// Numbas version: exam_results_page_options
{"name": "Negatives: multiplying negative numbers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Negatives: multiplying negative numbers", "tags": ["multiplication", "multiplying", "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": {"ans1": {"name": "ans1", "group": "Ungrouped variables", "definition": "n[0]*n[1]", "description": "", "templateType": "anything", "can_override": false}, "ans2": {"name": "ans2", "group": "Ungrouped variables", "definition": "n[2]*n[3]", "description": "", "templateType": "anything", "can_override": false}, "ans3": {"name": "ans3", "group": "Ungrouped variables", "definition": "m[0]*m[1]*m[2]", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "shuffle([-1,-2,-3,-4,-5,-10,-20])[0..3]", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "shuffle(-12..-2)[0..4]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n", "ans1", "ans2", "ans3", "m"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "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>$(\\var{n[0]})\\times(\\var{n[1]})$ =&nbsp;[[0]]</p>", "stepsPenalty": "1", "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>Consider $(\\var{n[0]})\\times (\\var{n[1]})$. Let's move the negatives out the front to get $--\\var{-n[0]}\\times \\var{-n[1]}$, we can just do the multiplication and get $--\\var{ans1}$, but this is the same as $\\var{ans1}$.</p>\n<p>In essence, we work out the numbers and the signs separately.</p>\n<hr/>\n<p>In general two negatives multiplied results in a positive.&nbsp;</p>\n<p>\\[+\\times+=+\\]</p>\n<p>\\[+\\times-=-\\]</p>\n<p>\\[-\\times+=-\\]</p>\n<p>\\[-\\times-=+\\]</p>\n<p>Any even number of negative symbols will be the same as a positive symbol and any odd number of negative symbols will be the same as a negative symbol. For example,</p>\n<p>\\[-\\times-\\times-\\times-\\times-=+\\times-=-\\]</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{ans1}", "maxValue": "{ans1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "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>$\\var{n[2]}\\times (\\var{n[3]})$ =&nbsp;[[0]]</p>", "stepsPenalty": "1", "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>This is actually&nbsp;the same process as the last question.&nbsp;The lack of brackets doesn't affect this question.</p>\n<hr/>\n<p>Consider $(\\var{n[2]})\\times (\\var{n[3]})$. Let's move the negatives out the front to get $--\\var{-n[2]}\\times \\var{-n[3]}$, we can just do the multiplication and get $--\\var{ans2}$, but this is the same as $\\var{ans2}$.</p>\n<p>In essence, we work out the numbers and the signs separately.</p>\n<hr/>\n<p>In general two negatives multiplied results in a positive.&nbsp;</p>\n<p>\\[+\\times+=+\\]</p>\n<p>\\[+\\times-=-\\]</p>\n<p>\\[-\\times+=-\\]</p>\n<p>\\[-\\times-=+\\]</p>\n<p>Any even number of negative symbols will be the same as a positive symbol and any odd number of negative symbols will be the same as a negative symbol. For example,</p>\n<p>\\[-\\times-\\times-\\times-\\times-=+\\times-=-\\]</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{ans2}", "maxValue": "{ans2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "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>$(\\var{m[0]})(\\var{m[1]})(\\var{m[2]})$ =&nbsp;[[0]]</p>", "stepsPenalty": "1", "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>Recall that $(\\var{m[0]})(\\var{m[1]})(\\var{m[2]})$ is a way of writing $(\\var{m[0]})\\times(\\var{m[1]})\\times(\\var{m[2]})$.</p>\n<hr/>\n<p>Let's move the negatives out the front to get $---\\var{-m[0]}\\times \\var{-m[1]}\\times \\var{-m[2]}$, we can just do the multiplication and get $---\\var{-ans3}$, but this is the same as $\\var{ans3}$.</p>\n<p>In essence, we work out the numbers and the signs separately.</p>\n<hr/>\n<p>In general two negatives multiplied results in a positive.&nbsp;</p>\n<p>\\[+\\times+=+\\]</p>\n<p>\\[+\\times-=-\\]</p>\n<p>\\[-\\times+=-\\]</p>\n<p>\\[-\\times-=+\\]</p>\n<p>Any even number of negative symbols will be the same as a positive symbol and any odd number of negative symbols will be the same as a negative symbol. For example,</p>\n<p>\\[-\\times-\\times-\\times-\\times-=+\\times-=-\\]</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{ans3}", "maxValue": "{ans3}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "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/"}]}