fcubook7

1. Select two 2-digit numbers with the same first digit.
2. Multiply their second digits (keep the carry). _ _ _ X
3. Multiply the sum of the second digits by the first digit,
4. add the carry (keep the carry). _ _ X _
5. Multiply the first digits (add the carry). X X _ _
   

Example:
If the first number is 42, choose 45 as the second number (any 2-digit number with first digit 4).

1. Multiply the last digits: 2 × 5 = 10 (keep carry)
   _ _ _ 0
2. Multiply the sum of the 2nd digits by the first:
   5 + 2 = 7; 7 × 4 = 28; 28 + 1 = 29 (keep carry)
   _ _ 9 _
3. Multiply the first digits (add the carry)
   4 × 4 = 16; 16 + 2 = 18
   1 8 _ _
4. So 42 × 45 = 1890.
   See the pattern?
   

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

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.
5. 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:
If the first number is 47, choose 43 as the second number (same first digit, second digits add to 10).

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

Multiplying two 2-digit numbers
(same 2nd digit)

1. Both numbers should have the same second digit.
2. Choose first digits whose sum is 10.
3. Multiply the first digits and add one second: X X _ _.
4. Multiply the second digits together: _ _ X X.
   

Example:
If the first number is 67, choose 47 as the second number (same second digit, first digits add to 10).

1. Multiply the 1st digits, add one 2nd.
2. 6x4 = 24, 24+7 = 31. 3 1 _ _
3. Multiply the 2nd digits. 7x7 = 49 _ _ 4 9
4. So 67 × 47 = 3149.

1. Select a 3-digit number with a middle digit of 0.
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 first digit(s) will be the square of the first digit:
   X _ _ _ _ or X X _ _ _ _.
4. The next digit will be the first digit of the numbers:
   _ X _ _ _ or _ _ X _ _ _.
5. The next digit is zero: _ _ 0 _ _ or _ _ _ 0 _ _.
6. The last two digits will be the product of the third digits:
   _ _ _ X X or _ _ _ _ X X.
   

Example:
If the first number is 407, choose 403 as the second number (same first digits, second digits add to 10).

1. 4 × 4 = 16 (square the first digit): 1 6 _ _ _ _.
2. The next digit will be the first digit of the numbers:
   _ _ 4 _ _ .
3. The next digit is zero: _ _ 0 _ _ .
4. 7 × 3 = 21 (the last two digits will be the product of the third digits: _ _ _ 2 1.
5. So 407 × 403 = 164021.

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 _ _ _ _.
7. 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:
If the first number is 814, choose 816 as the second number (same first digits, second digits add to 10).

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

FCUBOOK