Calcul littéral - 4e

Développements par simple distributivité

Exercice 1 : Développement très simple (avec soustraction et un relatif)

Développer l'expression suivante : \[ -6\left(8g - 7\right) \]

Exercice 2 : Développement avec piège 2x + 3 - 3(2x + 3)

Développer l'expression suivante : \[ 3x + 8 - 8\left(-5x + 4\right) \]

Exercice 3 : 1 variable, fractions, 2 termes

Développer l'expression suivante : \[ \dfrac{2}{5}n\left(\dfrac{-1}{2}n + 2n\right) -2n\left(\dfrac{-4}{3}n + 2n\right) \]

Exercice 4 : Développement de ax(bx+c) (fractions et coefficient entiers qui se simplifient))

Développer l'expression suivante : \[ 7x\left(\dfrac{6}{-56}x + \dfrac{-4}{21}\right) \]

Exercice 5 : Comprendre le fonctionnement d'un algorithme

L'algorithme suivant représente un calcul :
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Vous pouvez tenter de le modifier pour le comprendre.

{"options": {"runner": {"environment": "input/output", "test_cases": [[0, 0.0], [1, 1.3333333333333333], [2, 2.6666666666666665], [3, 4.0], [4, 5.333333333333333], [5, 6.666666666666667], [6, 8.0], [7, 9.333333333333334], [8, 10.666666666666666], [9, 12.0], [10, 13.333333333333334], [11, 14.666666666666666], [12, 16.0], [13, 17.333333333333332], [14, 18.666666666666668], [15, 20.0], [16, 21.333333333333332], [17, 22.666666666666668], [18, 24.0], [19, 25.333333333333332]]}, "blocks": {"base_numberinput": {"output": "Number", "colour": 260, "tooltip": "Fourni un nombre", "inputs": [{"type": "dummy_input", "fields": [{"name": "value", "default": 0.0, "type": "number_input"}], "align": "left"}]}, "simple_input_output_print": {"previous_statement": true, "next_statement": true, "colour": 160, "tooltip": "Afficher une valeur", "inputs": [{"type": "value_input", "fields": [{"text": "Afficher", "type": "text"}], "align": "left", "name": "value", "check": null}]}, "base_varvalue": {"output": true, "colour": 330, "tooltip": "Fourni la valeur d'une variable", "inputs": [{"type": "dummy_input", "fields": [{"name": "var_name", "default": "x", "type": "variable"}], "align": "left"}]}, "base_simplecalculus": {"output": "Number", "colour": 260, "tooltip": "Effectue un calcul simple", "inputs": [{"type": "value_input", "fields": [], "align": "left", "name": "value_1", "check": "Number"}, {"type": "dummy_input", "fields": [{"name": "op", "values": [["+", "PLUS"], ["-", "MINUS"], ["\u00d7", "TIMES"], ["\u00f7", "DIV"]], "type": "dropdown"}], "align": "left"}, {"type": "value_input", "fields": [], "align": "left", "name": "value_2", "check": "Number"}], "inline": true}, "base_setvar": {"previous_statement": true, "next_statement": true, "colour": 330, "tooltip": "Affecter une valeur \u00e0 une variable", "inputs": [{"type": "value_input", "fields": [{"text": "mettre", "type": "text"}, {"name": "var_name", "default": "x", "type": "variable"}, {"text": "\u00e0", "type": "text"}], "align": "left", "name": "value", "check": null}]}, "simple_input_output_readnumber": {"output": true, "colour": 160, "tooltip": "Demander un nombre \u00e0 l'utilisateur", "inputs": [{"type": "dummy_input", "fields": [{"text": "demander un nombre", "type": "text"}], "align": "left"}]}, "base_start": {"next_statement": true, "colour": 65, "tooltip": "D\u00e9marrage de l'algorithme", "inputs": [{"type": "dummy_input", "fields": [{"text": "Au d\u00e9marrage", "type": "text"}], "align": "left"}], "creatable": false, "on_event": "start"}}, "toolbox": [{"type": "base_numberinput"}, {"type": "base_setvar"}, {"type": "base_simplecalculus"}, {"type": "base_varvalue"}, {"type": "simple_input_output_print"}, {"type": "simple_input_output_readnumber"}]}, "ast": [[{"type": "base_start", "deletable": false, "editable": false}, {"type": "base_setvar", "value": {"type": "simple_input_output_readnumber"}, "var_name": "x"}, {"type": "base_setvar", "value": {"type": "base_simplecalculus", "value_1": {"type": "base_simplecalculus", "value_1": {"type": "base_varvalue", "var_name": "x"}, "value_2": {"type": "base_numberinput", "value": 8.0}, "op": "TIMES"}, "value_2": {"type": "base_numberinput", "value": 6.0}, "op": "DIV"}, "var_name": "total"}, {"type": "simple_input_output_print", "value": {"type": "base_varvalue", "var_name": "total"}}]]}

Si on donne à \( x \) la valeur \(-8N\) conjecturer la valeur de \( total \) à la fin de l'algorithme.
Exemple de réponse : \(-8N + 1\)

Si on donne à \( x \) la valeur \(3N\) conjecturer la valeur de \( total \) à la fin de l'algorithme.
Exemple de réponse : \(3N + 1\)

Si on donne à \( x \) la valeur \(2N\) conjecturer la valeur de \( total \) à la fin de l'algorithme.
Exemple de réponse : \(2N + 1\)

Indiquer l'expression littérale donnant \( total \).
Exemple de réponse : \(0.01x + 1\)

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