You must have known the fastest and easiest method of multiplying any 2-digit numbers together in just one line by now.
Here's the smarter way of multiplying numbers close to base 100.
  1. Find the difference between both of the numbers and 100.
  2. Multiply these two values together and write it down. Make sure the answer takes up 2 place values. For a single digit result add a ‘0’ before it and for a 3-digit result, carry the left digit.
  3. Subtract the difference found in step-1 of one of the numbers with the remaining number. You can subtract either way; you will always get the same answer. Write the result.
Suppose you want to multiply 88 by 98.


With ‘Vertically and Cross-wise’ you can give the answer immediately.
Both 88 and 98 are close to 100.
88 is 12 below 100 and 98 is 2 below 100.
You can imagine the sum set out like this:

            
Multiplying vertically both the differences (12 and 2) from 100 results in 24.
And, 86 comes from subtracting crosswise: 88 - 2 = 86 (or 98 - 12 = 86: you can subtract either way, you will always get the same answer).

So, 88 x 98 = 8624

This is so easy it is just mental arithmetic.

Multiplication can also be carried out starting from the left, which can be better because we write and pronounce numbers from left to right. In this case, remember to carry, if any.

Example, 96 by 92

96 is 4 below the base and 92 is 8 below.
We can cross-subtract either way: 96-8=88 or 92-4=88. This is the first part of the answer and multiplying the "differences" vertically 4x8=32 gives the second part of the answer.
                       
                  

Multiplying numbers just over 100

This works equally well for numbers above the base. Here we add the differences.
  • 103 x 104 =?
  • The answer is in two parts: 107 and 12,
    107 is just 103 + 4 (or 104 + 3), and 12 is just 3 x 4.
  • So, 103 x 104 = 10,712
  • Similarly 107 x 106 = 11,342
107 + 6 = 113 and 7 x 6 = 42

And, 105 x 111 = 11,655 

For 205x211; just double the first part of the answer, because 200 is 2x100.

Hence, 205x211=43,255
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