This question tests the student's ability to identify equivalent fractions through spotting a fraction which is not equivalent amongst a list of otherwise equivalent fractions. It also tests the students ability to convert mixed numbers into their equivalent improper fractions. It then does the reverse and tests their ability to convert an improper fraction into an equivalent mixed number.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "A mixed number is a number consisting of an integer and a proper fraction, i.e. a number in the form $ a \\displaystyle \\frac{b}{c}$ where $a$ is an integer and $\\displaystyle\\frac{b}{c}$ is a proper fraction: $b$ is smaller than $c$.
\nAn improper fraction is a fraction where the numerator is larger than the denominator, i.e. a number of the form $\\displaystyle\\frac{d}{e}$ where the numerator, $d$, is greater than the denominator, $e$.
\nTo convert a mixed number into an improper fraction, multiply the integer part of the mixed number, $a$, by the denominator, $c$.
\nThe numerator of the improper fraction will be equal to this added to what was already on the numerator of the proper fraction.
\nThe denominator of the proper fraction will stay the same when it converts to an improper fraction to give a final answer of
\n$\\displaystyle\\frac{({a}\\times{c})+b}{c}$.
\n\\[
{\\var{f}\\frac{\\var{g_coprime}}{\\var{h_coprime}}} = \\frac{({\\var{f}}\\times{\\var{h_coprime}})+{\\var{g_coprime}}}{{\\var{h_coprime}}}=\\simplify{{num}/{h_coprime}}\\text{.}
\\]
Use this link to find some resources which will help you revise this topic.
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", "templateType": "anything", "can_override": false}, "g_coprime": {"name": "g_coprime", "group": "Ungrouped variables", "definition": "g/gcd_gh", "description": "PART C
", "templateType": "anything", "can_override": false}, "gcd_gh": {"name": "gcd_gh", "group": "Ungrouped variables", "definition": "gcd(g,h)", "description": "PART C
", "templateType": "anything", "can_override": false}, "num": {"name": "num", "group": "Ungrouped variables", "definition": "((h_coprime*f)+g_coprime)", "description": "numerator for the improper fraction c(i)
", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "random(10 .. 24#1)", "description": "Random number between 1 and 24
", "templateType": "randrange", "can_override": false}, "h_coprime": {"name": "h_coprime", "group": "Ungrouped variables", "definition": "h/gcd_gh", "description": "PART C
", "templateType": "anything", "can_override": false}, "gcdb": {"name": "gcdb", "group": "Ungrouped variables", "definition": "gcd({num},{h_coprime})", "description": "gcd of num and h
", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "random(2 .. 5#1)", "description": "Random number between 1 and 5
", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["f", "g", "h", "gcd_gh", "g_coprime", "h_coprime", "num", "gcdb"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": "fraction {\n display: inline-block;\n vertical-align: middle;\n}\nfraction > numerator, fraction > denominator {\n float: left;\n width: 100%;\n text-align: center;\n line-height: 2.5em;\n}\nfraction > numerator {\n border-bottom: 1px solid;\n padding-bottom: 5px;\n}\nfraction > denominator {\n padding-top: 5px;\n}\nfraction input {\n line-height: 1em;\n}\n\nfraction .part {\n margin: 0;\n}\n\n.table-responsive, .fractiontable {\n display:inline-block;\n}\n.fractiontable {\n padding: 0; \n border: 0;\n}\n\n.fractiontable .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n border-bottom: 1px solid black; \n text-align: center;\n}\n\n\n.fractiontable tr {\n height: 3em;\n}\n"}, "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": "Write the mixed number as an improper fraction and reduce it down to its simplest form.
\n$\\displaystyle{\\var{f}\\frac{\\var{g_coprime}}{\\var{h_coprime}}} =$