Squaring Numbers
Multiplying Numbers
 same 1st digit
 same 1st digit, sum 10
 same 2nd digit
 3 digits, middle 0
 3 digits, middle 1
 3 digits, middle 2
 3 digits, middle 3
 3 digits, middle 4
 3 digits, middle 5
 difference of 1
 difference of 2
 difference of 3
 difference of 4
 difference of 6
 difference of 8
 difference of 10
 2 digits by 1 1/25
 2 digits by 1 1/16
 2 digits by 1 1/15
 2 digits by 1.1
 2 digits by 1 1/9
 2 digits by 1 1/8
 2 digits by 1 1/7
 2 digits by 1 1/6
 2 digits by 1 1/5
 2 digits by 1 2/9
 2 digits by 1 1/4
 2 digits by 1 2/7
 2 digits by 1.3
 2 digits by 1 1/3
 2 digits by 1 3/8
 2 digits by 1 2/5
 2 digits by 1 3/7
 2 digits by 1 1/2
 2 digits by 1 4/7
 2 digits by 1 3/5
 2 digits by 1.6
 2,3 digits by 1 2/3
 2 digits by 1.7
 2 digits by 1 5/7
 2 digits by 1 3/4
 2 digits by 1 4/5
 2 digits by 1 5/6
 2 digits by 1 6/7
 2 digits by 1.9
 2 digits by 2.1
 2 digits by 2 1/9
 2 digits by 2 1/7
 2 digits by 2 1/5
 2 digits by 2 2/9
 2 digits by 2 1/4
 2 digits by 2.3
 2 digits by 2 1/3
 2 digits by 2 3/8
 2 digits by 2 2/5
 2 digits by 2.4
 2 digits by 2 4/9
 2, 3 digits by 2 1/2
 2 digits by 2 4/7
 2 digits by 2.6
 2 digits by 2 5/8
 2 digits by 2 2/3
 2 digits by 2.7
 2 digits by 2 5/7
 2 digits by 2 3/4
 2 digits by 2.8
 2 digits by 2 7/9
 2 digits by 2 6/7
 2 digits by 2.9
 2 digits by 3.1
 2 digits by 3 1/8
 2 digits by 3 1/7
 2 digits by 3 1/6
 2 digits by 3.2
 2 digits by 3 2/9
 2 digits by 3 1/4
 2 digits by 3 1/3
 2 digits by 3.4
 2 digits by 3 3/7
 2 digits by 3 4/9
 2 digits by 3 1/2
 2 digits by 3.6
 2 digits by 3 4/7
 2 digits by 3 5/8
 2 digits by 3 2/3
 2 digits by 3.7
 2 digits by 3 5/7
 2 digits by 3 3/4
 2 digits by 3 4/5
 2 digits by 3 6/7
 2 digits by 3 7/8
 2 digits by 3.9
 2 digits by 4.1
 2 digits by 4 1/4
 2 digits by 4 1/7
 2 digits by 4 1/6
 2 digits by 4 1/5
 2 digits by 4 2/7
 2 digits by 4 1/3
 2 digits by 4.3
 2 digits by 4.4
 2 digits by 4 3/7
 2 digits by 4 4/9
 2 digits by 4 1/2
 2 digits by 4 5/9
 2 digits by 4.6
 2 digits by 4 2/3
 2 digits by 4.7
 2 digits by 4 3/4
 2 digits by 4 4/5
 2 digits by 4 5/6
 2 digits by 4 7/8
 2 digits by 4.9
 2 digits by 5.1
 2 digits by 5 1/8
 2 digits by 5 1/6
 2 digits by 5.2
 2 digits by 5 1/4
 2 digits by 5.3
 2 digits by 5 4/9
 2 digits by 5 1/2
 2 digits by 5 5/9
 2 digits by 5.6
 2 digits by 5.7
 2 digits by 5 4/7
 2 digits by 5 5/7
 2 digits by 5 4/5
 2 digits by 5 6/7
 2 digits by 5.9
 2 digits by 6.1
 2 digits by 6 1/8
 2 digits by 6 1/5
 2 digits by 6 1/4
 2 digits by 6.3
 2 digits by 6 1/3
 2 digits by 6 3/8
 2 digits by 6.4
 2 digits by 6 4/9
 2 digits by 6 1/2
 2 digits by 6 5/9
 2 digits by 6.6
 2 digits by 6 2/3
 2 digits by 6 7/9
 2 digits by 6 5/6
 2 digits by 6.8
 2 digits by 6 6/7
 2 digits by 6 8/9
 2 digits by 6.9
 2 digits by 7.1
 2 digits by 7 1/7
 2 digits by 7.2
 2 digits by 7 1/4
 2 digits by 7.3
 2 digits by 7 2/7
 2 digits by 7.4
 2 digits by 7 1/2
 2 digits by 7 3/5
 2 digits by 7.6
 2 digits by 7.7
 2 digits by 7 3/4
 2 digits by 7 4/5
