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{"name": "Ioannis's copy of Arithmetic with Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"b": {"group": "Ungrouped variables", "definition": "{m}*{d}", "name": "b", "templateType": "anything", "description": ""}, "d": {"group": "Ungrouped variables", "definition": "random(2..7 except c)", "name": "d", "templateType": "anything", "description": ""}, "m": {"group": "Ungrouped variables", "definition": "nm[1]", "name": "m", "templateType": "anything", "description": ""}, "n": {"group": "Ungrouped variables", "definition": "nm[0]", "name": "n", "templateType": "anything", "description": ""}, "nm": {"group": "Ungrouped variables", "definition": "satisfy(\n//variables to be defined using nm\n[n,m],\n//definition of variables\n[random(3..5),random(2..5)],\n//condition on the variables, m and n forcec to be coprime\n[gcd(m,n)=1]\n\n)", "name": "nm", "templateType": "anything", "description": ""}, "a": {"group": "Ungrouped variables", "definition": "{n}*{c}", "name": "a", "templateType": "anything", "description": ""}, "c": {"group": "Ungrouped variables", "definition": "random(6..10)", "name": "c", "templateType": "anything", "description": ""}}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<p>a) When adding fractions you first need to put them over a common denominator.</p>\n<p>See the section <a href=\"https://moodle.uel.ac.uk/mod/book/view.php?id=835143&amp;chapterid=60156\" target=\"_blank\" rel=\"noopener noreferrer\">adding fractions</a> on the Maths Study Skills page for explanations and examples.</p>\n<p>b) When multiplying $ \\dfrac{a}{b} \\times \\dfrac{c}{d}$ we get $ \\dfrac{ab}{cd}$. It might then be possible to simplify the answer by cancelling common factors.</p>\n<p>c) $ \\dfrac{\\var{a}}{\\var{b}} \\div \\dfrac{\\var{c}}{\\var{d}}$ is equivalent to $ \\dfrac{\\var{a}}{\\var{b}}&nbsp; \\times \\dfrac{\\var{d}}{\\var{c}}$.</p>\n<p>After cancelling this is $ \\dfrac{\\var{n}}{\\var{m}} $.</p>\n<p>See the section <a href=\"https://moodle.uel.ac.uk/mod/book/view.php?id=835143&amp;chapterid=60157\" target=\"_blank\" rel=\"noopener noreferrer\">multiply / divide fractions</a> on the Maths page on Study Skills on Moodle for explanations and examples.</p>", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Addition, multiplication and division of fractions.</p>"}, "tags": [], "functions": {}, "statement": "<p><strong>Evaluate and simplify</strong> the following, giving your answers as <strong>exact single fractions</strong>:</p>\n<p>(if your answer is, for example $\\displaystyle {\\dfrac {3} {2}}$, then you should input:<strong>&nbsp; 3 / 2 </strong>)</p>", "preamble": {"css": "", "js": ""}, "parts": [{"customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "<p>$\\displaystyle {\\dfrac {\\var{n}} {\\var{m}}} + {\\dfrac {\\var{d}} {\\var{c}}}$</p>\n<p>&nbsp;[[0]]</p>", "variableReplacements": [], "marks": 0, "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "useCustomName": false, "scripts": {}, "type": "gapfill", "gaps": [{"customMarkingAlgorithm": "", "valuegenerators": [], "variableReplacements": [], "marks": 1, "checkingType": "absdiff", "variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "showPreview": true, "useCustomName": false, "scripts": {}, "showCorrectAnswer": true, "checkingAccuracy": 0.001, "vsetRange": [0, 1], "adaptiveMarkingPenalty": 0, "notallowed": {"showStrings": false, "partialCredit": 0, "strings": ["."], "message": "<p>You need to give your answer as a fraction not a decimal.</p>"}, "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "showFeedbackIcon": true, "type": "jme", "failureRate": 1, "unitTests": [], "answer": "({c}*{n}+{m}*{d})/({m}*{c})", "customName": ""}], "showCorrectAnswer": true, "unitTests": [], "adaptiveMarkingPenalty": 0, "customName": ""}, {"customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "<p>&nbsp;$\\displaystyle {\\dfrac {\\var{b}} {\\var{a}}}&nbsp; \\times {\\dfrac {\\var{c}} {\\var{d}}}$</p>\n<p>&nbsp;[[0]]</p>", "variableReplacements": [], "marks": 0, "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "useCustomName": false, "scripts": {}, "type": "gapfill", "gaps": [{"customMarkingAlgorithm": "", "valuegenerators": [], "variableReplacements": [], "marks": 1, "checkingType": "absdiff", "variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "showPreview": true, "useCustomName": false, "scripts": {}, "showCorrectAnswer": true, "checkingAccuracy": 0.001, "vsetRange": [0, 1], "adaptiveMarkingPenalty": 0, "notallowed": {"showStrings": false, "partialCredit": 0, "strings": ["."], "message": "You need to give your answer as a fraction"}, "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "showFeedbackIcon": true, "type": "jme", "failureRate": 1, "unitTests": [], "answer": "{m}/{n}", "customName": ""}], "showCorrectAnswer": true, "unitTests": [], "adaptiveMarkingPenalty": 0, "customName": ""}, {"customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "<p>&nbsp;$\\displaystyle {\\dfrac {\\var{a}} {\\var{b}}}&nbsp; \\div {\\dfrac {\\var{c}} {\\var{d}}}$</p>\n<p>&nbsp;[[0]]</p>", "variableReplacements": [], "marks": 0, "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "useCustomName": false, "scripts": {}, "type": "gapfill", "gaps": [{"customMarkingAlgorithm": "", "valuegenerators": [], "variableReplacements": [], "marks": 1, "checkingType": "absdiff", "variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "showPreview": true, "useCustomName": false, "scripts": {}, "showCorrectAnswer": true, "checkingAccuracy": 0.001, "vsetRange": [0, 1], "adaptiveMarkingPenalty": 0, "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "showFeedbackIcon": true, "type": "jme", "failureRate": 1, "unitTests": [], "answer": "{n}/{m}", "customName": ""}], "showCorrectAnswer": true, "unitTests": [], "adaptiveMarkingPenalty": 0, "customName": ""}], "name": "Ioannis's copy of Arithmetic with Fractions", "variable_groups": [], "ungrouped_variables": ["a", "c", "b", "d", "m", "n", "nm"], "rulesets": {}, "extensions": [], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}, {"name": "Ioannis Lignos", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/757/"}]}]}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}, {"name": "Ioannis Lignos", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/757/"}]}