// Numbas version: finer_feedback_settings
{"name": "Combining algebraic fractions 1 (Video)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"a2": {"definition": "1", "name": "a2", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "a1": {"definition": "1", "name": "a1", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "s1": {"definition": "if(c<0,-1,1)", "name": "s1", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "c": {"definition": "random(-9..9 except [0,-a])", "name": "c", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "nb": {"definition": "if(c<0,'taking away','adding')", "name": "nb", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "a": {"definition": "random(1..9)", "name": "a", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "b": {"definition": "random(-9..9 except 0)", "name": "b", "description": "", "templateType": "anything", "group": "Ungrouped variables"}, "d": {"definition": "random(-9..9 except [0,round(b*a2/a1)])", "name": "d", "description": "", "templateType": "anything", "group": "Ungrouped variables"}}, "statement": "<p>Add the following two fractions together and express as a single fraction over a common denominator.</p>", "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "metadata": {"description": "<p>Express $\\displaystyle \\frac{a}{x + b} \\pm&nbsp; \\frac{c}{x + d}$&nbsp;as an algebraic single fraction over a common denominator.&nbsp;</p>\n<p>Contains a video&nbsp;in <em>Show steps</em>.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "name": "Combining algebraic fractions 1 (Video)", "extensions": [], "advice": "\n    <p>The formula for {nb} fractions is :</p>\n    <p>\\[\\simplify[std]{a / b + {s1} * (c / d) = (ad + {s1} * bc) / bd}\\]</p>\n    <p>and for this exercise we have $\\simplify{b=x+{b}}$, $\\simplify{d=x+{d}}$.<br/>Hence we have:<br/>\\[\\simplify[std]{{a} / ({a1}*x + {b}) + ({c} / ({a2}*x + {d})) = ({a} * ({a2}*x + {d}) + {c} * ({a1}*x + {b})) / (({a1}*x + {b}) * ({a2}*x + {d})) = ({a*a2 + c*a1} * x + {a * d + c * b}) / (({a1}*x + {b}) * ({a2}*x + {d}))}\\]</p>\n    ", "preamble": {"js": "", "css": ""}, "tags": ["algebra", "algebraic fractions", "algebraic manipulation", "chain rule", "combining algebraic fractions", "common denominator"], "functions": {}, "ungrouped_variables": ["a", "c", "b", "d", "nb", "a1", "a2", "s1"], "parts": [{"gaps": [{"variableReplacementStrategy": "originalfirst", "vsetRange": [10, 11], "checkingType": "absdiff", "checkingAccuracy": 1e-05, "showFeedbackIcon": true, "variableReplacements": [], "answer": "({a*a2 +  c*a1} * x + {a * d +  c * b})/ (({a1}*x + {b}) * ({a2}*x + {d}))", "scripts": {}, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "answerSimplification": "std", "failureRate": 1, "unitTests": [], "extendBaseMarkingAlgorithm": true, "marks": 2, "type": "jme", "showPreview": true, "notallowed": {"strings": [")-", ")+"], "message": "<p>Input as a single fraction.</p>", "showStrings": false, "partialCredit": 0}, "checkVariableNames": false, "expectedVariableNames": [], "vsetRangePoints": 5}], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "unitTests": [], "extendBaseMarkingAlgorithm": true, "marks": 0, "steps": [{"variableReplacementStrategy": "originalfirst", "unitTests": [], "extendBaseMarkingAlgorithm": true, "marks": 0, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "prompt": "<p>The formula for {nb} fractions is:</p>\n<p>\\[\\simplify[std]{a / b + {s1} * (c / d) = (ad + {s1} * bc) / bd}\\]</p>\n<p>and for this exercise we have $\\simplify{b=x+{b}}$, $\\simplify{d=x+{d}}$.</p>\n<p>Note that in your answer you do not need to expand the denominator.</p>\n<p>The following video goes through an example similar to this one.</p>\n<p><iframe width=\"640\" height=\"480\" src=\"https://player.vimeo.com/video/8169833\" frameborder=\"0\"></iframe></p>", "type": "information", "scripts": {}, "showCorrectAnswer": true, "variableReplacements": []}], "type": "gapfill", "stepsPenalty": 1, "prompt": "<p>Express</p>\n<p>\\[\\simplify{{a} / ({a1}x + {b}) + ({c} / ({a2}x + {d}))}\\]</p>\n<p>as a single fraction.</p>\n<p>Enter the fraction here: [[0]]</p>\n<p>Input your answer in the form $\\displaystyle \\frac{(ax+b)}{((cx+d)(ex+f))}$ with no other brackets than those shown.</p>\n<p>Click on <em>Show steps</em> if you need help. You will lose one mark if you do so.</p>"}], "variable_groups": [], "type": "question", "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}