// Numbas version: exam_results_page_options
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Use / as the fraction bar and use brackets to group the numerator and denominator separately, e.g. $\\dfrac{m+1}{2n}$ is written (m+1)/(2n)</p>", "advice": "<p>We need to get the denominators to be the same, preferably the lowest common denominator, at which point, we can simply <span data-jme-visible=\"addsub=1\">add</span><span data-jme-visible=\"addsub=-1\">subtract</span> the new numerators and put the result over the common denominator.</p>\n<p><span data-jme-visible=\"cf&lt;&gt;1\">Since the first denominator equals $\\var{cf}\\times\\var{ee}\\times x$ and the second equals $\\var{cf}\\times \\var{f}\\times x\\times y$, the lowest common denominator will be the product $\\var{cf}\\times \\var{ee}\\times \\var{f}\\times x\\times y$, that is, $\\var{ansden}xy$. Therefore, we will multiply the first fraction by $\\frac{\\var{f}y}{\\var{f}y}$ and the second fraction by $\\frac{\\var{ee}}{\\var{ee}}$ as follows.</span></p>\n<p><span data-jme-visible=\"cf=1\">Since the first denominator equals $\\var{ee}\\times x$ and the second equals $\\var{f}\\times x\\times y$, the lowest common denominator will be the product $\\var{ee}\\times \\var{f}\\times x\\times y$, that is, $\\var{ansden}xy$. Therefore, we will multiply the first fraction by $\\frac{\\var{f}y}{\\var{f}y}$ and the second fraction by $\\frac{\\var{ee}}{\\var{ee}}$ as follows.</span></p>\n<p><span data-jme-visible=\"addsub=1\">$\\begin{align*}\\displaystyle\\simplify{({a}x+{b})/({cf*ee}x)+{addsub}*(({c}x+{d}y)/({cf*f}x*y))}&amp;=\\simplify{({a}x+{b})/({cf*ee}x)}\\times\\dfrac{\\var{f}y}{\\var{f}y}+\\simplify{(({c}x+{d}y)/({cf*f}x*y))}\\times\\dfrac{\\var{ee}}{\\var{ee}}\\\\[3pt]&amp;=\\dfrac{\\simplify{{a*f}x*y+{b*f}y}}{\\var{ansden}xy}+\\dfrac{\\simplify{{c*ee}x+{d*ee}y}}{\\var{ansden}xy}\\\\[3pt]&amp;=\\dfrac{\\simplify{{a*f}x*y+{b*f+addsub*ee*d}y+{addsub*c*ee}x}}{\\var{ansden}xy}\\end{align*}$</span></p>\n<p><span data-jme-visible=\"addsub=-1\">$\\begin{align*}\\displaystyle\\simplify{({a}x+{b})/({cf*ee}x)+{addsub}*(({c}x+{d}y)/({cf*f}x*y))}&amp;=\\simplify{({a}x+{b})/({cf*ee}x)}\\times\\dfrac{\\var{f}y}{\\var{f}y}-\\simplify{(({c}x+{d}y)/({cf*f}x*y))}\\times\\dfrac{\\var{ee}}{\\var{ee}}\\\\[3pt]&amp;=\\dfrac{\\simplify{{a*f}x*y+{b*f}y}}{\\var{ansden}xy}-\\dfrac{\\simplify{{c*ee}x+{d*ee}y}}{\\var{ansden}xy}\\\\[3pt]&amp;=\\dfrac{\\simplify{{a*f}x*y+{b*f+addsub*ee*d}y+{addsub*c*ee}x}}{\\var{ansden}xy}\\end{align*}$</span></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"ansden": {"name": "ansden", "group": "Ungrouped variables", "definition": "cf*ee*f", "description": "", "templateType": "anything", "can_override": false}, "addSub": {"name": "addSub", "group": "Ungrouped variables", "definition": "random(-1,1)", "description": "<p>adding or subtracting</p>", "templateType": "anything", "can_override": false}, "numbers": {"name": "numbers", "group": "Ungrouped variables", "definition": "shuffle(shuffle(2..10)[0..2]+[-1,1])", "description": "", "templateType": "anything", "can_override": false}, "cf": {"name": "cf", "group": "Ungrouped variables", "definition": "random(1..4)", "description": "<p>common factor of denominators</p>", "templateType": "anything", "can_override": false}, "extrafactor": {"name": "extrafactor", "group": "Ungrouped variables", "definition": "shuffle([2,3,5,7])[0..2]", "description": "<p>extra factors in the denominators</p>", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "numbers[0]", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "numbers[1]", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "numbers[2]", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "numbers[3]", "description": "", "templateType": "anything", "can_override": false}, "ee": {"name": "ee", "group": "Ungrouped variables", "definition": "extrafactor[0]", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "extrafactor[1]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["numbers", "addSub", "cf", "extrafactor", "ansden", "a", "b", "c", "d", "ee", "f"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\displaystyle\\simplify{({a}x+{b})/({cf*ee}x)+{addsub}*(({c}x+{d}y)/({cf*f}x*y))}=$[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "({a*f}x*y+{b*f+addsub*ee*d}y+{addsub*c*ee}x)/({cf*ee*f}x*y)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "`! 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