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{"name": "Negatives: subtraction resulting in a negative number", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Negatives: subtraction resulting in a negative number", "tags": ["Arithmetic", "arithmetic", "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": {"small": {"name": "small", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "can_override": false}, "big": {"name": "big", "group": "Ungrouped variables", "definition": "random(12..19)", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "small-big", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["ans", "small", "big"], "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>$\\var{small} - \\var{big}$ =&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>When you are doing a subtraction that will result in a negative (that is, you are 'taking away' more than you have), many people reverse the order of the subtraction to make it easier and then put a negative in front of the answer.</p>\n<hr/>\n<p>For example, to determine $\\var{small}-\\var{big}$. We can see the answer will be a negative number (since $\\var{big}$ is bigger than $\\var{small}$). Let's do the related subtraction $\\var{big}-\\var{small}$ first. Here are two common methods:</p>\n<ul>\n<li>Subtract $\\var{small}$ from $\\var{big}$ <span data-jme-visible=\"big-10=small\">which we automatically know is $\\var{-ans}$ since $\\var{big}=\\var{-ans}+\\var{small}$.</span> <span data-jme-visible=\"big-10&gt;small\">which is $\\var{-ans}$ since $\\var{big-10}=\\var{small}+\\var{big-10-small}$.</span> <span data-jme-visible=\"big-10&lt;small\">by breaking $\\var{small}$ up into $\\var{big-10}$ and $\\var{small-big+10}$ and doing $\\var{big}-\\var{big-10}-\\var{small-big+10}=10-\\var{small-big+10}=\\var{-ans}$.</span></li>\n<li>You could determine how many you need to add to $\\var{small}$ to get $\\var{big}$, that is determine $\\var{small}+\\var{-ans}=\\var{big}$.</li>\n</ul>\n<p>Regardless, we find that $\\var{big}-\\var{small}=\\var{-ans}$ and so our answer to the original question is $\\var{small}-\\var{big}=\\var{ans}$.</p>\n<p></p>\n<hr/>\n<p>Why does this work? If you have seen brackets before the following explains it<br/><br/>\\[\\var{small}-\\var{big}=-(\\var{big}-\\var{small})\\]</p>\n<p>If this doesn't help, recall a subtraction tells you the difference between two numbers, it is the distance between two numbers on the number line, if you swap the numbers around in the subtraction you will cover the same distance on the number line just heading in the opposition direction. So if you know the answer will be negative, you can swap the numbers around, do the easier subtraction and then put a negative in front of your answer.</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": "{ans}", "maxValue": "{ans}", "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/"}]}