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Multiplying Two Selected 3-digit Numbers (middle Digit 1)

Multiplying Two Selected 3-digit Numbers (middle Digit 1)

Multiplying two selected 3-digit numbers   (middle digit 1)

  1. Select a 3-digit number with a middle digit of 1.
  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 two digits will be the product of the first digits:
    _ _ _ 0 X or _ _ _ _ X X.
  4. The third digit from the right will be 2:
    _ _ 2 _ _ or _ _ _ 2 _ _ .
  5. The next digit to the left will be 3 times the first digit of the number (keep carry):
    _ X _ _ _ or _ _ X _ _ _.
  6. The first digits will be the square of the first digit plus the carry:
    X _ _ _ _ or X X _ _ _ _.

    As you determine the digits in the answer from right to left, repeat them to yourself at each step until you have the whole answer.

   Example:
  1. If the first number is 814, choose 816 as the second number (same first digits, second digits add to 10).
  2. 4 × 6 = 24 (multiply the first digits) - last two digits:
    _ _ _ _ 2 4.
  3. The third digit from the right is 2: _ _ 2 _ _ .
  4. 8 × 3 = 24 (the next digit to the left is 3 times the first digit (keep carry 2): _ _ 4 _ _ _ .
  5. 8 × 8 = 64; 64 + 2 = 66 ( the first digits are the square of the first digit plus the carry: 6 6 _ _ _ _.
  6. So 814 × 816 = 664224.

   See the pattern?

  1. If the first number is 317, choose 313 as the multiplier (same first digits, second digits add to 10).
  2. 7 × 3 = 21 (multiply the first digits) - last two digits:
    _ _ _ _ 2 1.
  3. The third digit from the right is 2: _ _ 2 _ _ .
  4. 3 × 3 = 9 (the next digit to the left is 3 times the first digit (no carry): _ 9 _ _ _ .
  5. 3 × 3 = 9 ( the first digits are the square of the first digit: 9 _ _ _ _.
  6. So 317 × 313 = 99221.




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26 Sep, 2021, 03:28:09 AM