Squaring Numbers
Multiplying Numbers
Dividing Numbers
 any by 0.125
 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 1/4
 2 digits by 1 2/7
 2 digits by 1 1/3
 2 digits by 1 2/5
 2 digits by 1 3/7
 2 digits by 1 1/2
 2 digits by 1 3/5
 2 digits by 1 2/3
 2 digits by 1 3/4
 2 digits by 1 4/5
 2 digits by 2 2/9
 2 digits by 2 1/4
 2 digits by 2 1/3
 2,3 digits by 2 1/2
 2 digits by 2 2/3
 2 digits by 2 6/7
 2 digits by 3 1/8
 2,3 digits by 3 1/3
 2 digits by 3 1/2
 2 digits by 3 4/7
 2 digits by 4 1/6
 2 digits by 4 2/7
 2 digits by 4 4/9
 2 digits by 4 1/2
 2 digits by 5
 2 digits by 5 5/7
 2 digits by 6 1/4
 2 digits by 6 2/3
 2 digits by 7 1/7
 2 digits by 7 1/2
 2 digits by 8 1/3
 2 digits by 8 4/7
 2 digits by 12 1/2
 2 digits by 15
 2,3 digits by 16 2/3
 2,3 digits by 25
 2,3 digits by 33 1/3
 2,3 digits by 35
 2 digits by 37 1/2
 2 digits by 40
 2 digits by 45
 2 digits by 50
 2 digits by 62 1/2
 2 digits by 66 2/3
 2,3 digits by 75
 2 digits by 83 1/3
 2 digits by 87 1/2
 2 digits by 125
 2 digits by 166 2/3
 2 digits by 250
 2,3 digits by 333 1/3
 2 digits by 375
 2 digits by 625
 2 digits by 875
 3 digits rep./37+41
 6 digits rep. by 15873
 6 digits rep. by 7, then 13
 6 digits rep. by 13, then 11
 6 digits rep. by 7,11,13, subtract 101
 6 digits rep. by 37037 x 5
 mixed numbers by 2
 diff. of squares of 2 consec. 2digit numbers
 diff. of squares of 2 different 2digit numbers
 sqrt of squares of 2digit numbers ending in 1
 sqrt of perfect squares ending in 5
Adding Numbers
Subtracting Numbers
Finding Percents
Calculation
Practice Exercises
Full List

Find the difference of the squares of two
different
2digit numbers
 Select two consecutive 2digit numbers, one not more than 10 larger than the
other (experts need not use this limitation).
 Subtract the smaller number from the larger.
 Add the two numbers.
 Multiply the first answer by the second.
Examples:
 If 71 and 64 are selected:
 71  64 = 7.
 71 + 64 = 135
(Add left to right: 71 + 64 = 71 + 60 + 4 = 131 + 4 = 135)
 Multiply these results: 7 × 135 = 945
(Multiply left to right: 7 × 135 = 7 × (100+30+5) =
700 + 210 + 35 = 910 + 35 = 945)
 So the difference of the squares of 71 and 64 is 945.
See the pattern?
 If 27 and 36 are selected:
 36  27 = 9.
 36 + 27 = 63
(Think: 27 + 30 + 6 = 57 + 6 = 63)
 Multiply these results: 9 × 63 = 567
(Think: 9 × (60+3) = 540 + 27 = 567)
 So the difference of the squares of 27 and 36 is 567.
Practice multiplying and adding from left to right and this will become an easy
but impressive mental math feat.
