// Numbas version: finer_feedback_settings
{"name": "Year 11 Standard Practice Paper 1", "metadata": {"description": "", "licence": "None specified"}, "duration": 5400, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", ""], "questions": [{"name": "Fraction multiplication", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}], "advice": "<h4>a)</h4>\n<p>To multiply $\\displaystyle\\frac{\\var{a_coprime}}{\\var{c_coprime}}\\times\\frac{\\var{b_coprime}}{\\var{d_coprime}}$, address the numerators and denominators separately.</p>\n<p>Multiply the numerators across both fractions.</p>\n<p style=\"text-align: center;\">$\\var{a_coprime}\\times\\var{b_coprime}=\\var{ab}$,</p>\n<p>and then multiply the denominators across both fractions.</p>\n<p style=\"text-align: center;\">$\\var{c_coprime}\\times\\var{d_coprime}=\\var{cd}$.</p>\n<p>The values of the multiplied numerators and denominators will be the numerator and denominator of the new fraction: $\\displaystyle\\frac{\\var{ab}}{\\var{cd}}$.</p>\n<p>This answer may need simplifying down, and to do this, find the greatest common divisor in both the numerator and denominator and divide by this number.</p>\n<p>The greatest common divisor of $\\var{ab}$ and $\\var{cd}$ is $\\var{gcd}$.</p>\n<p>By using $\\var{gcd}$ to cancel down the fraction, the final answer is $\\displaystyle\\simplify{{ab}/{cd}}$.</p>\n<p></p>\n<h4>b)</h4>\n<p>To multiply $\\displaystyle\\simplify{{k_coprime}/{j_coprime}}\\times\\var{f}\\frac{\\var{g_coprime}}{\\var{h_coprime}}$, we first need to change the mixed number term into an improper fraction.&nbsp;</p>\n<p>To do this, we need to multiply $(\\var{f}\\times\\var{h_coprime}=\\var{fh})$ and add it to what was already on the numerator of the fraction, $\\var{g_coprime}$.</p>\n<p style=\"text-align: center;\">$\\displaystyle\\frac{(\\var{fh}+\\var{g_coprime})}{\\var{h_coprime}}= \\displaystyle\\frac{\\var{numif}}{\\var{h_coprime}}$.</p>\n<p>Next, we multiply the numerators and denominators across both fractions separately, as done in part <strong>a)</strong>.&nbsp;</p>\n<p style=\"text-align: center;\">$\\var{k_coprime}\\times\\var{numif} = \\var{num}$,</p>\n<p style=\"text-align: center;\">$\\var{j_coprime}\\times\\var{h_coprime}=\\var{denom}$.</p>\n<p>This gives the unsimplified version of the new fraction $\\displaystyle\\frac{\\var{num}}{\\var{denom}}$.</p>\n<p>To simplify, find the greatest common divisor in both the numerator and denominator and divide by this number.&nbsp;</p>\n<p>The greatest common divisor of $\\var{num}$ and $\\var{denom}$ is $\\var{gcdb}$.</p>\n<p>By using $\\var{gcdb}$ to cancel down the fraction, the final answer is $\\displaystyle\\simplify{{num}/{denom}}$.</p>\n<p></p>\n<p></p>\n<h4>c)</h4>\n<p>To square a fraction means to multiply the fraction by itself. To do this, multiply the numerators and denominators across individually.</p>\n<p style=\"text-align: center;\">$\\displaystyle\\bigg(\\frac{\\var{l_coprime}}{\\var{m_coprime}}\\bigg)^2=\\frac{\\var{l_coprime}}{\\var{m_coprime}}\\times\\frac{\\var{l_coprime}}{\\var{m_coprime}}=\\frac{\\var{l_coprime^2}}{\\var{m_coprime^2}}.$</p>\n<p>From this, we should look if it is possible to simplify by finding the highest common divisor of $\\var{l_coprime^2}$ and $\\var{m_coprime^2}.$</p>\n<p>The greatest common divisor is $\\var{gcd_lcmc}$.</p>\n<p><span data-jme-visible=\"gcd_lcmc = 1\">Therefore, it is not possible to simplify this further, and the final answer is</span></p>\n<p><span data-jme-visible=\"gcd_lcmc &gt; 1\">By simplifying with this value, the final answer is</span></p>\n<p style=\"text-align: center;\">$\\displaystyle\\frac{\\var{l_coprime2}}{\\var{m_coprime2}}$.</p>\n<p></p>\n<h4 style=\"text-align: left;\">d)</h4>\n<p style=\"text-align: left;\">Helen was on holiday for $28$ days and spent $\\displaystyle\\frac{\\var{aa}}{7}$ of her time in Spain.&nbsp;</p>\n<p style=\"text-align: center;\">$\\displaystyle\\frac{\\var{aa}}{7}\\times\\frac{28}{1}=\\frac{\\var{bb}}{7}=\\var{cc}$ days in Spain.&nbsp;</p>\n<p style=\"text-align: left;\">Whilst in Spain, she spends $\\displaystyle\\frac{\\var{dd}}{4}$ of her time in Barcelona.</p>\n<p style=\"text-align: center;\">$\\displaystyle\\frac{\\var{dd}}{4}\\times\\frac{\\var{cc}}{1}=\\frac{\\var{ddcc}}{4}=\\var{ee}$ days in Barcelona.&nbsp;</p>\n<h4></h4>", "statement": "<p>Evaluate the following multiplications, giving each fraction in its simplest form.</p>", "variables": {"k": {"name": "k", "group": "Part b", "templateType": "anything", "description": "<p>Random number between 1 and 20</p>", "definition": "random(1..7 except j)"}, "bb": {"name": "bb", "group": "Part d", "templateType": "anything", "description": "", "definition": "28*aa"}, "cc": {"name": "cc", "group": "Part d", "templateType": "anything", "description": "", "definition": "bb/7"}, "g": {"name": "g", "group": "Part b", "templateType": "randrange", "description": "<p>Random number between 1 and 20.</p>", "definition": "random(1..7#1)"}, "cd": {"name": "cd", "group": "Part a", "templateType": "anything", "description": "<p>Variable c times variable d.</p>", "definition": "c_coprime*d_coprime"}, "a": {"name": "a", "group": "Part a", "templateType": "anything", "description": "<p>Random number from 1 to 12.</p>", "definition": "random(2..12 except c)"}, "d": {"name": "d", "group": "Part a", "templateType": "randrange", "description": "<p>Random number from 1 to 12.</p>", "definition": "random(2..12#1)"}, "l": {"name": "l", "group": "Part c", "templateType": "anything", "description": "", "definition": "random(1..12)"}, "numif": {"name": "numif", "group": "Part b", "templateType": "anything", "description": "<p>Numerator of the improper fraction converted from a mixed number.