By Jean-Louis Fournier
J'ai longtemps cru que l'arithmetique n'avait ete inventee que pour resoudre les problemes de trains qui se croisent et de baignoires qui debordent. Quand j'ai ete grand, j'ai decouvert qu'elle pouvait mieux faire. M'aider, par exemple, a calculer le poids du cerveau d'un imbecile, le nombre de voitures que pourrait contenir Notre-Dame transformee en parking... Enfin, autant de questions que toute personne responsable devrait se poser.
Apres l. a. Grammaire francaise et impertinente, Jean-Louis Fournier, un des rares auteurs a savoir conjuguer pedagogie et plaisir, s'attaque a l'enseignement de l'arithmetique. Humour noir, sens aigu des jeux de mots absurdes, problemes cocasses et fantaisistes, mais methodes de raisonnement et ideas irrefutables et rigoureuses: voici un manuel imperative pour les petits ecoliers, leurs maitres et leurs parents.
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Extra info for Arithmétique appliquée et impertinente
Example text
The term containing x can be found by adding the product of the "inners" and the product of the "outers" : (2x 3)(5x - 2) I �x I + + (x - 1)(2x + 3) - l)(3x + 3) -2x - p(2-3x + 2x2 r oox3x +r +x (x + 1) ( 2 x + 3) 2x2 x -3. (2x 2)(2x -2) (�x +4x22)(2r -2) (2x m4xx - (2x + t)(2-4x -4x +Ox (2x + 2)(2x -2) 4x2 - 4. Thus, (2x 3)(5x - 2) Sum = 10x2 = -4x l lx I Ix - 6. EXAMPLE 4 Multiply. (a) We diagram the process so that you can learn to do these mentally. ) Sum = = Thus, (b) + Once more, we have + ) Sum = Thus, ((2xx+-3)2)(x(3x+ - = PROGRESS CHECK 4 Multiply mentally.
Let's work through this problem: (2x + 3)(5x - 2) = 2x(5x - 2) + 3(5x - 2) (2x)(5x) + 2x( - 2) + 3(5x) + 3( - 2) = l 0x 2 - 4x + 15x 6 = - 53 54 POLYNOMIALS We have stopped just short of the last step because we want to show the relationships between the factors and the products. If we take the product of the first term of each expression (2x + 3)(5 x - 2) 10x2 + we have the term containing x2• Similarly, taking the product of the last term of each expression (2x + 3)(5x - 2) -6 we have the constant term.
A) x < 0 Answers (a) (c) • • (b) x � - I I I + I + I I I -2 - 1 -2 - 1 0 0 2 2 (c) x < - 2 (b) I + I -2 - 1 0 I 2 • 31 32 THE REAL NUMBER SYSTEM We also write double inequalities such as - l ::; x < 2 The solution set to this inequality consists of all real numbers which satisfy - 1 ::; x and x < 2 that is, all numbers between - 1 and 2 and including - 1 itself. We can easily graph the solution set on a real number line. -5 I -4 I -3 + -2 I -1 0 -1 EXAMPLE 6 Graph -3 < x < - 1, 5 x 2 I 3 4 5 I 3 4 I <2 a real number.