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 two 2digit numbers
(difference
of 6)
 Choose a 2digit number.
 Select a number either 6 smaller or 6 larger.
 Find the middle number of the two (the average).
 Square this middle number.
 Subtract 9 from this square.
Example:
 If the first number is 78, choose 72 as the second number.
 The middle number (the average) is 75.
 Square this middle number: 75 × 75 = 5625. (Remember
how to square a 2digit number ending in 5?)
 Subtract 9 from this square: 5625  9 = 5616.
 So 78 × 72 = 5616.
See the pattern?
 If the first number is 31, choose 37 as the second number.
 The middle number (the average) is 34.
 Square this middle number: 34 × 34 = 1156. (Remember how
to square a 2digit number ending in 4?)
 Subtract 9 from this square: 1156  9 = 1147.
 So 31 × 37 = 1147.
Choose the second number that will give you the easier square, and use your square
shortcuts. Practice!