</p>", "definition": "(f*h_coprime)+g_coprime"}, "gcd_gh": {"name": "gcd_gh", "group": "Part b", "templateType": "anything", "description": "", "definition": "gcd(g,h)"}, "fh": {"name": "fh", "group": "Part b", "templateType": "anything", "description": "<p>Variable f times variable h</p>", "definition": "f*h_coprime"}, "g_coprime": {"name": "g_coprime", "group": "Part b", "templateType": "anything", "description": "", "definition": "g/gcd_gh"}, "j_coprime": {"name": "j_coprime", "group": "Part b", "templateType": "anything", "description": "", "definition": "j/gcd_kj"}, "gcd_kj": {"name": "gcd_kj", "group": "Part b", "templateType": "anything", "description": "", "definition": "gcd(k,j)"}, "f": {"name": "f", "group": "Part b", "templateType": "randrange", "description": "<p>Random number between 1 and 4 - integer part of the mixed number.</p>", "definition": "random(1..4#1)"}, "c_coprime": {"name": "c_coprime", "group": "Part a", "templateType": "anything", "description": "", "definition": "c/gcd_ac"}, "gcd": {"name": "gcd", "group": "Part a", "templateType": "anything", "description": "", "definition": "gcd(ab,cd)"}, "b": {"name": "b", "group": "Part a", "templateType": "randrange", "description": "<p>Random number from 1 to 12.</p>", "definition": "random(2..12#1)"}, "d_coprime": {"name": "d_coprime", "group": "Part a", "templateType": "anything", "description": "", "definition": "d/gcd_bd"}, "ddcc": {"name": "ddcc", "group": "Part d", "templateType": "anything", "description": "", "definition": "dd*cc"}, "gcdb": {"name": "gcdb", "group": "Part b", "templateType": "anything", "description": "", "definition": "gcd(num,denom)"}, "gcd_ac": {"name": "gcd_ac", "group": "Part a", "templateType": "anything", "description": "<p>PART A</p>", "definition": "gcd(a,c)"}, "denom": {"name": "denom", "group": "Part b", "templateType": "anything", "description": "<p>Denominator of new fraction.</p>", "definition": "j_coprime*(h_coprime/gcda)"}, "l_coprime": {"name": "l_coprime", "group": "Part c", "templateType": "anything", "description": "", "definition": "l/gcd_lm"}, "m": {"name": "m", "group": "Part c", "templateType": "anything", "description": "", "definition": "random(1..12 except l)"}, "a_coprime": {"name": "a_coprime", "group": "Part a", "templateType": "anything", "description": "", "definition": "a/gcd_ac"}, "h": {"name": "h", "group": "Part b", "templateType": "randrange", "description": "<p>Random number between 1 and 20.</p>", "definition": "random(7..10#1)"}, "num": {"name": "num", "group": "Part b", "templateType": "anything", "description": "<p>Numerator of gap 0</p>", "definition": "k_coprime*{numif/gcda}"}, "m_coprime": {"name": "m_coprime", "group": "Part c", "templateType": "anything", "description": "", "definition": "m/gcd_lm"}, "aa": {"name": "aa", "group": "Part d", "templateType": "anything", "description": "", "definition": "random(1..6)"}, "gcda": {"name": "gcda", "group": "Part b", "templateType": "anything", "description": "<p>gcd of the numerator of the improper fraction</p>", "definition": "gcd({numif},{h_coprime})"}, "h_coprime": {"name": "h_coprime", "group": "Part b", "templateType": "anything", "description": "", "definition": "h/gcd_gh"}, "ee": {"name": "ee", "group": "Part d", "templateType": "anything", "description": "", "definition": "ddcc/4"}, "c": {"name": "c", "group": "Part a", "templateType": "anything", "description": "<p>Random number from 1 to 12.</p>", "definition": "random(3,5,7,11)"}, "b_coprime": {"name": "b_coprime", "group": "Part a", "templateType": "anything", "description": "", "definition": "b/gcd_bd"}, "l_coprime2": {"name": "l_coprime2", "group": "Part c", "templateType": "anything", "description": "", "definition": "l_coprime^2/gcd_lcmc"}, "k_coprime": {"name": "k_coprime", "group": "Part b", "templateType": "anything", "description": "", "definition": "k/gcd_kj"}, "j": {"name": "j", "group": "Part b", "templateType": "anything", "description": "<p>Random number between 1 and 20</p>", "definition": "Random(3,5,7,11,13,17)"}, "dd": {"name": "dd", "group": "Part d", "templateType": "anything", "description": "", "definition": "random(1..3)"}, "gcd_lcmc": {"name": "gcd_lcmc", "group": "Part c", "templateType": "anything", "description": "", "definition": "gcd((l_coprime)^2,(m_coprime)^2)"}, "m_coprime2": {"name": "m_coprime2", "group": "Part c", "templateType": "anything", "description": "", "definition": "m_coprime^2/gcd_lcmc"}, "gcd_lm": {"name": "gcd_lm", "group": "Part c", "templateType": "anything", "description": "", "definition": "gcd(l,m)"}, "ab": {"name": "ab", "group": "Part a", "templateType": "anything", "description": "<p>Variable a times variable b</p>", "definition": "a_coprime*b_coprime"}, "gcd_bd": {"name": "gcd_bd", "group": "Part a", "templateType": "anything", "description": "", "definition": "gcd(b,d)"}, "gcd2": {"name": "gcd2", "group": "Part b", "templateType": "anything", "description": "", "definition": "gcd(num,denom)"}}, "tags": ["improper fractions", "mixed numbers", "multiplication of fractions", "multiplying fractions", "squared fraction", "taxonomy"], "ungrouped_variables": [], "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"}, "type": "question", "variable_groups": [{"variables": ["a", "b", "c", "d", "a_coprime", "b_coprime", "c_coprime", "d_coprime", "gcd_ac", "gcd_bd", "ab", "cd", "gcd"], "name": "Part a"}, {"variables": ["f", "g", "g_coprime", "h", "h_coprime", "gcd_gh", "k", "k_coprime", "j", "j_coprime", "gcd_kj", "fh", "numif", "num", "denom", "gcda", "gcdb", "gcd2"], "name": "Part b"}, {"variables": ["aa", "bb", "cc", "dd", "ddcc", "ee"], "name": "Part d"}, {"variables": ["l", "m", "gcd_lm", "l_coprime", "m_coprime", "gcd_lcmc", "l_coprime2", "m_coprime2"], "name": "Part c"}], "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"description": "<p>Several problems involving the multiplication of fractions, with increasingly difficult examples, including&nbsp;a mixed fraction and a squared fraction. The final part is a word problem.