// Numbas version: exam_results_page_options
{"name": "Negatives: subtracting negative numbers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Negatives: subtracting negative numbers", "tags": ["negative numbers", "Negative Numbers", "negatives", "subtraction"], "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}, "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"], "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>$\\var{n[0]}-(\\var{n[1]})$ =&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>Thinking about negative numbers as debt can help you understand these questions.</p>\n<hr/>\n<p>We can think of $\\var{n[0]}$ as being in debt by \\${-n[0]}. Suppose we then 'take away' another debt of \\${-n[1]}, that is, we pay back \\${-n[1]}. Now we are <span data-jme-visible=\"ans1&lt;0\">only in debt</span> <span data-jme-visible=\"ans1&gt;0\">actually in front</span> by \\${abs(ans1)}. That is, $\\var{n[0]}-(\\var{n[1]})=\\var{ans1}$.</p>\n<hr/>\n<p>Another way is to think of the minus sign as going in the reverse direction.&nbsp;</p>\n<hr/>\n<p>Suppose on the number line we are at $\\var{n[0]}$, and now instead of going another $\\var{-n[1]}$ to the left (which we would do if we were doing $\\var{n[0]}+(\\var{n[1]})$) we have to go the opposite way, we have to move $\\var{-n[1]}$ to the right (which is the same as $\\var{n[0]}+\\var{-n[1]}$, and we end up at $\\var{ans1}$.</p>\n<hr/>\n<p></p>\n<p>In general two negative symbols next to each other are the same as a positive symbol.&nbsp;</p>\n<p>\\[++=+\\]</p>\n<p>\\[+-=-\\]</p>\n<p>\\[-+=-\\]</p>\n<p>\\[--=+\\]</p>\n<p>Any even number of negative symbols will be the same as a positive symbol. For example,</p>\n<p>\\[-----=+-=-\\]</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>$\\var{n[2]}-\\var{n[3]}$ =&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>Thinking about negative numbers as debt can help you understand these questions.</p>\n<hr/>\n<p>We can think of $\\var{n[2]}$ as being in debt by \\${-n[2]}. Suppose we then 'take away' another debt of \\${-n[3]}, that is, we pay back \\${-n[3]}. Now we are <span data-jme-visible=\"ans2&lt;0\">only in debt</span> <span data-jme-visible=\"ans2&gt;0\">actually in front</span> by \\${abs(ans2)}. That is, $\\var{n[2]}-(\\var{n[3]})=\\var{ans2}$.</p>\n<hr/>\n<p>Another way is to think of the minus sign as going in the reverse direction.&nbsp;</p>\n<hr/>\n<p>Suppose on the number line we are at $\\var{n[2]}$, and now instead of going another $\\var{-n[3]}$ to the left (which we would do if we were doing $\\var{n[2]}+(\\var{n[3]})$) we have to go the opposite way, we have to move $\\var{-n[3]}$ to the right (which is the same as $\\var{n[2]}+\\var{-n[3]}$, and we end up at $\\var{ans2}$.</p>\n<hr/>\n<p></p>\n<p>In general two negative symbols next to each other is the same as a positive symbol.&nbsp;</p>\n<p>\\[++=+\\]</p>\n<p>\\[+-=-\\]</p>\n<p>\\[-+=-\\]</p>\n<p>\\[--=+\\]</p>\n<p>Any even number of negative symbols will be the same as a positive symbol. For example,</p>\n<p>\\[-----=+-=-\\]</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}], "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/"}]}