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Full Idea
The 'distributive' law says you will get the same result if you first add two numbers, and then multiply them by a third, or first multiply each by the third and then add the results (i.e. a · (b+c) = a · b + a · c ).
Gist of Idea
'Distributive' laws say if you add then multiply, or multiply then add, you get the same result
Source
R Kaplan / E Kaplan (The Art of the Infinite [2003], 2 'Tablets')
Book Ref
Kaplan,R and Kaplan,E: 'The Art of the Infinite' [Penguin 2004], p.35
A Reaction
Obviously this will depend on getting the brackets right, to ensure you are indeed doing the same operations both ways.
| 15712 | 1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan] |
| 15711 | The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan] |
| 15713 | The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan] |
| 15714 | 'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan] |
| 15715 | 'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan] |
| 15717 | Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan] |