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "parts": [{"scripts": {}, "showCorrectAnswer": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "variableReplacements": [], "mustBeReducedPC": 0, "minValue": "{ab}/{gcd}", "correctAnswerFraction": false, "allowFractions": false, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "scripts": {}, "maxValue": "{ab}/{gcd}", "showCorrectAnswer": true, "type": "numberentry", "marks": 1, "showFeedbackIcon": true}, {"notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "variableReplacements": [], "mustBeReducedPC": 0, "minValue": "{cd}/{gcd}", "correctAnswerFraction": false, "allowFractions": false, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "scripts": {}, "maxValue": "{cd}/{gcd}", "showCorrectAnswer": true, "type": "numberentry", "marks": 1, "showFeedbackIcon": true}], "type": "gapfill", "prompt": "<p>$\\displaystyle\\frac{\\var{a_coprime}}{\\var{c_coprime}}\\times\\frac{\\var{b_coprime}}{\\var{d_coprime}}$ =&nbsp;<fraction> <numerator>[[0]]</numerator> <denominator>[[1]]</denominator> </fraction></p>", "marks": 0, "variableReplacements": [], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}, {"scripts": {}, "showCorrectAnswer": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "variableReplacements": [], "mustBeReducedPC": 0, "minValue": "num/gcd2", "correctAnswerFraction": false, "allowFractions": false, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "scripts": {}, "maxValue": "num/gcd2", "showCorrectAnswer": true, "type": "numberentry", "marks": 1, "showFeedbackIcon": true}, {"notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "variableReplacements": [], "mustBeReducedPC": 0, "minValue": "denom/gcd2", "correctAnswerFraction": false, "allowFractions": false, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "scripts": {}, "maxValue": "denom/gcd2", "showCorrectAnswer": true, "type": "numberentry", "marks": 1, "showFeedbackIcon": true}], "type": "gapfill", "prompt": "<p>$\\displaystyle\\simplify{{k}/{j}}\\times\\var{f}\\frac{\\var{g}}{\\var{h}}$ =&nbsp;<fraction> <numerator>[[0]]</numerator> <denominator>[[1]]</denominator> </fraction></p>", "marks": 0, "variableReplacements": [], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}, {"scripts": {}, "showCorrectAnswer": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "variableReplacements": [], "mustBeReducedPC": 0, "minValue": "l_coprime2", "correctAnswerFraction": false, "allowFractions": false, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "scripts": {}, "maxValue": "l_coprime2", "showCorrectAnswer": true, "type": "numberentry", "marks": 1, "showFeedbackIcon": true}, {"notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "variableReplacements": [], "mustBeReducedPC": 0, "minValue": "m_coprime2", "correctAnswerFraction": false, "allowFractions": false, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "scripts": {}, "maxValue": "m_coprime2", "showCorrectAnswer": true, "type": "numberentry", "marks": 1, "showFeedbackIcon": true}], "type": "gapfill", "prompt": "<p>$\\displaystyle\\bigg(\\frac{\\var{l_coprime}}{\\var{m_coprime}}\\bigg)^2= $ <fraction> <numerator>[[0]]</numerator> <denominator>[[1]]</denominator> </fraction></p>", "marks": 0, "variableReplacements": [], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}, {"scripts": {}, "showCorrectAnswer": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "variableReplacements": [], "mustBeReducedPC": 0, "minValue": "ee", "correctAnswerFraction": false, "allowFractions": false, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "scripts": {}, "maxValue": "ee", "showCorrectAnswer": true, "type": "numberentry", "marks": 1, "showFeedbackIcon": true}], "type": "gapfill", "prompt": "<p>Helen went on holiday in Europe. She spent $\\displaystyle\\frac{\\var{aa}}{7}$ of her time on holiday in Spain. Whilst in Spain, she spent $\\displaystyle\\frac{\\var{dd}}{4}$ of her time in Barcelona.&nbsp;</p>\n<p>If her holiday lasted for $28$ days, how many days was she in Barcelona?&nbsp;</p>\n<p>Helen was in Barcelona for&nbsp;[[0]] days.</p>", "marks": 0, "variableReplacements": [], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}]}, {"name": "Create an algebraic expression from a word problem, simplify, and evaluate", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Bradley Bush", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1521/"}], "tags": ["algebraic expressions", "collect terms", "create algebraic expressions", "simplify algebraic expressions", "simplifying algebraic expressions", "taxonomy"], "metadata": {"description": "<p>Given a&nbsp;description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression, and finally evaluate it&nbsp;at a given point.</p>\n<p>The word problem is about the costs of sweets in a sweet shop.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>{pname} eats a lot of sweets. You are trying to work out the cost of the sweets that {pname} ate last week.</p>\n<p>{pname} ate $\\var{a1}$ packets of lollipops, $\\var{b1}$ packets of toffee and $\\simplify{{c1}}$ packets of jelly sweets.</p>\n<p>You know that a packet of toffee costs $&pound;1$ more than a packet of lollipops, and a packet of jelly sweets costs half as much as a packet of toffees.</p>", "advice": "<h4>a)</h4>\n<p>We are told&nbsp;that the price of a packet of lollipops is represented by the letter $x$.</p>\n<p>A packet of toffee costs $&pound;1$ more than a packet of lollipops, i.e. $x+1$.</p>\n<p>A packet of jelly sweets costs half as much as a packet of toffee, so $\\frac{1}{2}(x+1)$.</p>\n<h4>b)</h4>\n<p>To find the total cost, multiply the expressions above for the cost of each kind of sweet by the number of packets eaten, and add them together.