// Numbas version: finer_feedback_settings
{"name": "Lois's copy of 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": [{"functions": {}, "ungrouped_variables": ["a", "c", "d", "s1", "a2", "b1", "b2", "nb", "b", "a1", "f"], "name": "Lois's copy of Combining algebraic fractions 3.1", "tags": ["algebra", "algebraic fractions", "algebraic manipulation", "combining algebraic fractions"], "preamble": {"css": "", "js": ""}, "advice": "<p>When adding two fractions, as in part a, remember that \\[ \\dfrac{a}{b} + \\dfrac{c}{d} = \\dfrac{ad+bc}{bd} \\]</p>\n<p>The form of part b is:</p>\n<p>\\[\\simplify[std]{a + (c / d) = (ad +&nbsp;c) / d}\\]</p>\n<p>with $\\simplify{a={a}x+{b1}}$, $\\simplify{c={c}x+{b2}}$, $\\simplify{d={a2}x+{d}}$.</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>", "rulesets": {"std": ["all", "fractionNumbers", "!noLeadingMinus", "!collectNumbers"]}, "parts": [{"vsetrangepoints": 5, "prompt": "<p>\\[ \\dfrac{ y}{\\var{a1}} + \\dfrac{z}{\\var{b}} \\]</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "({b}y + {a1}z)/{f}", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"prompt": "<p>\\[\\simplify[std]{{a}x+{b1} } +\\simplify[std]{ ({c}x+{b2}) / ({a2}x + {d})}\\]</p>\n<p>&nbsp;[[0]]</p>\n<p>Make sure that you simplify the numerator (the top of the fraction).</p>\n<p></p>\n<p>&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "<p>Input as a single fraction. Also make sure that you simplify the numerator so that it is a quadratic.</p>", "showStrings": false, "strings": ["+(", "-(", ")+", ")-"], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 1e-05, "vsetrange": [10, 11], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "({a*a2}*x^2 + {c+b1*a2+a*d} * x + {b1 * d +  b2 })/ ( ({a2}*x + {d}))", "marks": 2, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme", "musthave": {"message": "<p>Input as a single fraction. Also make sure that you simplify the numerator.</p>", "showStrings": false, "strings": ["^"], "partialCredit": 0}}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Write the following expressions as a single fraction.</p>\n<p>&nbsp;</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(2,4,8,10)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2,4,8,10)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(-9..9 except [0,round(b2*a2/c)])", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "f": {"definition": "{a1}*{b}", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "s1": {"definition": "if(c<0,-1,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s1", "description": ""}, "a1": {"definition": "random(3,5,7,9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a2": {"definition": "1", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "b1": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "b2": {"definition": "random(-5..5 except  0)", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "nb": {"definition": "if(c<0,'taking away','adding')", "templateType": "anything", "group": "Ungrouped variables", "name": "nb", "description": ""}}, "metadata": {"description": "<p>Express $\\displaystyle ax+b+ &nbsp;\\frac{dx+p}{x + q}$&nbsp;as an algebraic single fraction.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}]}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}