// Numbas version: exam_results_page_options
{"name": "Negatives: dividing negative numbers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Negatives: dividing negative numbers", "tags": ["Dividing", "dividing", "division", "negative numbers", "Negative Numbers", "negatives"], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Complete the following without the use of a calculator:</p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"d": {"name": "d", "group": "Ungrouped variables", "definition": "n[2..4]", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "shuffle([-13,-11,-7,-5,-3,-2])[0..4]", "description": "", "templateType": "anything", "can_override": false}, "choices_a": {"name": "choices_a", "group": "Ungrouped variables", "definition": "[\n  '$\\\\displaystyle\\\\frac{\\\\var{n[0]}}{\\\\var{d[0]}}$',\n    '$\\\\displaystyle\\\\frac{\\\\var{-n[0]}}{\\\\var{-d[0]}}$',\n  '$\\\\var{-n[0]}\\\\div\\\\var{-d[0]}\\\\phantom{\\\\dfrac{1}{1}}$',\n  \n  '$\\\\displaystyle\\\\frac{\\\\var{-n[0]}}{\\\\var{d[0]}}$',\n  '$\\\\displaystyle\\\\frac{\\\\var{n[0]}}{\\\\var{-d[0]}}$',\n  '$\\\\displaystyle-\\\\frac{\\\\var{-n[0]}}{\\\\var{-d[0]}}$'\n]", "description": "", "templateType": "anything", "can_override": false}, "choices_b": {"name": "choices_b", "group": "Ungrouped variables", "definition": "[\n  '$\\\\displaystyle\\\\frac{\\\\var{n[1]}}{\\\\var{d[1]}}$',\n    '$\\\\displaystyle\\\\frac{\\\\var{-n[1]}}{\\\\var{-d[1]}}$',\n  '$\\\\var{-n[1]}\\\\div\\\\var{-d[1]}\\\\phantom{\\\\dfrac{1}{1}}$',\n  \n  '$\\\\displaystyle\\\\frac{\\\\var{-n[1]}}{\\\\var{d[1]}}$',\n  '$\\\\displaystyle\\\\frac{\\\\var{n[1]}}{\\\\var{-d[1]}}$',\n  '$\\\\displaystyle-\\\\frac{\\\\var{-n[1]}}{\\\\var{-d[1]}}$'\n]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n", "d", "choices_a", "choices_b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Which of the following are equal to $(\\var{n[0]})\\div(\\var{d[0]})$?</p>", "stepsPenalty": "3", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Dividing negative numbers can be done by pretending the numbers are positive, doing the division, and then determining whether the actual answer should be positive or negative.&nbsp;</p>\n<p>It is also crucial to realise division can be written as a fraction.&nbsp;</p>\n<hr/>\n<p>Consider $(\\var{n[0]})\\div(\\var{d[0]})$. Let's move the negatives out the front to get $--\\var{-n[0]}\\div\\var{-d[0]}$, we can just do the division and get $--\\frac{\\var{-n[0]}}{\\var{-d[0]}}$, but this is the same as $\\frac{\\var{-n[0]}}{\\var{-d[0]}}$.</p>\n<hr/>\n<p>In general two negatives divided results in a positive.&nbsp;</p>\n<p>\\[\\frac{+}{+}=+\\]</p>\n<p>\\[\\frac{+}{-}=-\\]</p>\n<p>\\[\\frac{-}{+}=-\\]</p>\n<p>\\[\\frac{-}{-}=+\\]</p>\n<p>This should not be surprising given that division is just multiplying by the reciprocal.</p>\n<p></p>"}], "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": "{choices_a}", "matrix": "[1,1,1,-1,-1,-1]"}, {"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Which of the following are equal to $\\var{n[1]}\\div\\var{-d[1]}$?</p>", "stepsPenalty": "3", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Dividing negative numbers can be done by pretending the numbers are positive, doing the division, and then determining whether the actual answer should be positive or negative.&nbsp;</p>\n<p>It is also crucial to realise division can be written as a fraction.&nbsp;</p>\n<hr/>\n<p>Consider $\\var{n[1]}\\div\\var{-d[1]}$. This will be the same as $-\\frac{\\var{-n[1]}}{\\var{-d[1]}}$, and $\\frac{\\var{n[1]}}{\\var{-d[1]}}$, and even the strange looking $\\frac{\\var{-n[1]}}{\\var{d[1]}}$.</p>\n<hr/>\n<p>In general two negatives divided results in a positive.&nbsp;</p>\n<p>\\[\\frac{+}{+}=+\\]</p>\n<p>\\[\\frac{+}{-}=-\\]</p>\n<p>\\[\\frac{-}{+}=-\\]</p>\n<p>\\[\\frac{-}{-}=+\\]</p>\n<p>This should not be surprising given that division is just multiplying by the reciprocal.</p>"}], "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": "{choices_b}", "matrix": "[-1,-1,-1,1,1,1]"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}