</p>\n<p>Without simplifying, we obtain:</p>\n<p>\\begin{align}<br/>\\text{Cost} &amp;= \\simplify[]{{a1}x+{b1}(x+1) + {c1}*(1/2)*(x+1)} \\\\<br/>&amp;= \\simplify[]{{a1}x+{b1}(x+1) + {c1/2}*(x+1)}<br/>\\text{.}<br/>\\end{align}</p>\n<h4>c)</h4>\n<p>The first step&nbsp;in simplifying this expression is to expand both sets of brackets:</p>\n<p>\\begin{align}<br/>\\simplify[]{ {a1}x + {b1}(x+1) + {c1/2}*(x+1)} &amp;= \\simplify[]{ {a1}x + {b1}x + {b1}*1 + {c1/2}x + {c1/2}*1} \\\\<br/>&amp;= \\simplify[] { {a1}x + {b1}x + {b1} + {c1/2}x + {c1/2} } \\text{.}<br/>\\end{align}</p>\n<p>Finally, collect&nbsp;like terms:</p>\n<p>\\begin{align}<br/>\\simplify[] { {a1}x + {b1}x + {b1} + {c1/2}x + {c1/2} } &amp;= \\simplify[]{ {a1+b1+c1/2}x + {b1+c1/2} } \\text{.}<br/>\\end{align}</p>\n<p></p>\n<h4>d)</h4>\n<p>Once we know that the price of a packet of lollipops is $&pound;2$, we can substitute this for $x$ in the equation above.</p>\n<p>\\begin{align}<br/>\\text{Cost}&amp;=\\simplify{ {a1+b1+c1/2}x+{b1+c1/2} }\\\\<br/>&amp;=\\var{a1+b1+c1/2} \\times 2+\\var{b1+c1/2} \\\\<br/>&amp;=\\var{(a1+b1+c1/2)*2+b1+c1/2} \\text{.}<br/>\\end{align}</p>\n<p>So {pname} spent $&pound;\\var{total}$ on sweets last week.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"b1": {"name": "b1", "group": "Number of packets eaten", "definition": "random(2..10 except a1)", "description": "<p>Number of packets of toffee eaten</p>", "templateType": "anything", "can_override": false}, "c1": {"name": "c1", "group": "Number of packets eaten", "definition": "random(2..5)*2", "description": "<p>Number of packets of jelly sweets eaten.</p>", "templateType": "anything", "can_override": false}, "pname": {"name": "pname", "group": "Ungrouped variables", "definition": "random('Jerry','Jessica')", "description": "", "templateType": "anything", "can_override": false}, "a1": {"name": "a1", "group": "Number of packets eaten", "definition": "random(5..10)", "description": "<p>Number of packets of lollipops eaten</p>", "templateType": "anything", "can_override": false}, "total": {"name": "total", "group": "Ungrouped variables", "definition": "(a1+b1+c1/2)*2 + b1+c1/2", "description": "<p>The total spent.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "gcd(a1,b1+c1/2)=1", "maxRuns": 100}, "ungrouped_variables": ["pname", "total"], "variable_groups": [{"name": "Number of packets eaten", "variables": ["a1", "b1", "c1"]}], "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>Let the cost of a packet of lollipops be $&pound;x$.</p>\n<p>Write an expression in terms of $x$ for the cost of each kind of sweet:</p>\n<p>Lollipops: &pound;[[0]]</p>\n<p>Toffees: &pound;[[1]]</p>\n<p>Jelly sweets: &pound;[[2]]<br/><em></em></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": "x", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"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": "x+1", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"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": "1/2(x+1)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}, {"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>Write an algebraic expression for the overall cost of the sweets {pname} ate, in terms of $x$.</p>\n<p>&pound;[[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": "({a1}+{b1}+{c1}/2)x+({b1}+{c1}/2)", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}, {"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>Now simplify your expression for the total cost.</p>\n<p>&pound;[[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": "({a1}+{b1}+{c1}/2)x+({b1}+{c1}/2)", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "$n*x + $n", "partialCredit": 0, "message": "Your answer is not fully simplified.", "nameToCompare": ""}, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}, {"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>You find out that a packet of lollipops costs $&pound;2$.</p>\n<p>Calculate {pname}'s total expenditure on sweets last week.</p>\n<p>&pound;[[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": "({a1}+{b1}+{c1}/2)2+{b1}+{c1}/2", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "notallowed": {"strings": ["(", ")"], "showStrings": true, "partialCredit": 0, "message": "<p>Don't use brackets</p>"}, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Algebra V: algebraic fractions (reasoning)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Luke Park", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/826/"}], "functions": {}, "ungrouped_variables": ["name"], "tags": [], "preamble": {"css": ".fractiontable table {\n  width: 40%; \n  padding: 0px; \n  border-width: 0px; \n  layout: fixed;\n}\n\n.fractiontable  .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n  width: 15%; \n  border-bottom: 1px solid black; \n  text-align: center;\n}\n\n.fractiontable .tdeq \n{\n  width: 5%; \n  border-bottom: 0px;\n  font-size: x-large;\n}\n\n\n.fractiontable th {\n    background-color:#aaa;\n}\n/*Fix the height of all cells EXCEPT table-headers to 40px*/\n.fractiontable td {\n    height:40px;\n}\n", "js": ""}, "advice": "<p>Algebraic fractions involve various rules and some important tips are:</p>\n<p>1.If we multiply or divide&nbsp;the top and bottom of a fraction by a&nbsp;number (not zero) we get an equivalent fraction. We say equivalent because they represent the same amount of the whole.</p>\n<p>2.When you have a fraction, say&nbsp;$\\displaystyle{\\frac{1+2a+3b}{5+x}}$, it represents the result of dividing everything on top by everything on the bottom, that is&nbsp;</p>\n<p>\\[\\frac{1+2a+3b}{5+x}=\\frac{1}{5+x}+\\frac{2a}{5+x}+\\frac{3b}{5+x}\\]</p>\n<p>3. Whenever we have such a 'fraction on a fraction' we want to rewrite the fraction to it is just one fraction. We can do this by multiplying by the denominator of the smaller/inner fraction.