// Numbas version: finer_feedback_settings
{"name": "NG4 Subtract fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "NG4 Subtract fractions", "tags": ["adding and subtracting fractions", "adding fractions", "converting between decimals and fractions", "converting integers to fractions", "Fractions", "fractions", "integers", "manipulation of fractions", "subtracting fractions", "taxonomy"], "metadata": {"description": "<p>Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer&nbsp;and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Evaluate the following additions and subtractions, giving each fraction in its simplest form. Write the numerator (the top number) as negative if the fraction is negative.</p>", "advice": "<p>$\\displaystyle\\frac{\\var{f_coprime}}{\\var{g_coprime}}-\\frac{\\var{h_coprime}}{\\var{j_coprime}}+2.$</p>\n<p></p>\n<p>The two fractions can be individually multiplied to achieve a common denominator of the lowest common multiple, $\\var{lcm2}.$</p>\n<p>$\\displaystyle\\frac{\\var{f_coprime}}{\\var{g_coprime}}$ becomes $\\displaystyle\\frac{\\var{flcm2_g}}{\\var{lcm2}}$ and $\\displaystyle\\frac{\\var{h_coprime}}{\\var{j_coprime}}$ becomes&nbsp;$\\displaystyle\\frac{\\var{hlcm2_j}}{\\var{lcm2}}.$</p>\n<p>We can now subtract the second fraction from the first.</p>\n<p style=\"text-align: center;\">$\\displaystyle\\frac{\\var{flcm2_g}}{\\var{lcm2}}-\\frac{\\var{hlcm2_j}}{\\var{lcm2}}=\\frac{\\var{flcmhlcm}}{\\var{lcm2}}.$</p>\n<p style=\"text-align: left;\"></p>\n<p style=\"text-align: left;\"><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Number\" target=\"_blank\" rel=\"noopener\">Find out more about this topic using our resource.</a></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"hlcm2_j": {"name": "hlcm2_j", "group": "Part b", "definition": "h_coprime*lcm2_j", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "lcm2": {"name": "lcm2", "group": "Part b", "definition": "lcm(g_coprime,j_coprime)", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "gcd_fg": {"name": "gcd_fg", "group": "Part b", "definition": "gcd(f,g)", "description": "<p>PART B gcd of first fraction num and denom</p>", "templateType": "anything", "can_override": false}, "j": {"name": "j", "group": "Part b", "definition": "random(2..10 except h)", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Part b", "definition": "random(1..10)", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Part b", "definition": "random(1..10)", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "h_coprime": {"name": "h_coprime", "group": "Part b", "definition": "h/gcd_hj", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "lcm2_j": {"name": "lcm2_j", "group": "Part b", "definition": "lcm2/j_coprime", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "j_coprime": {"name": "j_coprime", "group": "Part b", "definition": "j/gcd_hj", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "flcmhlcm": {"name": "flcmhlcm", "group": "Part b", "definition": "flcm2_g-hlcm2_j", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "g_coprime": {"name": "g_coprime", "group": "Part b", "definition": "g/gcd_fg", "description": "<p>PART B g_coprime</p>", "templateType": "anything", "can_override": false}, "gcd_hj": {"name": "gcd_hj", "group": "Part b", "definition": "gcd(h,j)", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "Part b", "definition": "random(2..10 except f except j)", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "flcm2_g": {"name": "flcm2_g", "group": "Part b", "definition": "f_coprime*lcm2_g", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "lcm2_g": {"name": "lcm2_g", "group": "Part b", "definition": "lcm2/g_coprime", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}, "f_coprime": {"name": "f_coprime", "group": "Part b", "definition": "f/gcd_fg", "description": "<p>PART B</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Part b", "variables": ["f", "f_coprime", "g", "g_coprime", "gcd_fg", "h", "h_coprime", "j", "j_coprime", "gcd_hj", "lcm2", "lcm2_g", "flcm2_g", "lcm2_j", "hlcm2_j", "flcmhlcm"]}], "functions": {}, "preamble": {"js": "", "css": "fraction {\n  display: inline-block;\n  vertical-align: middle;\n}\nfraction > numerator, fraction > denominator {\n  float: left;\n  width: 100%;\n  text-align: center;\n  line-height: 2.5em;\n}\nfraction > numerator {\n  border-bottom: 1px solid;\n  padding-bottom: 5px;\n}\nfraction > denominator {\n  padding-top: 5px;\n}\nfraction input {\n    line-height: 1em;\n}\n\nfraction .part {\n    margin: 0;\n}\n\n.table-responsive, .fractiontable {\n  display:inline-block;\n}\n.fractiontable {\n  padding: 0; \n  border: 0;\n}\n\n.fractiontable  .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n  border-bottom: 1px solid black; \n  text-align: center;\n}\n\n\n.fractiontable tr {\n    height: 3em;\n}\n"}, "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>$\\displaystyle\\frac{\\var{f_coprime}}{\\var{g_coprime}}-\\frac{\\var{h_coprime}}{\\var{j_coprime}}=$&nbsp;<fraction> <numerator>[[0]]</numerator> <denominator>[[1]]</denominator> </fraction></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "flcmhlcm", "maxValue": "flcmhlcm", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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": "lcm2", "maxValue": "lcm2", "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", "type": "question", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}]}