Pangkat 2

0

1^2 =0 1

2^2 =0 4

3^2 =0 9

4^2 = 16

5^2 = 25

6^2 = 36

7^2 = 49

8^2 = 64

9^2 = 81

Pangkat 2 :

123^2 = 1^2|2*1*2|2*1*3+2*2|2*2*3|3^2

000000= 1|4|6+4|12|9

000000= 1|4|10|12|9

000000= 1|4+1|0+1|2|9

000000= 1|5|1|2|9

000000= 15129 karena akhir 3^2 = 9

atau : 123*1|123*2|123*3

123|246|369

12|3+24|6+36|9

12|27|42|9

1|2+2|7+4|2|9

1|4|11|2|9

1|4+1|1|2|9

1|5|1|2|9

15129

Rumus Pembagian

0
123456789 : 23 =

1 x 23 =0 23
2 x 23 =0 46
3 x 23 =0 69
4 x 23 =0 92
5 x 23 = 115
6 x 23 = 138
7 x 23 = 161
8 x 23 = 184
9 x 23 = 207

00005
23 123|456789

000050003
000115+8 4|56789

000050003006
000115 69+15 5|6789

0000500030060007
000115 69 138+17 6|789

00005000300600070006
000115 69 138 161+15 7|89

000050003006000700060008
000115 69 138 161 138+19 8|9

0000500030060007000600080006
000115 69 138 161 138 184+14 9

0000500030060007000600080006
000115 69 138 161 138 184 138+11

5367686(11/23)

Cek :

(5367686 + 11/23) x 23 =

115|69|138|161|138|184|138+11

11|5+6|9+13|8+16|1+13|8+18|4+14|9

11|11|22|24|14|26|18|9

1|1+1|1+2|2+2|4+1|4+2|6+1|8|9

1|2|3|4|5|6|7|8|9

12345678

Rumus Pengurangan

0

123 - 45 =

01 002 003

000004 005

___________ _

1-0|2-4|3-5

001|0-2|-2

010-200|-2

0000008|-2

00007+1|-2

0007|10-2

00000078

Rumus Penjumlahan

0

123 + 456 + 789 =

001000002000003

004000005000006

007000008000009

_________________ +

1+4+7|2+5+8|3+6+9

00012|00150|18

01|02+10|05+10|8

0000001368

Rumus Perkalian Dengan 11

0

001 x 11 = 0011 =0001 1

011 x 11 = 0121 =001 2 1

121 x 11 = 1331 = 1 3 3 1

Rumus :

00a x 11 = a|a = aa

0ab x 11 = a|a + b|b

abc x 11 = a|a + b|b + c|c

Rumus Perkalian 2 Digit

0

ab x cd = a.ca.d + b.cb.d

Contoh :

12 x 34 = 1*31*4 + 2*32*4

00000000= 031008 = 03+10+08 = 0408

00000000= 408

98 x 76 = 9*79*6 + 8*78*6

00000000= 6354 + 5648 = 6311048

00000000= 6+13+10+48

00000000= 7448

00000000= 7448

Perkalian 2 Digit Yang Angka Terakhirnya Berjumlah 10

0

11 x 19 =0 209 = (1^2 + 1)1 * 9 = (1 * 2)1 * 9

12 x 18 =0 216 = (1^2 + 1)2 * 8 = (1 * 2)2 * 8

23 x 27 =0 621 = (2^2 + 2)3 * 7 = (2 * 3)3 * 7

24 x 26 =0 624 = (2^2 + 2)4 * 6 = (2 * 3)4 * 6

35 x 35 = 1225 = (3^2 + 3)5 * 5 = (3 * 4)5 * 5

45 x 45 = 2025 = (4^2 + 4)5 * 5 = (4 * 5)5 * 5

Rumus :

ab * a(10 - b) = (a * (a + 1))b * (10 - b)