</p>\n<p>For more information, check out this video-&nbsp;</p>\n<p><iframe width=\"500\" height=\"375\" src=\"//www.youtube.com/embed/ofchn9z8_lU\"></iframe></p>", "rulesets": {"std": ["all"]}, "parts": [{"stepsPenalty": "0", "prompt": "<p>{Name[0][0]} has written $\\displaystyle{\\simplify{({a}x+{b})/({c}y+{d})}}$ in the equivalent form $\\displaystyle{\\simplify{({ar}x+{br})/({cr}y+{dr})}}$.</p>\n<p></p>\n<p>What has {Name[0][0]} done to the first&nbsp;fraction in order to&nbsp;get the second? {Name[0][1]} has divided the top and bottom by&nbsp;[[0]]&nbsp;.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>If we multiply or divide&nbsp;the top and bottom of a fraction by a&nbsp;number (not zero) we get an equivalent fraction. We say equivalent because they represent the same amount of the whole.</p>\n<p></p>\n<p>Recall $\\frac{3}{6}$ is equivalent to $\\frac{1}{2}$, notice we can divide the top and bottom of $\\frac{3}{6}$ by 3 to get $\\frac{1}{2}$. Similarly, if we divide the top and bottom of $\\frac{10x-50y}{20a+10}$ by $10$ we would get the equivalent fraction $\\frac{x-5y}{2a+1}$.&nbsp;</p>\n<p></p>\n<p>When simplifying fractions we try to get the fraction so there is no common factor on the top and the bottom (if there was we would divide by it). It is important that this common factor is <em>common</em> to all the terms and not just a couple, otherwise dividing by it would leave you with a fraction on a fraction.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "amult", "minValue": "amult", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "0", "prompt": "<p>{Name[1][0]} has written $\\displaystyle{\\simplify{((x+{ar})/({f}x))/({br}y+{dr})}}$&nbsp;in the equivalent form $\\displaystyle{\\simplify{(x+{ar})/({f*br}x*y+{f*dr}x)}}$.</p>\n<p></p>\n<p>What has {Name[1][0]} done to the first&nbsp;fraction in order to&nbsp;get the second? {Name[1][1]} has multiplied the top and bottom by&nbsp;[[0]]&nbsp;.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>If we multiply or divide&nbsp;the top and bottom of a fraction by a&nbsp;number (not zero) we get an equivalent fraction. We say equivalent because they represent the same amount of the whole.</p>\n<p></p>\n<p>Recall $\\frac{1}{2}$ is equivalent to $\\frac{3}{6}$, notice we can multiply the top and bottom of $\\frac{1}{2}$ by 3 to get $\\frac{3}{6}$. Similarly, we can multiply the top and bottom of $\\frac{\\frac{x-3}{2x}}{x+1}$ by $2x$ to get the equivalent fraction $\\frac{x-3}{2x^2+2x}$.&nbsp;</p>\n<p></p>\n<p>Whenever we have such a 'fraction on a fraction' we want to rewrite the fraction to it is just one fraction. We can do this by multiplying by the denominator of the smaller/inner fraction.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{f}x", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "0", "maxAnswers": 0, "displayColumns": 0, "prompt": "<p>Which of the following are equivalent to $\\displaystyle{\\simplify{({g}x+{h})/(x+{h})}}$?</p>", "matrix": [0, 0, "1"], "shuffleChoices": true, "maxMarks": 0, "variableReplacements": [], "minAnswers": 0, "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>When you have a fraction, say&nbsp;$\\displaystyle{\\frac{1+2a+3b}{5+x}}$, it represents the result of dividing everything on top by everything on the bottom, that is&nbsp;</p>\n<p></p>\n<p>\\[\\frac{1+2a+3b}{5+x}=\\frac{1}{5+x}+\\frac{2a}{5+x}+\\frac{3b}{5+x}\\]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "distractors": ["What common factor did you use?", "What common factor did you use?", ""], "showCorrectAnswer": true, "scripts": {}, "warningType": "none", "marks": 0, "choices": ["<p>$\\var{g}$</p>", "<p>$\\simplify{{g-1}x+{h}}$</p>", "<p>$\\simplify{({g}x)/(x+{h})}+\\simplify{({h})/(x+{h})}$</p>"], "type": "m_n_2", "displayType": "checkbox", "minMarks": 0}, {"stepsPenalty": "0", "maxAnswers": 0, "displayColumns": 0, "prompt": "<p>$\\displaystyle{\\simplify{({j}x+{k})/({l}y)}}$ is equal to:</p>", "matrix": [0, 0, "1"], "shuffleChoices": true, "maxMarks": 0, "variableReplacements": [], "minAnswers": 0, "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>When you have a fraction, say&nbsp;$\\displaystyle{\\frac{1+2a+3b}{5+x}}$, it represents the result of dividing everything on top by everything on the bottom, that is&nbsp;</p>\n<p></p>\n<p>\\[\\frac{1+2a+3b}{5+x}=\\frac{1}{5+x}+\\frac{2a}{5+x}+\\frac{3b}{5+x}\\]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "distractors": ["What common factor did you use?", "What common factor did you use?", ""], "showCorrectAnswer": true, "scripts": {}, "warningType": "none", "marks": 0, "choices": ["<p>$\\displaystyle{\\simplify{(x+{k})/(2y)}}$</p>", "<p>$\\displaystyle{\\simplify{{x}/(2y)+{k}}}$</p>", "<p>$\\displaystyle{\\simplify{{x}/(2y)+{k}/({l}y)}}$</p>"], "type": "m_n_2", "displayType": "checkbox", "minMarks": 0}, {"stepsPenalty": "0", "prompt": "<div class=\"fractiontable\">\n<p>Please fill in the gap to simplify the fraction on the left.</p>\n<table>\n<tbody>\n<tr>\n<td class=\"tdnum\">$x+\\var{m}$</td>\n<td class=\"tdeq\" style=\"text-align: center;\">=</td>\n<td class=\"tdnum\">[[0]]</td>\n</tr>\n<tr>\n<td class=\"tddenom\">$(x+\\var{m})(x+\\var{n})$</td>\n<td></td>\n<td class=\"tddenom\">$x+\\var{n}$</td>\n</tr>\n</tbody>\n</table>\n</div>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>These are equivalent fractions so the same number that multiplied/divided the denominator must also multiply/divide the numerator.</p>\n<p></p>\n<p>Compare the two denominators, what has happened? We have divided the first denominator by $(x+\\var{m})$ to get the second denominator. The same must be done to the numerator, but something divided by itself is $1$.