// Numbas version: finer_feedback_settings
{"name": "Merryn's copy of Division of fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "<p>Several problems involving dividing fractions, with increasingly difficult examples, including mixed numbers and complex fractions.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "rulesets": {}, "type": "question", "ungrouped_variables": [], "extensions": [], "advice": "<h4 style=\"text-align: left;\">a)</h4>\n<p>When faced with dividing fractions, it much easier to switch one of the fractions around and multiply them together instead of divide them.</p>\n<p style=\"text-align: center;\">\\[ \\left( \\frac{\\var{f_coprime}}{\\var{g_coprime}}\\div\\frac{\\var{h_coprime}}{\\var{j_coprime}} \\right) \\equiv \\left( \\frac{\\var{f_coprime}}{\\var{g_coprime}}\\times\\frac{\\var{j_coprime}}{\\var{h_coprime}} \\right) = \\frac{\\var{fj}}{\\var{gh}} \\]</p>\n<p>Then, simplify by finding the highest common divisor in the numerator and denominator which in this case is $\\var{gcd1}$.&nbsp;</p>\n<p>This gives a final answer of $\\displaystyle\\simplify{{fj}/{gh}}$.</p>\n<p></p>\n<h4 style=\"text-align: left;\">b)</h4>\n<p style=\"text-align: center;\">\\[ \\frac{\\var{f1_coprime}}{\\var{g1_coprime}}\\div\\frac{\\var{h1_coprime}}{\\var{j1_coprime}} \\equiv \\left( \\frac{\\var{f1_coprime}}{\\var{g1_coprime}}\\times\\frac{\\var{j1_coprime}}{\\var{h1_coprime}} \\right)=\\frac{\\var{f1j1}}{\\var{g1h1}} \\]</p>\n<p>Then, simplify by finding the highest common divisor in the numerator and denominator which in this case is $\\var{gcd2}$.</p>\n<p>This gives a final answer of $\\displaystyle\\simplify{{f1j1}/{g1h1}}$.</p>\n<p></p>\n<h4>c)</h4>\n<p style=\"text-align: center;\">\\[ {\\var{f3}\\frac{\\var{g3_coprime}}{\\var{h3_coprime}}}\\div{\\var{f4}\\frac{\\var{g4_coprime}}{\\var{h4_coprime}}} \\]</p>\n<p>The first thing to do is to change the mixed numbers into improper fractions.</p>\n<p>An improper fraction is a fraction where the numerator is greater than the denominator. To change a mixed fraction to an improper fraction, multiply the integer part of the mixed number by the denominator, and add it to the existing numerator to make the new numerator of the improper fraction. The denominator will stay the same.&nbsp;</p>\n<p style=\"text-align: center;\">\\[ {\\var{f3}\\frac{\\var{g3_coprime}}{\\var{h3_coprime}}}\\equiv\\frac{(\\var{f3}\\times\\var{h3_coprime})+\\var{g3_coprime}}{\\var{h3_coprime}}=\\frac{\\var{f3h3}+\\var{g3_coprime}}{\\var{h3_coprime}}=\\frac{\\var{f3h3+g3_coprime}}{\\var{h3_coprime}} \\]</p>\n<p style=\"text-align: center;\">\\[ {\\var{f4}\\frac{\\var{g4_coprime}}{\\var{h4_coprime}}}\\equiv\\frac{(\\var{f4}\\times\\var{h4_coprime})+\\var{g4_coprime}}{\\var{h4_coprime}}=\\frac{\\var{f4h4}+\\var{g4_coprime}}{\\var{h4_coprime}}=\\frac{\\var{f4h4+g4_coprime}}{\\var{h4_coprime}} \\]</p>\n<p>We now have our mixed numbers as improper fractions.</p>\n<p style=\"text-align: center;\">\\[ \\frac{\\var{f3h3+g3_coprime}}{\\var{h3_coprime}}\\div\\frac{\\var{f4h4+g4_coprime}}{\\var{h4_coprime}} \\]</p>\n<p>Now, use the same method as in parts <strong>a)</strong> and <strong>b)</strong> to divide by switching around one fraction and changing the division symbol to multiplication.</p>\n<p style=\"text-align: center;\">\\[ \\frac{\\var{f3h3+g3_coprime}}{\\var{h3_coprime}}\\div\\frac{\\var{f4h4+g4_coprime}}{\\var{h4_coprime}}\\equiv\\frac{\\var{f3h3+g3_coprime}}{\\var{h3_coprime}}\\times\\frac{\\var{h4_coprime}}{\\var{f4h4+g4_coprime}}=\\frac{\\var{num}}{\\var{denom}} \\]</p>\n<p>Finally, the last thing to do is to simplify your answer down by finding the highest common divisor in the numerator and denominator, which in this case is $\\var{gcd3}$.