// Numbas version: finer_feedback_settings
{"name": "Combining algebraic fractions 0", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "name": "Combining algebraic fractions 0", "tags": ["algebra", "algebraic fractions", "algebraic manipulation", "combining algebraic fractions", "common denominator"], "advice": "\n  <p>We have:</p>\n    <p>\\[\\simplify[std]{{a} + ({c} / ({a2}*x + {d})) = ({a} * ({a2}*x + {d}) + {c}) &nbsp;/ (({a2}*x + {d})) = ({a*a2} * x + {a * d + c}) / ( ({a2}*x + {d}))}\\]</p>\n  ", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "parts": [{"stepspenalty": 1.0, "prompt": "<p>Express \\[\\simplify[std]{{a} &nbsp; &nbsp; + ({c} / ({a2}x + {d}))}\\] as a single algebraic fraction.</p>\n        <p>Input the fraction here: [[0]].</p>\n        <p>Input your answer in the form $\\displaystyle \\frac{(ax+b)}{(cx+d)}$ with no other brackets than those shown.</p>\n        <p>You can click on Show steps for help. You will lose 1 mark if you do so.</p>\n        <p>&nbsp;</p>", "gaps": [{"type": "jme", "checkingaccuracy": 1e-05, "minlength": {"length": 13.0, "message": "<p>Input as a single fraction.</p>", "partialcredit": 0.0}, "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 2.0, "answer": "({a*a2}x+{a*d+c})/({a2}x+{d})", "vsetrange": [10.0, 11.0], "musthave": {"message": "<p>Input as a single fraction</p>", "showstrings": false, "strings": [")/"], "partialcredit": 0.0}}], "steps": [{"prompt": "\n          <p>The formula for adding these expressions is :<br/>\\[\\simplify[std]{a + {s1} * (c / d) = (ad + {s1} * bc) / d}\\]</p>\n            <p>and for this exercise we have &nbsp;$\\simplify{d={a2}x+{d}}$.</p>\n            <p>&nbsp;</p>\n          ", "type": "information", "marks": 0.0}], "marks": 0.0, "type": "gapfill"}], "extensions": [], "statement": "\n  <p>Add the following &nbsp;together and express as a single algebraic fraction.</p>\n    <p>&nbsp;</p>\n  ", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "random(1..9)", "name": "a"}, "c": {"definition": "random(-9..9 except [0,-a*d])", "name": "c"}, "d": {"definition": "random(-9..9 except [0,a2])", "name": "d"}, "s1": {"definition": "if(c<0,-1,1)", "name": "s1"}, "a2": {"definition": "random(2..9)", "name": "a2"}, "nb": {"definition": "if(c<0,'taking away','adding')", "name": "nb"}}, "metadata": {"notes": "\n                                    \t\t                                                    \t\t                \t\t<p><strong>5/08/2012:</strong></p>\n                                    \t\t                                                    \t\t                \t\t        <p>Added tags.</p>\n                                    \t\t                                                    \t\t                \t\t        <p>Added description.</p>\n                                    \t\t                                                    \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                \t\t        <p><strong>12/08/2012:</strong></p>\n                                    \t\t                                                    \t\t                \t\t        <p>Back to one input of a fraction and trapped input in Forbidden Strings.</p>\n                                    \t\t                                                    \t\t                \t\t        <p>Used the except feature of ranges to get non-degenerate examples.</p>\n                                    \t\t                                                    \t\t                \t\t        <p>Checked calculation.OK.</p>\n                                    \t\t                                                    \t\t                \t\t        <p>Improved display in content areas.</p>\n                                    \t\t                                                    \t\t                \n                                    \t\t                                                    \n                                    \t\t", "description": "<p>Express $\\displaystyle a \\pm&nbsp; \\frac{c}{x + d}$&nbsp;as an algebraic single fraction.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}