 2 digits by 8.1
 2 digits by 8 1/6
 2 digits by 8.2
 2 digits by 8 2/7
 2 digits by 8.3
 2 digits by 8 1/3
 2 digits by 8 3/7
 2 digits by 8 4/7
 2 digits by 8 1/2
 2 digits by 8.6
 2 digits by 8 5/8
 2 digits by 8 2/3
 2 digits by 8 5/7
 2 digits by 8 7/9
 2 digits by 8.8
 2 digits by 8 7/8
 2 digits by 8 8/9
 2 digits by 8.9
 2 digits by 9.1
 2 digits by 9.2
 2 digits by 9.3
 2 digits by 9 1/3
 2 digits by 9.4
 2 digits by 9 1/2 (four steps)
 2 digits by 9 1/2 (two steps)
 2 digits by 9.6
 2 digits by 9 2/3
 2 digits by 9 5/7
 2 digits by 9.7
 2 digits by 9 3/4
 2 digits by 9 7/9
 2 digits by 9 4/5
 2 digits by 9 5/6
 2 digits by 9 6/7
 2 digits by 9 7/8
 2 digits by 9 8/9
 2 digits by 10.1
 2 digits by 10.4
 2 digits by 10.6
 2 digits by 10.7
 2 digits by 10 1/2
 2 digits by 11 1/2
 2 digits by 12 1/2
 2 digits by 15
 2,3 digits by 16 2/3
 2 digits by 18
 2 digits by 19 1/2
 2 digits by 20 1/2
 2 digits by 21
 2 digits by 22
 2 digits by 23
 2 digits by 24
 2,3 digits by 25
 2 digits by 26
 2 digits by 27
 2 digits by 28
 2 digits by 29
 2 digits by 29 1/2
 2 digits by 30 1/2
 2 digits by 31
 2 digits by 32
 2 digits by 33
 2 digits by 33 1/3
 2 digits by 34
 2 digits by 35
 2 digits by 36
 2 digits by 37
 2 digits by 37 1/2
 2 digits by 38
 2 digits by 39
 2 digits by 39 1/2
 2 digits by 40 1/2
 2 digits by 42
 2 digits by 43
 2 digits by 44
 2 digits by 45
 2 digits by 46
 2 digits by 47
 2 digits by 48
 2 digits by 49 (a)
 2 digits by 49 (b)
 2 digits by 49 1/2
 2 digits by 50 1/2
 2 digits by 51
 2 digits by 52
 2 digits by 53
 2 digits by 54
 2 digits by 55 (a)
 2 digits by 55 (b)
 2 digits by 56
 2 digits by 57
 2 digits by 58
 2 digits by 59
 2 digits by 59 1/2
 2 digits by 60 1/2
 2 digits by 61
 2 digits by 62
 2 digits by 63
 2 digits by 64
 2 digits by 65
 2 digits by 66
 2 digits by 67
 2 digits by 68
 2 digits by 69
 2 digits by 69 1/2
 2 digits by 70 1/2
 2 digits by 71
 2 digits by 72
 2 digits by 73
 2 digits by 74
 2,3 digits by 75
 2 digits by 76
 2 digits by 77
 2 digits by 78
 2 digits by 79
 2 digits by 79 1/2
 2 digits by 80 1/2
 2 digits by 81
 2 digits by 82
 2 digits by 83
 2 digits by 84
 2 digits by 85
 2 digits by 86
 2 digits by 87
 2 digits by 88
 2 digits by 89
 2 digits by 89 1/2
 2 digits by 90 1/2
 2 digits by 91
 2 digits by 92
 2 digits by 93
 2 digits by 94
 2 digits by 95
 2 digits by 97
 2 digits by 98
 2 digits by 99
 3 digits by 99
 2,3 digits by 101
 2 digits by 102 + 11
 2 digits by 103 + 12
 2 digits by 125
 3 digits by 143
 2 digits by 166 2/3
 2 digits by 198
 2 digits by 201 + 11
 2 digits by 202 + 11
 2 digits by 250
 2 digits by 297
 2 digits by 375
 2 digits by 396
 2 digits by 495
 2 digits by 594
 2 digits by 625
 2 digits by 693
 2 digits by 792
 2 digits by 875
 2 digits by 891
 2 digits by 999
 2,3 digits by 1001 + 21,201
 24 digits by 1000, + 21, 201, 2001
 25 digits by 100001
 1 rep. by 9 rep.
 1 rep. by 12 rep.
 1 rep. by 13 rep.
 1 rep. by 14 rep.
 1 rep. by 15 rep.
 1 rep. by 16 rep.
