// Numbas version: finer_feedback_settings
{"name": "Numerical fractions 4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "name": "Numerical fractions 4", "tags": ["Fractions", "Lowest terms", "fractions"], "advice": "\n  <p>Perform the various operations required in the order dictated by BIDMAS.</p>\n  <p>For addition and subtraction, write fractions so that they have a common denominator and then perform addition or subtraction on the numerators. One method of doing this is 'cross-multiplication'. The rules are :</p>\n  <p>\\[\\simplify{a/b+ c/d=(a*d+b*c)/(b*d)}.\\]<br/>\\[\\simplify{a/b- c/d=(a*d-b*c)/(b*d)}.\\]</p>\n  <p>For multiplication and division the rules are simpler:</p>\n  <p>\\[\\simplify{(a/b)} * \\simplify{(c/d)=(a*c)/(b*d)}.\\]<br/>\\[\\simplify{(a/b)} / \\simplify{(c/d)}=\\simplify{(a*d)/(b*c)}.\\]</p>\n  <p>Having applied these rules, it will be necessary to reduce the resulting fractions to lowest terms.</p>\n  ", "rulesets": {}, "parts": [{"prompt": "\n      <p>$\\dfrac{\\var{a2}}{\\var{b2}} + \\dfrac{\\var{c2}}{\\var{d2}} + \\dfrac{\\var{e2}}{\\var{f2}}$</p> <p>In lowest terms, the numerator is [[0]], the denominator is [[1]]</p>\n       \n        \n      ", "gaps": [{"minvalue": "{(a2*d2*f2+b2*c2*f2+b2*d2*e2)/i2}", "type": "numberentry", "maxvalue": "{(a2*d2*f2+b2*c2*f2+b2*d2*e2)/i2}", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "{(b2*d2*f2)/i2}", "type": "numberentry", "maxvalue": "{(b2*d2*f2)/i2}", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}, {"prompt": "\n      <p>$\\dfrac{\\var{a2}}{\\var{b2}} - \\dfrac{\\var{c2}}{\\var{d2}} + \\dfrac{\\var{e2}}{\\var{f2}}$</p> <p>In lowest terms, the numerator is [[0]], the denominator is [[1]]</p>\n       \n        \n      ", "gaps": [{"minvalue": "{(a2*d2*f2-b2*c2*f2+b2*d2*e2)/j2}", "type": "numberentry", "maxvalue": "{(a2*d2*f2-b2*c2*f2+b2*d2*e2)/j2}", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "{(b2*d2*f2)/j2}", "type": "numberentry", "maxvalue": "{(b2*d2*f2)/j2}", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}, {"prompt": "\n      <p>$\\dfrac{\\var{a2}}{\\var{b2}} - \\dfrac{\\var{c2}}{\\var{d2}} - \\dfrac{\\var{e2}}{\\var{f2}}$</p> <p>In lowest terms, the numerator is [[0]], the denominator is [[1]]</p>\n       \n        \n      ", "gaps": [{"minvalue": "{(a2*d2*f2-b2*c2*f2-b2*d2*e2)/k2}", "type": "numberentry", "maxvalue": "{(a2*d2*f2-b2*c2*f2-b2*d2*e2)/k2}", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "{(b2*d2*f2)/k2}", "type": "numberentry", "maxvalue": "{(b2*d2*f2)/k2}", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}, {"prompt": "\n      <p>$\\dfrac{\\var{a2}}{\\var{b2}} + \\dfrac{\\var{c2}}{\\var{d2}} \\times \\dfrac{\\var{e2}}{\\var{f2}}$</p> <p>In lowest terms, the numerator is [[0]], the denominator is [[1]]</p>\n       \n        \n      ", "gaps": [{"minvalue": "{(a2*d2*f2+b2*c2*e2)/l2}", "type": "numberentry", "maxvalue": "{(a2*d2*f2+b2*c2*e2)/l2}", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "{(b2*d2*f2)/l2}", "type": "numberentry", "maxvalue": "{(b2*d2*f2)/l2}", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}, {"prompt": "\n      <p>$\\dfrac{\\var{a2}}{\\var{b2}} + \\dfrac{\\var{c2}}{\\var{d2}} \\times \\dfrac{\\var{g2}}{\\var{h2}}+\\dfrac{\\var{e2}}{\\var{f2}}$</p> <p>In lowest terms, the numerator is [[0]], the denominator is [[1]]</p>\n       \n        \n      ", "gaps": [{"minvalue": "{(a2*d2*f2*h2+b2*c2*f2*g2+b2*d2*e2*h2)/m2}", "type": "numberentry", "maxvalue": "{(a2*d2*f2*h2+b2*c2*f2*g2+b2*d2*e2*h2)/m2}", "marks": 1.0, "showPrecisionHint": false}, {"minvalue": "{(b2*d2*f2*h2)/m2}", "type": "numberentry", "maxvalue": "{(b2*d2*f2*h2)/m2}", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}], "extensions": [], "statement": "<p>Evaluate the following as fractions in lowest terms. Write the numerator and denominator of the lowest term fraction in the boxes provided.</p>", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"f2": {"definition": "y2/z2", "name": "f2"}, "h2": {"definition": "p2/q2", "name": "h2"}, "j2": {"definition": "gcd(a2*d2*f2-b2*c2*f2+b2*d2*e2,b2*d2*f2)", "name": "j2"}, "w2": {"definition": "gcd(u2,v2)", "name": "w2"}, "b2": {"definition": "s2/t2", "name": "b2"}, "y2": {"definition": "random(2..11 except [u2,s2,v2,x2,x21,x22])", "name": "y2"}, "d2": {"definition": "v2/w2", "name": "d2"}, "q2": {"definition": "gcd(o2,p2)", "name": "q2"}, "s2": {"definition": "random(2..11 except r2)", "name": "s2"}, "u2": {"definition": "random(1..9)", "name": "u2"}, "k2": {"definition": "gcd(a2*d2*f2-b2*c2*f2-b2*d2*e2,b2*d2*f2)", "name": "k2"}, "m2": {"definition": "gcd(a2*d2*f2*h2+b2*c2*f2*g2+b2*d2*e2*h2,b2*d2*f2*h2)", "name": "m2"}, "x21": {"definition": "s2*v2*x2/(r2*v2-s2*u2)", "name": "x21"}, "o2": {"definition": "random(1..9)", "name": "o2"}, "x22": {"definition": "-x21", "name": "x22"}, "g2": {"definition": "o2/q2", "name": "g2"}, "i2": {"definition": "gcd(a2*d2*f2+b2*c2*f2+b2*d2*e2,b2*d2*f2)", "name": "i2"}, "v2": {"definition": "random(2..11 except [u2,s2,u21])", "name": "v2"}, "a2": {"definition": "r2/t2", "name": "a2"}, "x2": {"definition": "random(1..9)", "name": "x2"}, "c2": {"definition": "u2/w2", "name": "c2"}, "z2": {"definition": "gcd(x2,y2)", "name": "z2"}, "e2": {"definition": "x2/z2", "name": "e2"}, "p2": {"definition": "random(2..11 except o2)", "name": "p2"}, "r2": {"definition": "random(1..9)", "name": "r2"}, "t2": {"definition": "gcd(r2,s2)", "name": "t2"}, "l2": {"definition": "gcd(a2*d2*f2+b2*c2*e2,b2*d2*f2)", "name": "l2"}, "u21": {"definition": "s2*u2/r2", "name": "u21"}}, "metadata": {"notes": "", "description": "<p>Questions testing addition, subtraction, multiplication of numerical fractions and reduction to lowest terms. They also test BIDMAS in the context of fractions.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}