Step 1: Confirm whether the numbers you want to multiply meet both of the requirements listed. If either requirement is not met then this method can not be used.
Requirement 1: For two digit numbers, the tens place digit needs to be the same. 72 * 82 would not work since the tens place digits (7 and 8) are not the same.
Requirement 2: The sum of the ones place digits is equal to 10. If the sum is greater than or less than 10 then this method can not be used. 74 * 74 and 76 * 79 each would not work since the sum of their ones place digits (4+4) and (6+9) are not equal to 10.
Two examples where this method can work:
Example 1: 28 * 22 Both numbers, 28 and 22, have the same digit in the tens place, 2, and the ones place digits (8 + 2) sum to 10
Example 2: 59 * 51 Both numbers, 59 and 51, have the same digit in the tens place, 5, and the ones place digits (9 + 1) sum to 10
Step 2: Since there will not be any carryover we will solve our answer working left to right. Add 1 to the tens place digit.
Example 1: 2 + 1 = 3
Example 2: 5 + 1 = 6
Step 3: Multiply the tens place digit by the result in Step 2, the number that is one greater than the tens place digit. The product represents the two digits to the far left in the answer.
Example 1: 2 * 3 = 06 Answer 1: 0 6 _ _
Example 2: 5 * 6 = 30 Answer 2: 3 0 _ _
Step 4: Multiply the ones place digits together. The '9' in 59 and the '1' in 51 are multiplied together in example 2. The product represents the two digits to the far right in the answer.
Example 1: 8 * 2 = 16 Answer 1: 0 6 1 6
Example 2: 9 * 1 = 09 Answer 2: 3 0 0 9
Notes:
1) We use four digits for the answer when multiplying a two digit number by a two digit number.
2) You can drop the zero if it is the left most digit in the answer. We can restate Answer 1 as 616, dropping the leading zero. We need to keep the zero if it is not the far left most digit, as shown in Answer 2 where we keep the zeroes in the answer's tens and hundreds place digits.
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