// Numbas version: finer_feedback_settings
{"name": "The order of operations: brackets, powers and the four basics", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "The order of operations: brackets, powers and the four basics", "tags": ["order of operations", "precedence"], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Write the following questions down on paper and evaluate them&nbsp;without using a calculator.</p>\n<p>If you are unsure of how to do&nbsp;a question, click on&nbsp;<em>Show steps</em>&nbsp;to see the full working. Then, once you understand how to do the question, click on&nbsp;<em>Try another question like this one</em>&nbsp;to start again.</p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "list[0]", "description": "", "templateType": "anything", "can_override": false}, "base": {"name": "base", "group": "Ungrouped variables", "definition": "list[4]", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "list[2]", "description": "", "templateType": "anything", "can_override": false}, "subs": {"name": "subs", "group": "Ungrouped variables", "definition": "sub^2", "description": "", "templateType": "anything", "can_override": false}, "ans2": {"name": "ans2", "group": "Ungrouped variables", "definition": "h*(f-g)", "description": "", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "list[3]", "description": "", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "list[5]", "description": "", "templateType": "anything", "can_override": false}, "tsub": {"name": "tsub", "group": "Ungrouped variables", "definition": "2*sub", "description": "", "templateType": "anything", "can_override": false}, "ans3": {"name": "ans3", "group": "Ungrouped variables", "definition": "base+a", "description": "", "templateType": "anything", "can_override": false}, "denom": {"name": "denom", "group": "Ungrouped variables", "definition": "-base+tsub", "description": "", "templateType": "anything", "can_override": false}, "diffs": {"name": "diffs", "group": "Ungrouped variables", "definition": "diff^2", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(2,3,4)", "description": "", "templateType": "anything", "can_override": false}, "diff": {"name": "diff", "group": "Ungrouped variables", "definition": "base-sub", "description": "", "templateType": "anything", "can_override": false}, "sub": {"name": "sub", "group": "Ungrouped variables", "definition": "random(1..3 except base/2)", "description": "", "templateType": "anything", "can_override": false}, "ans1": {"name": "ans1", "group": "Ungrouped variables", "definition": "a*b^c+d", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "if(c-3>=0,random(1,2,3),random(1..12))", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "list[1]", "description": "", "templateType": "anything", "can_override": false}, "num": {"name": "num", "group": "Ungrouped variables", "definition": "subs-diffs", "description": "", "templateType": "anything", "can_override": false}, "list": {"name": "list", "group": "Ungrouped variables", "definition": "shuffle(2..12)[0..6]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["list", "a", "b", "c", "d", "ans1", "f", "h", "g", "ans2", "base", "sub", "diff", "subs", "diffs", "num", "tsub", "denom", "ans3"], "variable_groups": [], "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>$\\var{d}+\\var{a}\\times\\var{b}^\\var{c}=$&nbsp;[[0]]</p>", "stepsPenalty": "1", "steps": [{"type": "information", "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>The order of operation dictates that we deal with powers&nbsp;before multiplication/division and also&nbsp;deal with multiplication/division before addition/subtraction , that is&nbsp;</p>\n<table>\n<tbody>\n<tr>\n<td>$\\var{d}+\\var{a}\\times\\var{b}^\\var{c}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{d}+\\var{a}\\times\\var{b^c}$</td>\n</tr>\n<tr>\n<td></td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{d}+\\var{a*b^c}$</td>\n</tr>\n<tr>\n<td></td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{ans1}$</td>\n</tr>\n</tbody>\n</table>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{ans1}", "maxValue": "{ans1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "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>$\\var{h}(\\var{f}-\\var{g})=$&nbsp;[[0]]</p>", "stepsPenalty": "1", "steps": [{"type": "information", "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><strong>Note:</strong> $\\var{h}(\\var{f}-\\var{g})$ means $\\var{h}\\times(\\var{f}-\\var{g})$.</p>\n<p></p>\n<p>The order of operation dictates that we deal with brackets (grouping symbols) before multiplication, that is&nbsp;</p>\n<table>\n<tbody>\n<tr>\n<td>$\\var{h}(\\var{f}-\\var{g})$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{h}(\\var{f-g})$</td>\n</tr>\n<tr>\n<td></td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{ans2}$</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>Note however, that the <em>distributive law</em>&nbsp;allows for another method!&nbsp;</p>\n<table style=\"height: 54px;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 147.094px;\">$\\var{h}(\\var{f}-\\var{g})$</td>\n<td style=\"height: 18px; width: 23.75px;\">$=$</td>\n<td style=\"text-align: left; height: 18px; width: 262.266px;\">$\\var{h}\\times\\var{f}-\\var{h}\\times\\var{g})$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 147.094px;\"></td>\n<td style=\"height: 18px; width: 23.75px;\">$=$</td>\n<td style=\"text-align: left; height: 18px; width: 262.266px;\">$\\var{h*f}-\\var{h*g}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px; width: 147.094px;\"></td>\n<td style=\"height: 18px; width: 23.75px;\">$=$</td>\n<td style=\"text-align: left; height: 18px; width: 262.266px;\">$\\var{ans2}$</td>\n</tr>\n</tbody>\n</table>\n<p></p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{ans2}", "maxValue": "{ans2}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "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>$\\displaystyle{\\var{a}+\\frac{\\var{sub}^2-(\\var{base}-\\var{sub})^2}{-\\var{base}+2\\times\\var{sub}}} =$&nbsp;[[0]]</p>", "stepsPenalty": "1", "steps": [{"type": "information", "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><strong>Note:</strong> A fraction $\\frac{a}{b}$ is the same as&nbsp;$(a)\\div (b)$, so we have to evaluate the numerator and denominator before doing the division. We can evaluate the numerator at the same time as we evaluate the denominator.</p>\n<table>\n<tbody>\n<tr>\n<td>$\\displaystyle{\\var{a}+\\frac{\\var{sub}^2-(\\var{base}-\\var{sub})^2}{-\\var{base}+2\\times\\var{sub}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\var{a}+\\frac{\\var{sub}^2-(\\var{diff})^2}{-\\var{base}+2\\times\\var{sub}}}$</td>\n<td style=\"text-align: left;\">(work on the innermost bracketed expression first)</td>\n</tr>\n<tr>\n<td></td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\var{a}+\\frac{\\var{subs}-\\var{diffs}}{-\\var{base}+2\\times\\var{sub}}}$</td>\n<td style=\"text-align: left;\">(doing the powers on the numerator, and multiplication on the denominator)</td>\n</tr>\n<tr>\n<td></td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\var{a}+\\frac{\\var{num}}{-\\var{base}+\\var{tsub}}}$</td>\n<td style=\"text-align: left;\">(doing multiplication on the denominator and addition on the numerator)</td>\n</tr>\n<tr>\n<td></td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\var{a}+\\frac{\\var{num}}{\\var{denom}}}$</td>\n<td style=\"text-align: left;\">(continue working on the denominator)</td>\n</tr>\n<tr>\n<td></td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\var{a}+\\var{base}}$</td>\n<td style=\"text-align: left;\">(do the division, or simplify the fraction)</td>\n</tr>\n<tr>\n<td></td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{ans3}$</td>\n<td style=\"text-align: left;\">(finally do the last addition)</td>\n</tr>\n</tbody>\n</table>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{ans3}", "maxValue": "{ans3}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}