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"notallowed": {"message": "", "showStrings": false, "strings": ["/"], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "1", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "0", "prompt": "<div class=\"fractiontable\">\n<p>The expression $\\displaystyle{\\frac{\\var{p}z}{\\frac{\\var{p}}{\\var{p}z}}}$ can be simplified to [[0]]&nbsp;.</p>\n</div>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>If we multiply or divide&nbsp;the top and bottom of a fraction by a&nbsp;number (not zero) we get an equivalent fraction. We say equivalent because they represent the same amount of the whole.</p>\n<p></p>\n<p>Recall $\\frac{1}{2}$ is equivalent to $\\frac{3}{6}$, notice we can multiply the top and bottom of $\\frac{1}{2}$ by 3 to get $\\frac{3}{6}$. Similarly, we can multiply the top and bottom of $\\frac{\\frac{x-3}{2x}}{x+1}$ by $2x$ to get the equivalent fraction $\\frac{x-3}{2x^2+2x}$.&nbsp;</p>\n<p></p>\n<p>Whenever we have such a 'fraction on a fraction' we want to rewrite the fraction to it is just one fraction. We can do this by multiplying by the denominator of the smaller/inner fraction.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"notallowed": {"message": "", "showStrings": false, "strings": ["/", "^-", "^(-"], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": ["z"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{p}z^2", "marks": 1, "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "0", "prompt": "<div class=\"fractiontable\">\n<p>Please fill in the gaps to simplify the fraction on the left.&nbsp;</p>\n<table>\n<tbody>\n<tr>\n<td class=\"tdnum\">$\\simplify{{q}x^2y+{r}x*y+{s}x*y^2}$</td>\n<td class=\"tdeq\" style=\"text-align: center;\">=</td>\n<td class=\"tdnum\">[[0]]</td>\n</tr>\n<tr>\n<td class=\"tddenom\">$\\var{t}xy$</td>\n<td></td>\n<td class=\"tddenom\">[[1]]</td>\n</tr>\n</tbody>\n</table>\n</div>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>By looking for common factors, we see that $\\var{common}xy$ is a factor of every term (in the numerator and the denominator), there is also no larger term that is common, we call $\\var{common}xy$ the <em>highest common factor</em>. We divide the numerator and the denominator by the highest common factor to get the simplified fraction.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"notallowed": {"message": "", "showStrings": false, "strings": ["/"], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{list[0]}x+{list[1]}+{list[2]}y", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{list[3]}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>In the following questions, fill in the gaps &nbsp;by simplifying algebraic fractions:<br/>NOTE: To write powers like- $x^2$, write x^2 and so on</p>", "variable_groups": [{"variables": ["amult", "ar", "a", "br", "b", "cr", "c", "dr", "d", "f"], "name": "a"}, {"variables": ["g", "h"], "name": "partc"}, {"variables": ["primes", "j", "k", "l"], "name": "partd"}, {"variables": ["m", "n"], "name": "parte"}, {"variables": ["p"], "name": "partf"}, {"variables": ["common", "list", "q", "r", "s", "t"], "name": "partg"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"m": {"definition": "random(1..25)", "templateType": "anything", "group": "parte", "name": "m", "description": ""}, "ar": {"definition": "random(-12..12 except 0)", "templateType": "anything", "group": "a", "name": "ar", "description": ""}, "cr": {"definition": "random(-12..12 except [0,a])", "templateType": "anything", "group": "a", "name": "cr", "description": ""}, "primes": {"definition": "shuffle([3,5,7,11,13,17])[0..2]", "templateType": "anything", "group": "partd", "name": "primes", "description": ""}, "amult": {"definition": "random([-10,-5,-3,-2,-1,2,3,5,10])", "templateType": "anything", "group": "a", "name": "amult", "description": ""}, "common": {"definition": "random(2,3,4,5,6)", "templateType": "anything", "group": "partg", "name": "common", "description": ""}, "br": {"definition": "random(-12..12 except 0)", "templateType": "anything", "group": "a", "name": "br", "description": ""}, "dr": {"definition": "random(-12..12 except [0,a,-a,c,-c])", "templateType": "anything", "group": "a", "name": "dr", "description": ""}, "d": {"definition": "dr*amult", "templateType": "anything", "group": "a", "name": "d", "description": ""}, "a": {"definition": "ar*amult", "templateType": "anything", "group": "a", "name": "a", "description": ""}, "c": {"definition": "cr*amult", "templateType": "anything", "group": "a", "name": "c", "description": ""}, "b": {"definition": "br*amult", "templateType": "anything", "group": "a", "name": "b", "description": ""}, "name": {"definition": "repeat(random([\"Ben\", \"He\"], [\"Annie\", \"She\"], [\"Matt\", \"He\"], [\"David\", \"He\"], [\"Steve\", \"He\"], [\"David\", \"He\"], [\"Scott\", \"He\"], [\"Fran\", \"She\"], [\"Jenny\", \"She\"], [\"Lyn\", \"She\"], [\"Judy-anne\", \"She\"], [\"Courtney\", \"She\"]),2)", "templateType": "anything", "group": "Ungrouped variables", "name": "name", "description": ""}, "g": {"definition": "random(2..15)", "templateType": "anything", "group": "partc", "name": "g", "description": ""}, "f": {"definition": "random(2..12)", "templateType": "anything", "group": "a", "name": "f", "description": ""}, "h": {"definition": "random(-12..12 except [0,-g,g])", "templateType": "anything", "group": "partc", "name": "h", "description": ""}, "k": {"definition": "primes[1]", "templateType": "anything", "group": "partd", "name": "k", "description": ""}, "j": {"definition": "primes[0]", "templateType": "anything", "group": "partd", "name": "j", "description": ""}, "list": {"definition": "shuffle([2,3,5,7,11,6,9,4])[0..4]", "templateType": "anything", "group": "partg", "name": "list", "description": ""}, "l": {"definition": "2*j", "templateType": "anything", "group": "partd", "name": "l", "description": ""}, "n": {"definition": "random(1..25)", "templateType": "anything", "group": "parte", "name": "n", "description": ""}, "q": {"definition": "list[0]*common", "templateType": "anything", "group": "partg", "name": "q", "description": ""}, "p": {"definition": "random(2..12)", "templateType": "anything", "group": "partf", "name": "p", "description": ""}, "s": {"definition": "list[2]*common", "templateType": "anything", "group": "partg", "name": "s", "description": ""}, "r": {"definition": "list[1]*common", "templateType": "anything", "group": "partg", "name": "r", "description": ""}, "t": {"definition": "list[3]*common", "templateType": "anything", "group": "partg", "name": "t", "description": ""}}, "metadata": {"description": "<p>A detailed look at how algebraic fractions can be manipulated and simplified.