// Numbas version: finer_feedback_settings
{"name": "Combining algebraic fractions 3.2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"s1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(c<0,-1,1)", "description": "", "name": "s1"}, "b2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "sgn(c)*random(1..5 except [round(c*d/a2)])", "description": "", "name": "b2"}, "a2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "1", "description": "", "name": "a2"}, "b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-9..9 except 0)", "description": "", "name": "b"}, "c": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-9..9 except 0)", "description": "", "name": "c"}, "nb": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(c<0,'taking away','adding')", "description": "", "name": "nb"}, "b1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-5..5 except [0,round(a*b/a1)])", "description": "", "name": "b1"}, "d": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-9..9 except [0,round(b*a2/a1)])", "description": "", "name": "d"}, "a1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "1", "description": "", "name": "a1"}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "name": "a"}}, "ungrouped_variables": ["a", "c", "b", "d", "nb", "a1", "a2", "b1", "b2", "s1"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Combining algebraic fractions 3.2", "functions": {}, "showQuestionGroupNames": false, "parts": [{"stepsPenalty": 1, "scripts": {}, "gaps": [{"answer": "({a*a2+a1*c}*x^2 + {b*c+a1*b2+b1*a2+a*d} * x + {b1 * d +  b2 * b})/ (({a1}*x + {b}) * ({a2}*x + {d}))", "vsetrange": [10, 11], "checkingaccuracy": 1e-05, "showCorrectAnswer": true, "expectedvariablenames": [], "notallowed": {"message": "<p>Input as a single fraction.</p>", "showStrings": false, "partialCredit": 0, "strings": [")-", ")+"]}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "answersimplification": "std", "marks": 2, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "<p>Express \\[\\simplify{({a}x+{b1}) / ({a1}x + {b}) + ({c}x+{b2}) / ({a2}x + {d})}\\] as a single fraction.</p>\n      <p>Input the fraction here: [[0]].</p>\n      <p>Click on Show steps for more information. You will lose one mark if you do so.</p>\n      <p>&nbsp;</p>", "steps": [{"type": "information", "prompt": "<p>The formula for {nb} fractions is :<br/>\\[\\simplify[std]{a / b + {s1} * (c / d) = (ad + {s1} * bc) / bd}\\]</p>\n          <p>and for this exercise we have $\\simplify{a={a}x+{b1}}$, $\\simplify{c={abs(c)}x+{abs(b2)}}$, $\\simplify{b=x+{b}}$, $\\simplify{d=x+{d}}$.</p>\n          <p>Note that in your answer you do not need to expand the denominator.</p>", "showCorrectAnswer": true, "scripts": {}, "marks": 0}], "showCorrectAnswer": true, "marks": 0}], "statement": "\n  <p>Add the following two fractions together and express as a single fraction over a common denominator.</p>\n  <p>&nbsp;</p>\n  \n    ", "tags": ["SFY0001", "algebra", "algebraic fractions", "algebraic manipulation", "checked2015", "combining algebraic fractions", "common denominator"], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "\n                                        \t\t            \t\t<p><strong>5/08/2012:</strong></p>\n                                        \t\t            \t\t        <p>Added tags.</p>\n                                        \t\t            \t\t        <p>Added description.</p>\n                                        \t\t            \t\t        <p>Changed to two questions, for the numerator and denomimator, rather than one as difficult to trap student input for this example. Still some ambiguity however.</p>\n                                        \t\t            \t\t        <p><strong>12/08/2012:</strong></p>\n                                        \t\t            \t\t        <p>Back to one input of a fraction and trapped input in Forbidden Strings.</p>\n                                        \t\t            \t\t        <p>Used the except feature of ranges to get non-degenerate examples.</p>\n                                        \t\t            \t\t        <p>Checked calculation.OK.</p>\n                                        \t\t            \t\t        <p>Improved display in content areas.</p>\n                                        \t\t            \n                                        \t\t", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Express $\\displaystyle \\frac{ax+b}{x + c} \\pm&nbsp; \\frac{dx+p}{x + q}$&nbsp;as an algebraic single fraction over a common denominator.&nbsp;</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<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 $\\simplify{a={a}x+{b1}}$, $\\simplify{c={abs(c)}x+{abs(b2)}}$, $\\simplify{b=x+{b}}$, $\\simplify{d=x+{d}}$.</p>\n  <p>Hence we have:<br/>\\[\\begin{eqnarray*}\\simplify{({a}x+{b1}) / ({a1}*x + {b}) + ({c}x+{b2}) / ({a2}*x + {d})} &amp;=&amp; \\simplify{(({a}x+{b1}) * ({a2}*x + {d}) + ({c}x+{b2}) * ({a1}*x + {b})) / (({a1}*x + {b}) * ({a2}*x + {d}))}\\\\ &amp;=&amp;\\simplify[std]{ (({a*a2} * x^2 + {b1*a2+ a*d}x+{b1*d})+({a1*c}x^2+{b*c+a1*b2}x+{b*b2})) / (({a1}*x + {b}) * ({a2}*x + {d}))}\\\\&amp;=&amp;\\simplify[std]{ ({a*a2 + c*a1} * x^2 + {a * d +a1*b2+b1*a2+ c * b}x+{b1*d+b*b2}) / (({a1}*x + {b}) * ({a2}*x + {d}))}\\end{eqnarray*}\\]</p>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}