</p>\n<p>By doing this, you will get a final answer of</p>\n<p style=\"text-align: center;\">\\[ \\simplify{{num}/{denom}} \\]</p>\n<h4>d)</h4>\n<p style=\"text-align: center;\">\\[ \\frac{\\var{a}}{(\\simplify[all,!collectNumbers]{{b}-{c}/{d}})} \\]</p>\n<p style=\"text-align: left;\">Consider the denominator first, as following the rules of BODMAS, you should address brackets first.</p>\n<p style=\"text-align: left;\">You need to get a common denominator for both terms on the denominator, like this:</p>\n<p style=\"text-align: center;\">\\[ \\var{b}\\times\\frac{\\var{d}}{\\var{d}} = \\frac{\\var{bd}}{\\var{d}} \\]</p>\n<p style=\"text-align: left;\">This now allows you to complete the addition or subtraction as both terms have a common denominator.&nbsp;</p>\n<p style=\"text-align: center;\">\\[ {\\simplify[all,!collectNumbers]{{bd}/{d}-{c}/{d}}} = \\frac{\\var{bd_c}}{\\var{d}} \\]</p>\n<p style=\"text-align: left;\">This means that the expression is now:</p>\n<p style=\"text-align: center;\">\\[ \\frac{\\var{a}}{\\frac{\\var{bd_c}}{\\var{d}}} \\]</p>\n<p style=\"text-align: left;\">Dealing with this requires a bit of manipulation. You have to change&nbsp;the divisor of the denominator to be a mulitplier of the numerator. The denominator, ${\\var{bd_c}}$ was being divided by ${\\var{d}}$ but by flipping it around, the numerator, ${\\var{a}}$ will be mulitplied by&nbsp;${\\var{d}}$. The value of the expression remains the same.</p>\n<p style=\"text-align: center;\">\\[ \\frac{\\var{a}}{\\frac{\\var{bd_c}}{\\var{d}}}\\equiv \\frac{(\\var{a})\\times(\\var{d})}{\\var{bd_c}}= \\frac{\\var{ad}}{\\var{bd_c}} \\]</p>\n<p style=\"text-align: left;\">From this, you can try to cancel the expression down by finding the highest common factor of the numerator and denominator, to give a final answer of</p>\n<p style=\"text-align: center;\">\\[ \\simplify{{ad}/{bd_c}} \\]</p>", "variable_groups": [{"name": "part d", "variables": ["a", "b", "c", "d", "bd", "ad", "gcd", "ad_gcd", "bcd_gcd", "bd_c"]}, {"name": "part a", "variables": ["f", "g", "f_coprime", "g_coprime", "h", "j", "h_coprime", "j_coprime", "fj", "gh", "gcd1"]}, {"name": "part b", "variables": ["f1", "g1", "f1_coprime", "g1_coprime", "h1", "j1", "h1_coprime", "j1_coprime", "f1j1", "g1h1", "gcd2"]}, {"name": "part c", "variables": ["f3", "g3", "h3", "g3_coprime", "h3_coprime", "f4", "g4", "h4", "g4_coprime", "h4_coprime", "f3h3", "f4h4", "num", "denom", "gcd3"]}], "statement": "<p>Evaluate the following sums&nbsp;involving division of fractions. Simplify your answers where possible.&nbsp;</p>", "name": "Merryn's copy of Division of fractions", "parts": [{"scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showCorrectAnswer": true, "prompt": "<p>$\\displaystyle\\frac{\\var{f_coprime}}{\\var{g_coprime}}\\div\\frac{\\var{h_coprime}}{\\var{j_coprime}}=$&nbsp;<fraction> <numerator>[[0]]</numerator> <denominator>[[1]]</denominator> </fraction></p>", "variableReplacements": [], "showFeedbackIcon": true, "marks": 0, "gaps": [{"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "showFeedbackIcon": true, "marks": 1, "minValue": "fj/gcd1", "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "fj/gcd1", "mustBeReduced": false, "allowFractions": false, "variableReplacements": [], "correctAnswerStyle": "plain", "showCorrectAnswer": true}, {"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "showFeedbackIcon": true, "marks": 1, "minValue": "gh/gcd1", "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "gh/gcd1", "mustBeReduced": false, "allowFractions": false, "variableReplacements": [], "correctAnswerStyle": "plain", "showCorrectAnswer": true}]}, {"scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showCorrectAnswer": true, "prompt": "<p>$\\displaystyle\\frac{\\var{f1_coprime}}{\\var{g1_coprime}}\\div\\frac{\\var{h1_coprime}}{\\var{j1_coprime}}=$&nbsp;<fraction> <numerator>[[0]]</numerator> <denominator>[[1]]</denominator> </fraction></p>", "variableReplacements": [], "showFeedbackIcon": true, "marks": 