 900 +20 = 9120

(10 + a)(10 - b) = 100 + (a-b)10 - ab

Contoh :

1. 13 x 8 = (10 + 3) (10 – 2) = 100 + (3-2)10 – 3.2 = 104

2. 14 x 7 = (10 + 4) (10 – 3) = 100 + (4-3)10 – 4.3 = 98

Dengan pengelompokan :

1. 751 x 754 = 75^2|(1+4).75|1.4 = 5625+37|5|4 = 566254

2. 325 x 425 = 3.4|(3+4).25|25^2 = 12+1|75+6|25 = 138125

3. 2512 x 2512 = 25^2|25.24|12.12 = 625+6|00+1|44 = 6310144

4. 2011 x 2011 = 2^2|2.022|011^2 = 4|044|121 = 4044121

Contoh pembagian :

1. 4949 : 7 = (4900 : 7) + (49 : 7) = 700 + 7 = 707

2. 5463 : 9 = (5400 : 9) + (63 : 9) = 600 + 7 = 607

3. 4249 : 7 = … = 607

4. 2436 : 4 = … = 609

5. 3515 : 5 = … = 703

6. 6432 : 8 = … = 804