Calcul littéral - 4e

Développements par simple distributivité

Exercice 1 : Développement très simple

Développer l'expression suivante : \[ 6\left(q + 6\right) \]

Exercice 2 : Développement et réduction de ax(bx+c)+d(ex+f) (entiers relatifs)

Développer et réduire l'expression suivante : \[ 6x\left(7x + 5\right) + 9\left(3x + 3\right) \]

Exercice 3 : Développement de a(bx + c)+-(dx)^2 + ex(f+g) (fractions)

Développer l'expression suivante : \[ \dfrac{5}{3}\left(\dfrac{6}{45}x + \dfrac{21}{40}\right) - \left(6x\right)^{2} + 3x\left(\dfrac{6}{27} + \dfrac{9}{15}\right) \]

Exercice 4 : Développement de ax(bx+c) (entiers naturels)

Développer et réduire l'expression suivante : \[ 2x\left(7x + 5\right) \]

Exercice 5 : Comprendre la notion de variable

L'algorithme suivant représente un calcul :
{"options": {"blockly": {"readOnly": true}, "blocks": {"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"}]}, "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_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}, "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_numberinput": {"output": "Number", "colour": 260, "tooltip": "Fourni un nombre", "inputs": [{"type": "dummy_input", "fields": [{"name": "value", "default": 0.0, "type": "number_input"}], "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"}, "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}]}}}, "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": -7.0}, "op": "MINUS"}, "value_2": {"type": "base_numberinput", "value": -5.0}, "op": "DIV"}, "var_name": "total"}, {"type": "simple_input_output_print", "value": {"type": "base_varvalue", "var_name": "total"}}]]}
Vous pouvez tenter de le modifier pour le comprendre.

{"options": {"runner": {"environment": "input/output", "test_cases": [[0, -1.4], [1, -1.6], [2, -1.8], [3, -2.0], [4, -2.2], [5, -2.4], [6, -2.6], [7, -2.8], [8, -3.0], [9, -3.2], [10, -3.4], [11, -3.6], [12, -3.8], [13, -4.0], [14, -4.2], [15, -4.4], [16, -4.6], [17, -4.8], [18, -5.0], [19, -5.2]]}, "blocks": {"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"}]}, "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_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}, "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_numberinput": {"output": "Number", "colour": 260, "tooltip": "Fourni un nombre", "inputs": [{"type": "dummy_input", "fields": [{"name": "value", "default": 0.0, "type": "number_input"}], "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"}, "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}]}}, "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": -7.0}, "op": "MINUS"}, "value_2": {"type": "base_numberinput", "value": -5.0}, "op": "DIV"}, "var_name": "total"}, {"type": "simple_input_output_print", "value": {"type": "base_varvalue", "var_name": "total"}}]]}

On choisit \(x\) comme nombre d'entrée.
Indiquer l'expression littérale simplifiée donnant \( total \).
(Exemple de réponse : \(0.01 \times x + 1\))

Revenir au choix du niveau