</p>\n<p></p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Algebra V: algebraic fractions (operations: $+,-,\\times,\\div$)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Luke Park", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/826/"}], "functions": {}, "ungrouped_variables": [], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>Learn from your mistakes and have another attempt by clicking on 'Try another question like this one' until you get full marks.</p>", "rulesets": {}, "parts": [{"stepsPenalty": "0", "prompt": "<p>$\\displaystyle\\frac{\\var{a}x}{\\var{b}}+\\frac{x+\\var{c}}{\\var{b}}=$&nbsp;[[0]]</p>\n<p>$\\displaystyle\\frac{\\var{d}}{\\var{c}y}-\\frac{\\var{a}}{\\var{c}y}=$&nbsp;[[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p><em>Add/ the numerators, leave the denominators&nbsp;the same</em> as these fractions have a common denominator.</p>\n<p></p>\n<p>Let's say you need to evaluate $\\frac{2}{3}+\\frac{5}{3}$, in words this is 'two thirds plus five thirds', so how many thirds are there in total? Seven&nbsp;thirds!</p>\n<p style=\"text-align: left;\">So we have</p>\n<p style=\"text-align: center;\">\\[\\frac{2}{3}+\\frac{5}{3}=\\frac{2+5}{3}=\\frac{7}{3}\\]</p>\n<p>The same logic is used for subtraction. Suppose you had seven&nbsp;fourths and someone borrowed three fourths, then you are left with&nbsp;four&nbsp;fourths.&nbsp;</p>\n<p>That is</p>\n<p style=\"text-align: center;\">\\[\\frac{7}{4}-\\frac{3}{4}=\\frac{7-3}{4}=\\frac{4}{4}=1\\]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "simplifyFractions", "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? / ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $m/n$.');\n}"}}, "answer": "({a+1}x+{c})/{b}", "marks": 1, "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": ["y"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "simplifyFractions", "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? / ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $m/n$.');\n}"}}, "answer": "{d-a}/({c}y)", "marks": 1, "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "0", "prompt": "<p>$\\displaystyle\\simplify{(a+{f})/{g}+({h}a+1)/{j}}=$&nbsp;[[0]]</p>\n<p>$\\displaystyle\\simplify{(b+{h})/{f}-(b+{j})/{g}}=$&nbsp;[[1]]</p>\n<p>$\\displaystyle \\frac{\\var{a}}{\\var{d}r}+\\var{f}r=$&nbsp;[[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p><em>Rewrite the fractions so they have a common denominator by scaling up. Then perform the addition or subtraction as required.</em></p>\n<p>If your question was $\\frac{5}{4}+\\frac{3}{8}$ we could rewrite the first fraction as $\\frac{10}{8}$ (by multiplying the top and bottom by 2) and then both fractions would have a denominator of 8. At this point, we can perform the addition. Our working might&nbsp;look like this:</p>\n<p style=\"text-align: center;\">\\[\\frac{5}{4}+\\frac{3}{8}=\\frac{5\\times 2}{4\\times 2}+\\frac{3}{8}=\\frac{10}{8}+\\frac{3}{8}=\\frac{13}{8}\\]</p>\n<p style=\"text-align: left;\"></p>\n<p style=\"text-align: left;\">Often we need to rewrite both fractions to get a common denominator, for instance, $\\frac{5}{4}-\\frac{2}{3}$. We could multiply the first fraction by 3 on the top and bottom, so that it's denominator was 12, and then multiply the second fraction by 4 on the top and bottom&nbsp;so that it also had a denominator of 12. Then we could perform the subtraction. Our working might look like this:</p>\n<p style=\"text-align: center;\">\\[\\frac{5}{4}-\\frac{2}{3}=\\frac{5\\times 3}{4\\times 3}-\\frac{2\\times 4}{3\\times 4}=\\frac{15}{12}-\\frac{8}{12}=\\frac{7}{12}\\]</p>\n<p style=\"text-align: left;\"></p>\n<p>Also, recall that whole numbers are just fractions with a denominator of 1, for example $3=\\frac{3}{1}$.</p>\n<p style=\"text-align: left;\"></p>\n<p style=\"text-align: left;\">In general, the best denominator is the lowest common multiple (LCM) of the two denominators.&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["a"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "simplifyFractions", "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? / ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $m/n$.');\n}"}}, "answer": "({j+g*h}a+{f*j+g})/{g*j}", "marks": "1", "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": ["b"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "simplifyFractions", "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? / ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $m/n$.');\n}"}}, "answer": "({g-f}b+{g*h-f*j})/{f*g}", "marks": "1", "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": ["r"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "simplifyFractions", "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? / ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $m/n$.');\n}"}}, "answer": "({a}+{f*d}r^2)/({d}r)", "marks": "1", "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "0", "prompt": "<p>$\\displaystyle\\frac{m+1}{n+1}\\times \\frac{y}{x}=$&nbsp;[[0]]</p>\n<p>$\\displaystyle -\\frac{\\var{f}+w}{\\var{j}}\\times \\var{d}=$&nbsp;[[1]]</p>\n<p></p>\n<p></p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p><em>Multiply the numerators and the denominators.