Tutorial 123
Multiplying two selected 3-digit numbers (middle digit 5)

  1. Select a 3-digit number with a middle digit of 5 (last digit not zero).
  2. Choose a multiplier with the same first two digits, whose third digit sums to 10 with the third digit of the first 3-digit number.
  3. The last three digits will be 0 and the product of the third digits: _ _ _ 0 X X.
  4. The third digit from the right will be the first digit + 3 (keep the carry): _ _ X _ _.
  5. The first digit will be the first digit times the next number plus the carry: X X _ _ _ _.

    Repeat those digits from left to right as you get them.


   Example:

  1. If the first number is 752, choose 758 as the second number (same first digits, third digits add to 10).
  2. Last three digits: 0 and the product of the third digits:
    2 × 8 = 16: _ _ 0 1 6
  3. Next digit: first digit + 3: 7 + 3 = 10 (keep carry 1):
    _ _ 0 _ _ _
  4. First two digits: first digit times next number plus carry: 7 × 8 = 56, 56 + 1 = 57: 5 7 _ _ _ _
  5. So 752 × 758 = 570016.

   See the pattern?

  1. If the first number is 654, choose 656 as the second number (same first digits, third digits add to 10).
  2. Last three digits: 0 and the product of the third digits:
    4 × 6 = 24: _ _ 0 2 4
  3. Next digit: first digit + 3: 6 + 3 = 9: _ _ 9 _ _ _
  4. First two digits: first digit times next number:
    6 × 7 = 42: 4 2 _ _ _ _
  5. So 654 × 656 = 429024.