Trick 111 - Multiplying two 2-digit numbers (same 1st digit)

Multiplying two 2-digit numbers (same 1st digit)

. -

1. Select two 2-digit numbers with the same first digit.
2. Multiply their second digits (keep the carry).   _ _ _ X
3. Multiply the sum of the second digits by the first digit,
   add the carry (keep the carry).   _ _ X _
4. Multiply the first digits (add the carry).   X X _ _

   Example:

If the first number is 42, choose 45 as the second number (any 2-digit number with first digit 4).

Multiply the last digits: 2 × 5 = 10 (keep carry)  
_ _ _ 0

Multiply the sum of the 2nd digits by the first:
5 + 2 = 7; 7 × 4 = 28; 28 + 1 = 29 (keep carry)  
_ _ 9 _

Multiply the first digits (add the carry)
4 × 4 = 16; 16 + 2 = 18                           
1 8 _ _

So 42 × 45 = 1890.

   See the pattern?

1. If the first number is 62, choose 67 as the second number
   (any 2-digit number with first digit 6).
2. Multiply the last digits: 2 × 7 = 14 (keep carry)  
   _ _ _ 4
3. Multiply the sum of the 2nd digits by the first (add carry):
   2 + 7 = 9; 6 × 9 = 54; 54 + 1 = 55 (keep carry)  
   _ _ 5 _
4. Multiply the first digits (add the carry)
   6 × 6 = 36; 36 + 5 = 41                           
   4 1 _ _
   
   
5. So 62 × 67 = 4154.