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 From B. Lee Clay

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Multiplying a 2-digit number by 6 6/7

1. Select a 2-digit number.
2. Multiply the number by 5.
3. Add a zero.
4. Subtract original number.
5. Subtract original number again.
6. Divide by 7.

Example:

1. The 2-digit number chosen to multiply by 6 6/7 is 21.
2. Multiply by 5: 5 × 21 = 105.
3. Add a zero: 1050.
4. Subtract original number. 1050 - 21 = 1050 - 20 - 1 = 1030 - 1 = 1029
5. Subract original number again. 1029 - 21 = 1029 - 20 - 1 = 1008.
6. Divide by 7. 1008/7 = 144.
7. So 21 × 6 6/7 = 144.

See the pattern?

1. The 2-digit number chosen to multiply by 6 6/7 is 52.
2. Multiply by 5. 5x52=250+10=260
3. Add a zero: 2600.
4. Subtract original number. 2600 - 52 = 2600 - 50 - 2 = 2550 - 2 = 2548
5. Subtract original number again. 2548 - 52 = 2548 - 50 - 2 = 2498 - 2 = 2496
6. Divide by 7. 2496/7 = 356 4/7.
7. So 52 × 6 6/7 = 356 4/7.
With some practice (especially subtracting left to right) you will be able to give these answers quickly.

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