You must write your answer in the form p/q for integers p and q
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", "partialCredit": 0}, "checkingtype": "absdiff", "scripts": {}, "answersimplification": "std", "type": "jme", "showCorrectAnswer": true, "marks": 1, "vsetrangepoints": 5}], "type": "gapfill", "showCorrectAnswer": true, "prompt": "\\[\\simplify{{g} / ({a} + {s1} * ({b * g} / {f}))}\\]
Input your answer here: [[0]]
Your answer must be of the form a/b for suitable integers a and b. No decimal numbers allowed.
\nDo not include brackets in your answer.
", "marks": 0}], "variables": {"s1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(a*f+s*b*g=1,-s,s)", "name": "s1", "description": ""}, "b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "switch(f=2,1,f=3,random(1,2),f=4,random(1,3),f=5, random(1..4),f=6,random(1,5),f=7,random(1..5),f=8,random(1,3,5),f=9,random(1,2,4,5),f=10,random(1,3),f=11,random(1..5))", "name": "b", "description": ""}, "f": {"templateType": "anything", "group": "Ungrouped variables", "definition": "switch(g=2,random(3..7#2),g=3,random(2,4,5),g=4,random(3,5),g=5, random(2,3,4),g=6,random(5,7),g=7,random(2,3,4),g=8,random(3,5,7),g=9,random(2,4,5),g=10,random(3,7),g=11,random(2..5))", "name": "f", "description": ""}, "s": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1,-1)", "name": "s", "description": ""}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..7)", "name": "a", "description": ""}, "g": {"templateType": "anything", "group": "Ungrouped variables", "definition": "switch(a=1, random(2..7),a=2,random(3..7#2),a=3,random(4,5,7),a=4,random(5,7),a=5, random(6,7,8),a=6,random(7,11),a=7,random(8,9))", "name": "g", "description": ""}}, "ungrouped_variables": ["a", "b", "g", "f", "s1", "s"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Simplifying fractions", "functions": {}, "variable_groups": [], "showQuestionGroupNames": false, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "Write the following expression as a single fraction in its lowest form:
", "tags": ["checked2015", "Fractions", "fractions", "lowest form", "mas1601", "MAS1601", "simplifying fractions"], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "5/08/2012:
\nAdded description.
", "licence": "Creative Commons Attribution 4.0 International", "description": "Find $\\displaystyle \\frac{a} {b + \\frac{c}{d}}$ as a single fraction in the form $\\displaystyle \\frac{p}{q}$ for integers $p$ and $q$.
"}, "advice": "We have:
\\[\\simplify[std]{{g} / ({a} + {s1} * ({b * g} / {f})) = {g} / (({a} * {f} + {s1} * {b * g}) / {f}) ={g} / (({a * f + s1 * b * g}) / {f})= ({f}*{g}) / ({a * f + s1 * b * g}) = ({g * f} / {(a * f + s1 * b * g)})}\\]
Here we use the result that dividing by a fraction $\\frac{a}{b}$ is the same as multiplying by $\\frac{b}{a}$.
The resulting fraction is in lowest form i.e. the top and bottom do not have a common factor.