## BEATCALC:  Beat the Calculator!

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 From B. Lee Clay

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### Adding even numbers from two through               a selected 2-digit even number

1. Divide the even number by 2 (or multiply by 1/2).
2. Multiply this result by the next number.

#### Example:

1. If the 2-digit even number selected is 24:
2. Divide 24 by 2 (24/2 = 12) or multiply by 1/2 (1/2 × 24 = 12).
3. The next number is 13; 12 × 13 = 156.
Ways to multiply 13 by 12:
• Square 12, then add 12: 12 × 12 = 144, 144 + 12 = 156.
• Multiply left to right. 12 × 13 can be done in steps: 12 × (10+3) = (12 × 10) + (12 × 3) = 120 + 36 = 156.
4. So the sum of all the even numbers from two through 24 is 156.

See the pattern?

1. If the 2-digit even number selected is 42:
2. Divide 42 by 2 (42/2 = 21) or multiply by 1/2 (1/2 × 42 = 21).
3. The next number is 22; 21 × 22 = 462.
Ways to multiply 22 by 21:
• Square 21, then add 21: 21 × 21 = 441, 441 + 21 = 462.
• Multiply left to right. 21 × 22 can be done in steps: 21 × 22 = (21 × 20) + (21 x 2) = 420 + 42 = 462.
4. So the sum of all the even numbers from two through 42 is 462.