0, "gaps": [{"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "showFeedbackIcon": true, "marks": 1, "minValue": "f1j1/gcd2", "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "f1j1/gcd2", "mustBeReduced": false, "allowFractions": false, "variableReplacements": [], "correctAnswerStyle": "plain", "showCorrectAnswer": true}, {"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "showFeedbackIcon": true, "marks": 1, "minValue": "g1h1/gcd2", "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "g1h1/gcd2", "mustBeReduced": false, "allowFractions": false, "variableReplacements": [], "correctAnswerStyle": "plain", "showCorrectAnswer": true}]}, {"scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showCorrectAnswer": true, "prompt": "<p>$\\displaystyle{\\var{f3}\\frac{\\var{g3_coprime}}{\\var{h3_coprime}}}\\div{\\var{f4}\\frac{\\var{g4_coprime}}{\\var{h4_coprime}}}=$&nbsp;<fraction> <numerator>[[0]]</numerator> <denominator>[[1]]</denominator> </fraction></p>", "variableReplacements": [], "showFeedbackIcon": true, "marks": 0, "gaps": [{"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "showFeedbackIcon": true, "marks": 1, "minValue": "num/gcd3", "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "num/gcd3", "mustBeReduced": false, "allowFractions": false, "variableReplacements": [], "correctAnswerStyle": "plain", "showCorrectAnswer": true}, {"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "showFeedbackIcon": true, "marks": 1, "minValue": "denom/gcd3", "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "denom/gcd3", "mustBeReduced": false, "allowFractions": false, "variableReplacements": [], "correctAnswerStyle": "plain", "showCorrectAnswer": true}]}, {"scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showCorrectAnswer": true, "prompt": "<p>$\\displaystyle\\frac{\\var{a}}{(\\simplify[all,!collectNumbers]{{b}-{c}/{d}})} =$&nbsp;<fraction> <numerator>[[0]]</numerator> <denominator>[[1]]</denominator> </fraction></p>", "variableReplacements": [], "showFeedbackIcon": true, "marks": 0, "gaps": [{"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "showFeedbackIcon": true, "marks": 1, "minValue": "ad_gcd", "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "ad_gcd", "mustBeReduced": false, "allowFractions": false, "variableReplacements": [], "correctAnswerStyle": "plain", "showCorrectAnswer": true}, {"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "showFeedbackIcon": true, "marks": 1, "minValue": "bcd_gcd", "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "bcd_gcd", "mustBeReduced": false, "allowFractions": false, "variableReplacements": [], "correctAnswerStyle": "plain", "showCorrectAnswer": true}]}], "tags": ["dividing fractions", "division of fractions", "fractions", "Fractions", "mixed numbers", "taxonomy"], "preamble": {"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", "js": ""}, "functions": {}, "variables": {"f4h4": {"description": "<p>variable f4 times h4.</p>\n<p>Used in part c)</p>", "group": "part c", "definition": "f4*h4_coprime", "name": "f4h4", "templateType": "anything"}, "g4_coprime": {"description": "<p>PART C</p>", "group": "part c", "definition": "g4/gcd(g4,h4)", "name": "g4_coprime", "templateType": "anything"}, "h4": {"description": "<p>Random number but not the same number as variable g4.</p>\n<p>Used in part c.</p>", "group": "part c", "definition": "random(5..8 except g4)", "name": "h4", "templateType": "anything"}, "g": {"description": "<p>Random number between 2 and 10 and not the same number as variable f.</p>\n<p>Used in part a).</p>", "group": "part a", "definition": "random(f..12 except f) ", "name": "g", "templateType": "anything"}, "a": {"description": "<p>Random number between 1 and 20</p>\n<p>Used by part d)</p>", "group": "part d", "definition": "random(1..10#1)", "name": "a", "templateType": "randrange"}, "bd_c": {"description": "<p>Unsimplified denominator for part d).