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Distributive rules
 Cleverly distributing numbers

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When there is multiplication and addition or multiplication and subtraction you can also win advantages by cleverly distributing numbers.

Example: What is 7 · 28?

 

You can now divide (take apart) the umbers as you wish, 7 for examples (5 + 2) or 28 is (20 + 8) or it is (20 + 5 + 3).

Calculation:

(5+2)

·

(20+5+3)

 

That makes this calculation:

5·20+5·5+5·3  +  2·20+2·5+2·3

= 100+25+15  +  40+10+6

= 140 + 56

= 196

All of that is very complicated and can be simplified. You could divide just one number for example and this would come out: 7 · 20 + 7 · 5 + 7 · 3 = 150 + 35 + 21 = 196. There is also a completely different option where you do not divide the sums but subtract and minimize: 7 · (30-2). 

7

·

(30-2)

 

This is the calculation that results:

7·30 - 7·2

= 210 - 14

= 196

 

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02/09/07