Simple Product of Big Numbers

Some people find it hard to multiply big numbers. There is a trick to do it simpler. This is applicable for numbers near a base. A base can be 10, 100, 1000 or higher.

Example:
98 x 94 = ?

This question can be answered in seconds. The answer is 9212.

Both 98 and 94 are numbers near 100. First, take their differences from 100.
100 - 98 = 2
100 - 94 = 6
Then, subtract one difference from the other number.
98 - 6 = 92
94 - 2 = 92
It will always have the same answer, so choose which one is easier for you. This is the first two digits of the final answer. The other two digits is the product of the differences 2 and 6.
2 x 6 = 12
Putting 92 & 12 together, we have 9212 as the answer.

 -2    -6
98 x 94 = ?
98 - 6 = 92 
2  x  6 = 12
98 x 94 = 9,212

More examples:

98 x 87 = ?

-2   -13
98 x 87 = ?
87 - 2 = 85
2 x 13 = 26
98 x 87 = 8,526

998 x 986 = ?

  -2    -14
998 x 986 = ?
986 - 2 = 984
2  x  14 = 028   (base is 1000, 3 zeros means 3 digits for answer)
998 x 986 = 984,028

7 x 8 = ? 

-3    -2
7  x  8 = ?
7  -  2 = 5
3  x  2 = 6   (base is 10, 1 zero means 1 digit for answer)
7  x 8 = 56

For numbers above the base, the trick becomes easier. Instead of subtracting the differences, add.

    3       5
103 x 105 = ?
103  +  5 = 108
3 x 5 = 15   (base is 100, 2 zeros means 2 digits for answer)
103 x 105 = 10,815

    7       8
107 x 108 = ?
107 + 8 = 115
7 x 8 = 56   (base is 100, 2 zeros means 2 digits for answer)
107 x 108 = 11,556

  3      5
13 x 15 = ?
13 + 5 = 18
3 x 5 = 15   (base is 10, 1 zero means 1 digit for answer. Therefore add 1 to 18, 18+1=19)
13 x 15 = 195

For numbers that one is below the base and the other one is above the base, subtract the base to these numbers and consider the positive and negative differences.

Example:
96 x 108 = ?

 -4     +8
96 x 108 = ?
96 + 8 = 104
108 - 4 = 104 (same answer)
(-4) x 8 = (-32) 
96 x 108 = 10,4(-32)
96 x 108 = 10,400 - 32
96 x 108 = 10,368

More examples:

98 x 114 = ?

 -2   +14
98 x 114 = ?
114 - 2 = 112
98 + 14 = 112 (same answer)
(-2) x 14 = (-28) 
98 x 114 = 11,2(-28)
98 x 114 = 11,200 - 28
98 x 114 = 11,172

102 x  97 = ?

    2    -3
102 x 97 = ?
102 -  3 = 99
97 + 2 = 99 (same answer)
2 x (-3) = (-06)   (base is 100, 2 zeros means 2 digit for answer.)
102 x 97 = 99(-06)
102 x 97 = 9,900 - 06
102 x 97 = 9,894

These are long when written, but just quick in the mind.

#Matamata