Multiplying Two Digit Numbers - Tens are mirrors and ones sum ends in zeroes

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.

Squares ending in 5 - Two Digit Numbers

You can use this shortcut when multiplying a two digit number by itself that ends with a five.

Example: 75 * 75 (this can be shown as 75² and pronounced 75 squared)

Step 1) The last two digits of the answer will be 25 since the number we are squaring ends in a 5
_ _ 2 5

Step 2) To get the first two digits of the answer we need to do first have to to add one to the the non-five digit (7).
7 + 1 = 8

Step 3) Next, multiply the non-five digit by the result from Step 2.
7 * 8 = 56

Step 4) The first two digits in the answer is the product from Step 3. Our final answer is:
5 6 2 5

Multipying By 11 - Three digit numbers

We utilize the same foundation for multiplying three digit numbers by 11 as we do for two digit numbers, with one additional step. When multiplying a two digit number by 11 we calculate the middle digit in the answer by adding each of the two digits in the non-11 number together. When multiplying a three digit number by 11 we need to get an additional digit in our answer so we add another set of digits together. In two digit numbers there is only one set of digits next to each other (neighbors), whereas in three digit numbers there are two sets of pairs - (7 & 2) and (2 & 6) in the example below.

Example:   627 * 11 =  6897

Step 1) Take the digit to the far right (7) in the ones place as the first digit in our answer 
_ _ _ 7

Step 2) Add the digit in the far right (7) to the digit to its left in the tens place (7); (7 + 2) 
_ _ 9 7

Step 3) Add the digit in the tens place (2) to the digit to its left (6); (6+2)
_ 8 9 7

Step 4) Take the digit to the far left (6) as the last digit in our answer
6 8 9 7

Multipying By 11 - Two digit numbers with carry over

We can expand on the first tip to learn how to multiply the number eleven faster and more accurately with some more complications.  If you have any questions or feedback please feel free to add a comment to the post.

Example: 75 * 11 = 825.

Detailed Explanation: 
When multiplying a two digit number by 11 there are three steps to follow for the non-eleven multiplier to quickly get the answer.

Step 1) The ones place in the answer is equal to the ones place in the non-eleven multiplier, the far right digit - the number 5 in our example. Our answer now has one digit filled in  _ _ 5

Step 2) The next number in the answer is the sum of the two digits in the non-eleven multiplier; 7 and 5 in the example, which is equal to 12. We take the digit in the sum's ones place as the next digit in our answer.
The answer is missing only one more digit _ 25

Since the sum of of 7 and 5 is 12, which has two digits, we carry over the ten's place digit (1) into step 3.

Step 3) The last digit in the answer is the digit in the ten's place in the non-eleven multiplier (7) plus the carry over from Step 2 (1). The last digit in our answer is the sum of 7+1.  The answer is 825.

In Step 3 the most we would add to the digit is 1 because the highest carryover is the number 1; no two digit sums are equal to or greater than 20.

Multipying By 11 - Two digit numbers

Our first tip helps you multiply the number eleven faster and more accurately. We illustrate the concept using an example. This example serves as a foundation for more complex variations and larger numbers. If you have any questions or feedback please feel free to add a comment to the post.

Tip #1: 72 * 11 = the first digit (7), sum of the first two digits (7+2), second digit (2) = 792

Detailed Explanation: 
When multiplying a two digit number by 11 there are three steps to follow for the non-eleven multiplier to quickly get the answer.

Step 1) The ones place in the answer is equal to the ones place in the non-eleven multiplier, the far right digit - the number 2 in our example. _ _ 2

Step 2) The next number in the answer is the sum of the two digits in the non-eleven multiplier; 7 and 2 in the example, which is equal to 9.  _ 92

Step 3) The last digit in the answer is the digit to the ten's place in the non-eleven multiplier, the far left digit - the number 7 in our example. 792