Rumus-Rumus Praktis Pangkat Angka Ajaib 5

015^2 =00 225 = ( 1 *0 2).5^2

025^2 =00 625 = ( 2 *0 3).5^2

035^2 =0 1225 = ( 3 *0 4).5^2

045^2 =0 2025 = ( 4 *0 5).5^2

055^2 =0 3025 = ( 5 *0 6).5^2

065^2 =0 4225 = ( 6 *0 7).5^2

075^5 =0 5625 = ( 7 *0 8).5^2

085^5 =0 7225 = ( 8 *0 9).5^2

095^2 =0 9025 = ( 9 * 10).5^2

105^2 = 11025 = (10 * 11).5^2

Rumus umum : (a5)^2 = (a * (a + 1)).5^2

51^2 = 2601 = (5^2 + 1).1^2

52^2 = 2704 = (5^2 + 2).2^2

53^2 = 2809 = (5^2 + 3).3^2

54^2 = 2916 = (5^2 + 4).4^2

55^2 = 3025 = (5^2 + 5).5^2

56^2 = 3136 = (5^2 + 6).6^2

57^2 = 3249 = (5^2 + 7).7^2

58^2 = 3364 = (5^2 + 8).8^2

59^2 = 3481 = (5^2 + 9).9^2

Rumus umum : (5a)^2 = (5^2 + a).a^2

Rumus-Rumus Praktis Untuk Perkalian

Perkalian

a * b = a * b

ab * cd = ab * c0 + d * a0 + b * d 0000atau

0000000000cd * a0 + b * c0 + b * d

abc * def = abc * d00 + ef * a00 + (bc * ef) =

000000000000abc * d00 + ef * a00 + b * c * e0 +

000000000000f * b0 + c * f

000000000000atau

000000000000def * a00 + bc * d00 + e * f * b0 +

000000000000c * e0 + c * f

000000000000abc * de0 + f * ab0 + c * f 0000atau

000000000000def * ab0 + c * de0 + c * f

Pangkat

a^2 = a * a

(ab)^2 = (ab + b) * a0 + b^2 0000bisa juga

(ab)^2 = a^2 * 10^2 + 2 * a * b * 10 + b^2

(abc)^2 = (abc + bc) * a00 + (bc)^2 =

0000000000(abc + bc) * a00 + (bc + c) * b0 + c^2

0000000000atau

0000000000(abc + c) * ab0 + c^2 0000atau

(abc)^2 diuraikan a 00= (a^2) 000000000000* 10^4

000000000000000000ab 0= (2 * a * b) 000000* 10^3

000000000000000000abc0= (2 * a * c + b^2) * 10^2

000000000000000000bc 0= (2 * b * c) 000000* 10

000000000000000000c 00= (c^2)

000000000000000000000000______________________ +

(abcd)^2 = a 000= (a^2) * 10^(2(n-(2.i)/2))

00000000000ab000=

00000000000abc 0=

00000000000abcd = (2 * a * d + 2 * b * c)

0000000000000000000* 10^(2(n - (2.i)/2))

00000000000bcd 0=0

00000000000cd 00=

00000000000d 000=

0000000000000000000___________________________ +

Keterangan :

n = Berapa angka yang ingin dipangkatkan

i = 1 ... (2.n - 1)

Tip's dan Trik Menghitung dengan Cepat 3

Perkalian :

000123 x 18

1. Pertama-tama kalikan 3 dengan 8 = 24 diletakkan

000pada urutan pertama

0001 2 3

0000000|

0000000|

0000 1 8

000_____ x

00000024

2. Kemudian kalikan 2 dengan 8 = 16 ditambah 1 x 3

000= 3, 16 + 3 = 19, diletakkan pada urutan kedua

000dari kanan.

0001 2 3

00000\0/

00000/0\

0000 1 8

000_____ x

00000024

0000019

000_____ +

00000214

3. Selanjutnya kalikan 1 dengan 8 = 8 ditambah 2 x

0001 = 2 ditambah 0 x 3 = 0, 8 + 2 + 0 = 10,

000diletakkan pada urutan ke 3 dari kanan.

000 123

000 \|/

000 /|\

000 018

000_____ x

00001024

0000019

000_____ +

00001214

4. Untuk urutan ke 4 dari kiri kalikan 1 dengan 1

000= 1 ditambah 0 x 2 = 0, 1 + 0 = 1

0001 2 3

00 \ /

00 / \

0000 1 8

000_____ x

00001024

0000119

000_____ +

00002214

5. Terakhir kalikan 1 dengan 0 = 0

0001 2 3

00 |

00 |

0000 1 8

000_____ x

00001024

0000119

000_____ +

00002214

6. Kesimpulan 123 x 18 = 2214