</em></p>\n<p>For example&nbsp;</p>\n<p style=\"text-align: center;\">\\[\\frac{4}{5}\\times \\frac{2}{3}=\\frac{4\\times 2}{5 \\times 3}=\\frac{8}{15}\\]</p>\n<p style=\"text-align: center;\"></p>\n<p style=\"text-align: left;\">Also recall that whole numbers are just fractions with a denominator of 1, for example $7=\\frac{7}{1}$.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["m", "n", "x", "y"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "simplifyFractions", "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? / ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $m/n$.');\n}"}}, "answer": "((m+1)*y)/((n+1)*x)", "marks": 1, "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": ["w"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "simplifyFractions", "scripts": {}, "answer": "-({d*f}+{d}w)/{j}", "marks": 1, "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "0", "prompt": "<p>$\\displaystyle{\\simplify{({f}+{a}x)^2/{h}}}\\div \\simplify{(({f}+{a}x){g})/({j}x)}=$&nbsp;[[0]]</p>\n<p>$\\displaystyle \\frac{\\var{b}q}{\\var{c}q}\\div (\\var{d}+t)=$&nbsp;[[1]]</p>\n<p>$\\displaystyle \\var{j}z\\div \\left(\\frac{\\var{-d}(z+1)^2}{\\var{f}z}\\right)=$&nbsp;[[2]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p><em>Flip the second fraction and then multiply.</em></p>\n<p></p>\n<p>Flipping a fraction is also known as taking the reciprocal of the fraction (or inverting a fraction). Note that a whole number is also a fraction with a denominator of 1, for example, $6=\\frac{6}{1}$.</p>\n<p>How do you find half of a number? You could 'divide it by 2', or you could 'multiply by $\\frac{1}{2}$. Notice that $\\frac{1}{2}$ is the reciprocal of 2. When we divide by a number this is actually the same as multiplying by its reciprocal.</p>\n<p></p>\n<hr/>\n<p></p>\n<p>Suppose you need to evaluate $\\frac{3}{7}\\div\\frac{5}{4}$. Recall this is the same as asking 'how many $\\frac{5}{4}$s are in $\\frac{3}{7}$?', but that doesn't seem to be very helpful here! What is helpful is realising that dividing by $\\frac{5}{4}$ is the same as multiplying by $\\frac{4}{5}$. Our working could&nbsp;look like this</p>\n<p>\\[\\frac{3}{7}\\div\\frac{5}{4}=\\frac{3}{7}\\times\\frac{4}{5}=\\frac{3\\times 4}{7\\times 5}=\\frac{12}{35}\\]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "simplifyFractions", "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? / ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $m/n$.');\n}"}}, "answer": "({a*j}x^2+{j*f}x)/{g*h}", "marks": "1", "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "simplifyFractions", "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? / ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $m/n$.');\n}"}}, "answer": "{b}/({c}({d}+t))", "marks": "1", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "simplifyFractions", "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? / ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $m/n$.');\n}"}}, "answer": "({j*f}z^2)/({-d}(z+1)^2)", "marks": "1", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": "0", "prompt": "<p>$\\displaystyle \\frac{\\frac{\\var{b}a+b}{c+d}}{\\frac{ \\var{b}a}{d}}=$&nbsp;[[0]]</p>\n<p></p>\n<p>$\\displaystyle \\frac{\\frac{w+\\var{f}}{\\var{g}w}}{w+\\var{f}}=$&nbsp;[[1]]</p>\n<p></p>\n<p>$\\displaystyle \\frac{\\var{j}r}{\\frac{\\var{h}r}{\\var{c}r}}=$&nbsp;[[2]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p><em>The fraction bar means division.</em></p>\n<p>The fraction $\\frac{2}{3}$ means 2 divided by 3. So these questions are just division questions! It is important to note which fraction bar is big and which are small, so you know the order of the divisions. &nbsp;</p>\n<p></p>\n<p>Here are some examples:</p>\n<p>\\[\\frac{7}{\\frac{5}{6}}=7\\div\\frac{5}{6} =7\\times\\frac{6}{5}=\\frac{42}{5}\\]</p>\n<p>\\[\\frac{\\frac{7}{5}}{6}=\\frac{7}{5}\\div 6=\\frac{7}{5}\\times \\frac{1}{6}=\\frac{7}{30}\\]</p>\n<p>\\[\\frac{\\frac{9}{11}}{\\frac{5}{3}}=\\frac{9}{11}\\div\\frac{5}{3}=\\frac{9}{11}\\times \\frac{3}{5}=\\frac{27}{55}\\]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["a", "b", "c", "d"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "simplifyFractions", "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? / ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $m/n$.');\n}"}}, "answer": "(d({b}a+b))/({b}a(c+d))", "marks": "1", "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": ["w"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "simplifyFractions", "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? / ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $m/n$.');\n}"}}, "answer": "1/({g}w)", "marks": "1", "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "expectedvariablenames": ["r"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "simplifyFractions", "scripts": {"mark": {"order": "after", "script": "// Parse the student's answer as a syntax tree\nvar studentTree = Numbas.jme.compile(this.studentAnswer,Numbas.jme.builtinScope);\n\n// Create the pattern to match against \n// We just want to check that the student has written \"something to the power of something\"\nvar rule = Numbas.jme.compile('?? / ??');\n\n// Check the student's answer matches the pattern. \nvar m = Numbas.jme.display.matchTree(rule,studentTree,true);\n\n// If not, take away marks\nif(!m) {\n  this.multCredit(0,'Your answer is not in the form $m/n$.');\n}"}}, "answer": "{j*c}r/{h}", "marks": "1", "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Evaluate the following and write your answer as a single fraction. Use &nbsp;/ to signify a fraction or division, for example $\\frac{2a-1}{x+3}$ is written (2a-1)/(x+3). 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