## BEATCALC:  Beat the Calculator!

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 From B. Lee Clay

Squaring Numbers

Multiplying Numbers

Dividing Numbers

Subtracting Numbers

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

1. Select a 3-digit number with a middle digit of 3 (last digit not zero).
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 third digits: _ _ _ _ X X.
4. The third digit from the right will be 2: _ _ 2 _ _.
5. The next digit to the left will be 7 times the first digit of the number plus 1 (keep carry): _ _ X _ _ _.
6. The first digits will be the square of the first digit plus the carry: 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 631, choose 639 as the second number (same first digits, third digits add to 10).
2. 1 × 9 = 09 (multiply the third digits) - last two digits:
_ _ _ _ 0 9.
3. The third digit from the right is 2: _ _ 2 _ _ _.
4. 7 × 6 = 42, 42 + 1 = 43 (the next digit to the left is 7 times the first digit plus 1 (keep carry 4): _ _ 3 _ _ _ .
5. 6 × 6 = 36; 36 + 4 = 40 ( the first digits are the square of the first digit plus the carry: 4 0 _ _ _ _.
6. So 631 × 639 = 403209.

See the pattern?

1. If the first number is 236, choose 234 as the second number (same first digits, third digits add to 10).
2. 6 × 4 = 24 (multiply the third digits) - last two digits: _ _ _ _ 2 4.
3. The third digit from the right is 2: _ _ 2 _ _ _.
4. 7 × 2 = 14, 14 + 1 = 15 (the next digit to the left is 7 times the first digit plus 1 (keep carry 1): _ _ 5 _ _ _ .
5. 2 × 2 = 4; 4 + 1 = 5 ( the first digits are the square of the first digit plus the carry: 0 5 _ _ _ _.
6. So 236 × 234 = 55224.