Trick 112 - Multiplying two 2-digit numbers (same 1st digit, 2nd digits sum to 10)

Multiplying two 2-digit numbers (same 1st digit, 2nd digits sum to 10)

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1. Both numbers should have the same first digit.
2. Choose second digits whose sum is 10.
3. Multiply the first digit by one number greater than itself; this number will be the first part of the answer:
   X X _ _.
4. Multiply the two second digits together; the product
   will be the last part of the answer: _ _ X X.

Note: If the two second digits are 1 and 9 (or, more generally, have a product that is less than ten), insert a 0 (zero) for the first X in step 4.

(Thanks to Michael Richardson, age 10, for this note.)

   Example:

1. If the first number is 47, choose 43 as the second number (same first digit, second digits add to 10).
2. 4 × 5 = 20 (multiply the first digit by one number greater than itself): the first part of the answer is
   2 0 _ _.
3. 7 × 3 = 21 (multiply the two second digits together); the last part of the answer is _ _ 2 1.
4. So 47 × 43 = 2021.

   See the pattern?

1. If the first number is 62, choose 68 as the second number (same first digit, second digits add to 10).
2. 6 × 7 = 42 (multiply the first digit by one greater), the first part of the answer is 4 2 _ _.
3. 2 × 8 = 16 (multiply the two second digits together); the last part of the answer is _ _ 1 6.
4. So 62 × 68 = 4216.