</p>", "group": "part d", "definition": "(bd-c)", "name": "bd_c", "templateType": "anything"}, "h3_coprime": {"description": "<p>PART C</p>", "group": "part c", "definition": "h3/gcd(g3,h3)", "name": "h3_coprime", "templateType": "anything"}, "f_coprime": {"description": "<p>PART A</p>", "group": "part a", "definition": "f/gcd(f,g)", "name": "f_coprime", "templateType": "anything"}, "g_coprime": {"description": "<p>PART A</p>", "group": "part a", "definition": "g/gcd(f,g)", "name": "g_coprime", "templateType": "anything"}, "j1_coprime": {"description": "<p>PART B</p>", "group": "part b", "definition": "j1/gcd(h1,j1)", "name": "j1_coprime", "templateType": "anything"}, "gcd2": {"description": "<p>greatest common divisor of variables f1j1 and g1h1.</p>\n<p>Used in part b).</p>", "group": "part b", "definition": "gcd(f1j1,g1h1)", "name": "gcd2", "templateType": "anything"}, "c": {"description": "<p>Random prime number between -10 and 10.</p>\n<p>Used by part d).</p>", "group": "part d", "definition": "random([-7,-5,-3,-2,-1,1,2,3,5,7] except d)", "name": "c", "templateType": "anything"}, "ad_gcd": {"description": "<p>Correct answer for the numerator in part d)</p>", "group": "part d", "definition": "ad/gcd", "name": "ad_gcd", "templateType": "anything"}, "g1_coprime": {"description": "<p>PART B</p>", "group": "part b", "definition": "g1/gcd(f1,g1)", "name": "g1_coprime", "templateType": "anything"}, "h1_coprime": {"description": "<p>PART B</p>", "group": "part b", "definition": "h1/gcd(h1,j1)", "name": "h1_coprime", "templateType": "anything"}, "gcd3": {"description": "<p>greatest common denominator for part c.&nbsp;</p>", "group": "part c", "definition": "gcd(num,denom)", "name": "gcd3", "templateType": "anything"}, "bd": {"description": "<p>Variable b times variable d.</p>\n<p>Used in part d)</p>", "group": "part d", "definition": "b*d", "name": "bd", "templateType": "anything"}, "j1": {"description": "<p>Random number between 2 and 20 and not the same value as variable h1.</p>\n<p>Used in part b).</p>", "group": "part b", "definition": "random(h1..11 except h1)", "name": "j1", "templateType": "anything"}, "g1h1": {"description": "<p>variable g1 times h1.&nbsp;</p>\n<p>Used in part b).</p>", "group": "part b", "definition": "g1_coprime*h1_coprime", "name": "g1h1", "templateType": "anything"}, "f": {"description": "<p>Random number between 2 and 10.</p>\n<p>Used in part a).</p>", "group": "part a", "definition": "random(2..10)", "name": "f", "templateType": "anything"}, "b": {"description": "<p>Random number between 1 and 10.</p>\n<p>Used by part d)</p>", "group": "part d", "definition": "random(1..10#1)", "name": "b", "templateType": "randrange"}, "bcd_gcd": {"description": "<p>Correct answer for the denominator in part d).</p>", "group": "part d", "definition": "{bd_c}/gcd", "name": "bcd_gcd", "templateType": "anything"}, "f4": {"description": "<p>Random number.</p>\n<p>Used in part c).</p>", "group": "part c", "definition": "random(1..3)", "name": "f4", "templateType": "anything"}, "f1": {"description": "<p>Random number between 2 and 20.</p>\n<p>Used in part b)</p>", "group": "part b", "definition": "random(2..10)", "name": "f1", "templateType": "anything"}, "d": {"description": "<p>Random prime number between 10 and 20.</p>\n<p>Used in part d).</p>", "group": "part d", "definition": "random(7,11,13,17)", "name": "d", "templateType": "anything"}, "g3": {"description": "<p>Random number.</p>\n<p>Used in part c).</p>", "group": "part c", "definition": "random(1..3)", "name": "g3", "templateType": "anything"}, "f3h3": {"description": "<p>variable f3 times h3.</p>", "group": "part c", "definition": "f3*h3_coprime", "name": "f3h3", "templateType": "anything"}, "h": {"description": "<p>Random number from 2 to 10.