// Numbas version: finer_feedback_settings
{"name": "SHORTENED VERSION of Algebra V: algebraic fractions (simplification)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["n1", "d1", "ans", "a1", "a2", "n2", "p2", "b1", "b2", "b3", "b4", "c1", "c2", "e1", "e2", "e3", "co1", "co2", "f1", "f2", "co3", "co4", "p3", "g1", "g2"], "name": "SHORTENED VERSION of Algebra V: algebraic fractions (simplification)", "tags": [], "advice": "<p>Click 'Try another question like this one' if you need more practice.</p>", "rulesets": {}, "parts": [{"stepsPenalty": "0", "notallowed": {"message": "<p>Please simplify further.</p>", "showStrings": false, "strings": ["^", "x*x"], "partialCredit": 0}, "variableReplacements": [], "prompt": "<p>$\\simplify{({n1}{a1}x^2+{n1}{a2}x)/({d1}{a1}x+{d1}{a2})}$</p>\n<p></p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>${\\simplify{({n1}{a1}x^2+{n1}{a2}x)/({d1}{a1}x+{d1}{a2})}}$</p>\n<p>Factorise the numerator and denominator so that the binomials in both are the same.</p>\n<p>${\\big(\\frac{\\var{n1}x}{\\var{d1}}\\big)\\big(\\frac{\\var{a1}x+\\var{a2}}{\\var{a1}x+\\var{a2}}\\big)}$</p>\n<p>The binomials cancel, leaving $x$ and its coefficient:</p>\n<p>$\\big({\\simplify{{n1}/{d1}}}\\big)x$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "answersimplification": "!basic", "marks": 1, "scripts": {}, "answer": "{{n1}/{d1}}*x", "showCorrectAnswer": true, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1], "maxlength": {"length": "0", "message": "", "partialCredit": 0}}, {"stepsPenalty": "0", "notallowed": {"message": "", "showStrings": false, "strings": ["^", "n*n"], "partialCredit": 0}, "variableReplacements": [], "prompt": "<p>$\\simplify{(({n2}{b1}n^({p2}+1)+{n2}{b2}n^{p2})/({n2}{b3}n^({p2}+1)+{n2}{b4}n^{p2}))}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>${\\simplify{(({n2}{b1}n^({p2}+1)+{n2}{b2}n^{p2})/({n2}{b3}n^({p2}+1)+{n2}{b4}n^{p2}))}}$</p>\n<p>As before, factorise the numerator and denominator. This time, however, you'll notice that the factors themselves are the same.</p>\n<p>$\\big(\\frac{\\var{n2}n}{{\\var{n2}}n}\\big)\\big(\\frac{\\var{b1}n+\\var{b2}}{\\var{b3}n+\\var{b4}}\\big)$</p>\n<p>The factors cancel, leaving:</p>\n<p>$\\big(\\frac{\\var{b1}n+\\var{b2}}{\\var{b3}n+\\var{b4}}\\big)$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 1, "scripts": {}, "answer": "({b1}n+{b2})/({b3}n+{b4})", "showCorrectAnswer": true, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"stepsPenalty": "0", "notallowed": {"message": "", "showStrings": false, "strings": ["^", "^2"], "partialCredit": 0}, "variableReplacements": [], "prompt": "<p>$\\simplify{(x^2+({c1}+{c2})x +{c1}{c2})/(x+{c1})}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>${\\simplify{(x^2+({c1}+{c2})x +{c1}{c2})/(x+{c1})}}$</p>\n<p>Here, the quadratic expression in the numerator needs to be factorised into the product of two binomials.</p>\n<p>$\\frac{({\\simplify{x+{c1}}})({\\simplify{x+{c2}}})}{({\\simplify{x+{c1}}})}$</p>\n<p>You will notice that one of the binomials in the numerator is the same as the denominator, which means that they can be cancelled. This leaves the expression:</p>\n<p>${\\simplify{x+{c2}}}$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 1, "scripts": {}, "answer": "x+{c2}", "showCorrectAnswer": true, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "extensions": [], "statement": "<p><strong>Simplify the following algebraic expressions.</strong></p>\n<p><strong><em>Note:</em></strong> <em>Although the question may accept coefficients in their decimal forms, it would be more appropriate to keep them in their most simplified fraction forms.</em></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"f1": {"definition": "random(-5..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "f1", "description": ""}, "f2": {"definition": "random(-5..5 except f1)", "templateType": "anything", "group": "Ungrouped variables", "name": "f2", "description": ""}, "ans": {"definition": "n1/d1", "templateType": "anything", "group": "Ungrouped variables", "name": "ans", "description": ""}, "b4": {"definition": "random(1..9 except b3)", "templateType": "anything", "group": "Ungrouped variables", "name": "b4", "description": ""}, "b1": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "b2": {"definition": "random(1..9 except b1)", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "b3": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "b3", "description": ""}, "d1": {"definition": "random(1..9 except n1)", "templateType": "anything", "group": "Ungrouped variables", "name": "d1", "description": ""}, "co1": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "co1", "description": ""}, "co3": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "co3", "description": ""}, "co2": {"definition": "random(2..5 except co1)", "templateType": "anything", "group": "Ungrouped variables", "name": "co2", "description": ""}, "co4": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "co4", "description": ""}, "g2": {"definition": "random(-5..5 except 0 except g1)", "templateType": "anything", "group": "Ungrouped variables", "name": "g2", "description": ""}, "g1": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "g1", "description": ""}, "a1": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a2": {"definition": "random(1..9 except a1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "c2": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "c2", "description": ""}, "c1": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}, "e1": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "e1", "description": ""}, "e3": {"definition": "random(-5..5 except 0 except e2)", "templateType": "anything", "group": "Ungrouped variables", "name": "e3", "description": ""}, "e2": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "e2", "description": ""}, "p2": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "p2", "description": ""}, "p3": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "p3", "description": ""}, "n1": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "n1", "description": ""}, "n2": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "n2", "description": ""}}, "metadata": {"description": "<p>A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Sarah Turner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/881/"}]}]}], "contributors": [{"name": "Sarah Turner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/881/"}]}