 1 rep. by 17 rep.
 1 rep. by 18 rep.
 1 rep. by 19 rep.
 1 rep. by 21
 1 rep. by 22
 1 rep. by 23
 1 rep. by 24
 1 rep. by 25
 1 rep. by 26
 1 rep. by 27
 1 rep. by 29
 1 rep. by 33
 1 rep. by 41
 1 rep. by 44
 1 rep. by 45
 1 rep. by 55
 1 rep. by 66
 1 rep. by 77
 1 rep. by 88
 1 rep. by 99
 1 rep. by 222
 1 rep. by 333
 2 rep. by 5 rep.
 2 rep. by 9 rep.
 2 rep. by 12
 2 rep. by 13
 2 rep. by 14
 2 rep. by 15
 2 rep. by 16
 2 rep. by 17
 2 rep. by 22
 2 rep. by 24
 2 rep. by 28
 2 rep. by 29
 2 rep. by 33
 2 rep. by 44
 2 rep. by 45
 2 rep. by 55
 2 rep. by 66
 2 rep. by 77
 2 rep. by 88
 2 rep. by 99
 3 rep. by 6 rep.
 3 rep. by 9 rep.
 3 rep. by 13
 3 rep. by 14
 3 rep. by 15
 3 rep. by 22
 3 rep. by 23
 3 rep. by 24
 3 rep. by 35
 3 rep. by 55
 3 rep. by 66
 3 rep. by 77
 3 rep. by 88
 3 rep. by 99
 4 rep. by 13
 4 rep. by 14
 4 rep. by 15
 4 rep. by 17
 4 rep. by 22
 4 rep. by 24
 4 rep. by 28
 4 rep. by 31
 4 rep. by 36
 4 rep. by 42
 4 rep. by 44
 4 rep. by 55
 4 rep. by 66
 4 rep. by 88
 4 rep. by 99
 4 rep. by 3 rep.
 4 rep. by 5 rep.
 4 rep. by 9 rep.
 5 rep. by 15
 5 rep. by 25
 5 rep. by 28
 5 rep. by 33
 5 rep. by 55
 5 rep. by 66
 5 rep. by 77
 5 rep. by 88
 5 rep. by 99
 5 rep. by 9 rep.
 6 rep. by 9 rep.
 6 rep. by 12
 6 rep. by 15
 6 rep. by 16
 6 rep. by 22
 6 rep. by 31
 6 rep. by 32
 6 rep. by 33
 6 rep. by 43
 6 rep. by 55
 6 rep. by 66
 6 rep. by 77
 6 rep. by 88
 6 rep. by 444
 6 rep. by 888
 7 rep. by 9 rep.
 7 rep. by 15
 7 rep. by 17
 7 rep. by 32
 7 rep. by 33
 7 rep. by 42
 7 rep. by 44
 7 rep. by 55
 7 rep. by 66
 7 rep. by 77
 7 rep. by 88
 7 rep. by 99
 8 rep. by 9 rep.
 8 rep. by 22
 8 rep. by 23
 8 rep. by 24
 8 rep. by 29
 8 rep. by 36
 8 rep. by 44
 8 rep. by 55
 8 rep. by 66
 8 rep. by 88
 9 rep. by 14
 9 rep. by 22
 9 rep. by 25
 9 rep. by 27
 9 rep. by 33
 9 rep. by 44
 9 rep. by 55
 9 rep. by 77
 9 rep. by 88
 9 rep. by 99
 3 repeating by 2, /37
 3 repeating by 5, /37
 9 rep. by 3, /12345679
 multidigits by 8 + last digit
 by 8, add number,  20
 integer + 1/2 times, + 1
 sum,difference of 2,1 digits
 two mixed numbers
 two mixed numbers,fractions
 4 digits by 99
 4 digits by 137, then 73; 1200
 5 digits by 9091, then 11; 1200
Dividing Numbers
Adding Numbers
Subtracting Numbers
Finding Percents
Calculation
Practice Exercises
Full List

Multiplying a repeating 9's number by 77
 Choose a repeating 9's number (e.g., 9999).
 The product is made up of:
 first two digits are 76.
 next digits are repeating 9's  two fewer than repeating 9's in original number.
 last two digits are 23.
Example:
 The repeating 9's number chosen to multiply by
77 is 999.
 First two digits are 76.
 Next digits are repeating 9's  two fewer than repeating 9's in original number: 9.
 Last two digits are 23.
 So 77 × 999 is 76923.
See the pattern?
 The repeating 9's number chosen to multiply by 77 is 99999.
 First two digits are 76.
 Next digits are repeating 9's  two fewer than repeating 9's in original number: 999.
 Last two digits are 23.
 So 77 × 99999 is 7699923.
Follow these three steps and you will be giving these
large products quickly.
