// Numbas version: finer_feedback_settings
{"name": "Combining algebraic fractions 3.0", "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 3.0", "tags": ["algebra", "algebraic fractions", "algebraic manipulation", "combining algebraic fractions"], "advice": "<p>The formula for adding these expressions is:</p>\n    <p>\\[\\simplify[std]{a + (c / d) = (ad +&nbsp;c) / d}\\]</p>\n    <p>and for this exercise we have $\\simplify{a={b1}}$, $\\simplify{c={c}x+{b2}}$, $\\simplify{d={a2}x+{d}}$.</p>\n    <p>Hence we have:<br/>\\[\\begin{eqnarray*} \\simplify[std]{{b1} } +\\simplify[std]{ ({c}x+{b2}) / ({a2}x + {d})}&nbsp;&nbsp;&amp;=&amp; \\simplify[basic,unitFactor]{(({b1}) * ({a2}*x + {d}) + ({c}x+{b2}) ) / ( ({a2}*x + {d}))}\\\\ &amp;=&amp;\\simplify[std]{ (({b1*a2}x+{b1*d})+{c}x+{b2}) / ( ({a2}*x + {d}))}\\\\&amp;=&amp;\\simplify[std]{ ( {b1*a2+ c }x+{b1*d+b2}) / (({a2}*x + {d}))}\\end{eqnarray*}\\]</p>", "rulesets": {"std": ["all", "fractionNumbers", "!noLeadingMinus", "!collectNumbers"]}, "parts": [{"stepspenalty": 1.0, "prompt": "\n      <p>Express \\[\\simplify[std]{{a}x+{b1} } +\\simplify[std]{ ({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 to get more information. You will lose one mark if you do so.</p>\n        <p>&nbsp;</p>\n      \n      ", "gaps": [{"notallowed": {"message": "<p>Input as a single fraction.</p>", "showstrings": false, "strings": [")+", ")-", "-(", "+("], "partialcredit": 0.0}, "checkingaccuracy": 1e-05, "vsetrange": [10.0, 11.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 2.0, "answer": "( {c+b1*a2} * x + {b1 * d +  b2 })/ ( ({a2}*x + {d}))", "type": "jme"}], "steps": [{"prompt": "\n          <p>Note that:<br/>\\[\\simplify[std]{a + &nbsp;(c / d) = (ad + c) / d}\\]</p>\n          <p>&nbsp;</p>\n          \n          ", "type": "information", "marks": 0.0}], "marks": 0.0, "type": "gapfill"}], "extensions": [], "statement": "\n  <p>Express the following as a single fraction.</p>\n  <p>&nbsp;</p>\n  \n  ", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": 0.0, "name": "a"}, "c": {"definition": "random(1..9 except a)", "name": "c"}, "d": {"definition": "random(-9..9 except [0,round(b2*a2/c)])", "name": "d"}, "s1": {"definition": "if(c<0,-1,1)", "name": "s1"}, "a2": {"definition": 1.0, "name": "a2"}, "b1": {"definition": "random(-5..5 except 0)", "name": "b1"}, "b2": {"definition": "random(-5..5 except  0)", "name": "b2"}, "nb": {"definition": "if(c<0,'taking away','adding')", "name": "nb"}}, "metadata": {"notes": "<p><strong>18/08/2012:</strong></p>\n        <p>Added tags.</p>\n        <p>Added description.</p>\n        <p>Modified copy of&nbsp;Combining algebraic fractions 3.</p>\n        <p>Checked calculations.OK.</p>\n        <p><strong>29/01/2013:</strong></p>\n        <p>Edited advice so that simplification steps were correct in the solution.</p>\n        <p>&nbsp;</p>\n        <p><strong>&nbsp;</strong></p>", "description": "<p>Express $\\displaystyle b+ &nbsp;\\frac{dx+p}{x + q}$&nbsp;as an algebraic single fraction.&nbsp;</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/"}]}