// Numbas version: finer_feedback_settings
{"name": "Combining algebraic fractions 3.1", "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)", "name": "s1", "description": ""}, "a2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "1", "name": "a2", "description": ""}, "d": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-9..9 except [0,round(b2*a2/c)])", "name": "d", "description": ""}, "c": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..9 except a)", "name": "c", "description": ""}, "b1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "name": "b1", "description": ""}, "nb": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(c<0,'taking away','adding')", "name": "nb", "description": ""}, "b2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-5..5 except  0)", "name": "b2", "description": ""}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..9)", "name": "a", "description": ""}}, "ungrouped_variables": ["a", "c", "d", "s1", "a2", "b1", "b2", "nb"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Combining algebraic fractions 3.1", "functions": {}, "showQuestionGroupNames": false, "parts": [{"marks": 0, "scripts": {}, "gaps": [{"answer": "({a*a2}*x^2 + {c+b1*a2+a*d} * x + {b1 * d +  b2 })/ ( ({a2}*x + {d}))", "vsetrange": [10, 11], "checkingaccuracy": 1e-05, "checkvariablenames": false, "expectedvariablenames": [], "notallowed": {"message": "<p>Input as a single fraction.</p>", "showStrings": false, "partialCredit": 0, "strings": ["+(", "-(", ")+", ")-"]}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "answersimplification": "std", "type": "jme", "showCorrectAnswer": true, "marks": 2, "vsetrangepoints": 5}], "type": "gapfill", "showCorrectAnswer": true, "steps": [{"type": "information", "showCorrectAnswer": true, "prompt": "<p>Note that:<br/>\\[\\simplify[std]{a + &nbsp;(c / d) = (ad + c) / d}\\]</p>\n            <p>&nbsp;</p>", "marks": 0, "scripts": {}}], "prompt": "<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>", "stepsPenalty": 1}], "statement": "<p>Express the following as a single fraction.</p>\n    <p>&nbsp;</p>", "tags": ["SFY0001", "algebra", "algebraic fractions", "algebraic manipulation", "checked2015", "combining algebraic fractions"], "rulesets": {"std": ["all", "fractionNumbers", "!noLeadingMinus", "!collectNumbers"]}, "preamble": {"css": "", "js": ""}, "type": "question", "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>&nbsp;</p>\n    <p><strong>&nbsp;</strong></p>", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Express $\\displaystyle ax+b+ &nbsp;\\frac{dx+p}{x + q}$&nbsp;as an algebraic single fraction.&nbsp;</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "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 $\\simplify{a={a}x+{b1}}$, $\\simplify{c={c}x+{b2}}$, $\\simplify{d={a2}x+{d}}$.</p>\n  <p>Hence we have:<br/>\\[\\begin{eqnarray*} \\simplify[std]{{a}x+{b1} } +\\simplify[std]{ ({c}x+{b2}) / ({a2}x + {d})}&nbsp;&nbsp;&amp;=&amp; \\simplify{(({a}x+{b1}) * ({a2}*x + {d}) + ({c}x+{b2}) ) / ( ({a2}*x + {d}))}\\\\ &amp;=&amp;\\simplify[std]{ (({a*a2} * x^2 + {b1*a2+ a*d}x+{b1*d})+{c}x+{b2}) / ( ({a2}*x + {d}))}\\\\&amp;=&amp;\\simplify[std]{ ({a*a2} * x^2 + {a * d +b1*a2+ c }x+{b1*d+b2}) / (({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/"}]}