Tutorial 115
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.