## BEATCALC:  Beat the Calculator!

Back to Calculation Tips & Tricks

 From B. Lee Clay

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### Multiplying a repeating 5's number by 45

1. Choose a repeating 5's number (5555, etc.)
2. Multiply it by 45
3. The product is:
- the first two digits are 24
- the next digits are repeating 9's -- two fewer than repeating 5's in the original number
- the last two digits are 75

#### Example:

1. If the first number is 55555:
- the first two digits are 24: 24
- the next digits are repeating 9's -- two fewer than repeating 5's in the original number: 999
- the last two digits are 75: 75.
2. So 45 × 55555 = 2499975.

See the pattern?

1. Next pick is 555555555:
- the first two digits are 24: 24.
- the next digits are repeating 9's -- two fewer than repeating 5's in the original number: 9999999.
- the last two digits are 75: 75.
2. So 45 × 555555555 = 24999999975.

Follow these three rules and you will be able to produce these products with ease.

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