</p>\n<p>Used in part a).</p>", "group": "part a", "definition": "random(2..10)", "name": "h", "templateType": "anything"}, "gh": {"description": "<p>variable g times variable h.</p>\n<p>Used in part a).</p>", "group": "part a", "definition": "g_coprime*h_coprime", "name": "gh", "templateType": "anything"}, "j_coprime": {"description": "<p>PART A</p>", "group": "part a", "definition": "j/gcd(h,j)", "name": "j_coprime", "templateType": "anything"}, "denom": {"description": "<p>Unsimplified denominator of part c.</p>", "group": "part c", "definition": "h3_coprime*(f4h4+g4_coprime)", "name": "denom", "templateType": "anything"}, "j": {"description": "<p>Random number between 2 and 10 and not the same value as h.</p>\n<p>Used in part a).</p>", "group": "part a", "definition": "random(h..12 except h)", "name": "j", "templateType": "anything"}, "f1j1": {"description": "<p>variable f1 times j1.</p>\n<p>Used in part b).</p>", "group": "part b", "definition": "f1_coprime*j1_coprime", "name": "f1j1", "templateType": "anything"}, "h4_coprime": {"description": "<p>PART C</p>", "group": "part c", "definition": "h4/gcd(g4,h4)", "name": "h4_coprime", "templateType": "anything"}, "g1": {"description": "<p>Random number between 2 and 30 and not the same value as variable f1.</p>\n<p>Used in part b).</p>", "group": "part b", "definition": "random(f1..11 except f1) ", "name": "g1", "templateType": "anything"}, "fj": {"description": "<p>variable f times variable j.</p>\n<p>Used in part a).</p>", "group": "part a", "definition": "f_coprime*j_coprime", "name": "fj", "templateType": "anything"}, "gcd": {"description": "<p>Greatest common divisor of ad and bd_c.&nbsp;</p>\n<p>Used in part d).&nbsp;</p>", "group": "part d", "definition": "gcd(ad,bd_c)", "name": "gcd", "templateType": "anything"}, "f3": {"description": "<p>Random number between 2 and 6.</p>\n<p>Used in part c).</p>", "group": "part c", "definition": "random(1..3#1)", "name": "f3", "templateType": "randrange"}, "f1_coprime": {"description": "<p>PART B</p>", "group": "part b", "definition": "f1/gcd(f1,g1)", "name": "f1_coprime", "templateType": "anything"}, "h3": {"description": "<p>Random number and not the same value as variable g3.&nbsp;</p>\n<p>Used in part c).</p>", "group": "part c", "definition": "random(5..8)", "name": "h3", "templateType": "anything"}, "gcd1": {"description": "<p>greatest common divisor of variable fj and gh.</p>\n<p>Used in part a).</p>", "group": "part a", "definition": "gcd(fj,gh)", "name": "gcd1", "templateType": "anything"}, "g3_coprime": {"description": "<p>PART C</p>", "group": "part c", "definition": "g3/gcd(g3,h3)", "name": "g3_coprime", "templateType": "anything"}, "h_coprime": {"description": "<p>PART A</p>", "group": "part a", "definition": "h/gcd(h,j)", "name": "h_coprime", "templateType": "anything"}, "g4": {"description": "<p>Random number.</p>\n<p>Used in part c).</p>", "group": "part c", "definition": "random(1..5)", "name": "g4", "templateType": "anything"}, "h1": {"description": "<p>Random number between 2 and 20.&nbsp;</p>\n<p>Used in part b).</p>", "group": "part b", "definition": "random(2..10)", "name": "h1", "templateType": "anything"}, "num": {"description": "<p>numerator of the improper fraction in part c. Unsimplified.&nbsp;</p>", "group": "part c", "definition": "h4_coprime*(f3h3+g3_coprime)", "name": "num", "templateType": "anything"}, "ad": {"description": "<p>Variable a times variable d.</p>\n<p>Used in part d).</p>", "group": "part d", "definition": "a*d", "name": "ad", "templateType": "anything"}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "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/"}, {"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "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/"}, {"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}