## BEATCALC:  Beat the Calculator!

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 From B. Lee Clay

Squaring Numbers

Multiplying Numbers

Dividing Numbers

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### Multiplying two mixed numbers with fractions adding to 1

1. Select a mixed number. (3 1/4 or 7 1/8)
2. Select a multiplier using the same whole number and a fraction that sums to 1 with the first number's fractional part. (3 1/4 × 3 3/4 or 7 1/8 × 7 7/8)
3. The whole number in the answer will be the whole number times the next number.
4. To find the fraction, multiply the two fractional parts.

#### Example:

1. The first mixed number chosen is 4 1/3.
2. Select 4 2/3 as the multiplier (same whole number,
fraction that sums to 1 with the first fraction.
3. The product's whole number will be 4 × 5 (next number) = 20.
4. The product's fraction will be 1/3 × 2/3 = 2/9.
5. So 4 1/3 × 4 2/3 = 20 2/9.

See the pattern?

1. The first mixed number chosen is 2 1/8.
2. Select 2 7/8 as the multiplier (same whole number,
fraction that sums to 1 with the first fraction.
3. The product's whole number will be 2 × 3 (next number) = 6.
4. The product's fraction will be 1/8 × 7/8 = 7/64.
5. So 2 1/8 × 2 7/8 = 6 7/24.