// Numbas version: finer_feedback_settings
{"name": "Johan's copy of 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": [{"statement": "", "type": "question", "name": "Johan's copy of The order of operations: brackets, powers and the four basics", "ungrouped_variables": ["list", "a", "b", "c", "d", "ans1", "f", "h", "g", "ans2", "base", "sub", "diff", "subs", "diffs", "num", "tsub", "denom", "ans3"], "preamble": {"js": "", "css": ""}, "advice": "", "functions": {}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "", "notes": ""}, "rulesets": {}, "tags": ["order of operations", "precedence"], "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"denom": {"group": "Ungrouped 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"templateType": "anything", "description": "", "definition": "list[2]", "name": "f"}, "ans1": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "a*b^c+d", "name": "ans1"}, "subs": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "sub^2", "name": "subs"}, "c": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(0,2,3,4)", "name": "c"}}, "parts": [{"scripts": {}, "type": "gapfill", "marks": 0, "steps": [{"scripts": {}, "type": "information", "marks": 0, "variableReplacementStrategy": "originalfirst", "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>", "variableReplacements": [], "showCorrectAnswer": true}], "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "prompt": "<p>$\\var{d}+\\var{a}\\times\\var{b}^\\var{c}=$&nbsp;[[0]]</p>", "variableReplacements": [], "showCorrectAnswer": true, "gaps": [{"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "maxValue": "{ans1}", "allowFractions": false, "marks": 1, "correctAnswerFraction": false, "minValue": "{ans1}", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true}]}, {"scripts": {}, "type": "gapfill", "marks": 0, "steps": [{"scripts": {}, "type": "information", "marks": 0, "variableReplacementStrategy": "originalfirst", "prompt": "<p><strong>Note:</strong> $\\var{h}(\\var{f}-\\var{g})$ means $\\var{h}\\times(\\var{f-g})$.</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>", "variableReplacements": [], "showCorrectAnswer": true}], "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "prompt": "<p>$\\var{h}(\\var{f}-\\var{g})=$&nbsp;[[0]]</p>", "variableReplacements": [], "showCorrectAnswer": true, "gaps": [{"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "maxValue": "{ans2}", "allowFractions": true, "marks": 1, "correctAnswerFraction": true, "minValue": "{ans2}", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true}]}, {"scripts": {}, "type": "gapfill", "marks": 0, "steps": [{"scripts": {}, "type": "information", "marks": 0, "variableReplacementStrategy": "originalfirst", "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>", "variableReplacements": [], "showCorrectAnswer": true}], "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "prompt": "<p>$\\displaystyle{\\var{a}+\\frac{\\var{sub}^2-(\\var{base}-\\var{sub})^2}{-\\var{base}+2\\times\\var{sub}}} =$&nbsp;[[0]]</p>", "variableReplacements": [], "showCorrectAnswer": true, "gaps": [{"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "maxValue": "{ans3}", "allowFractions": true, "marks": 1, "correctAnswerFraction": true, "minValue": "{ans3}", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true}]}], "question_groups": [{"pickingStrategy": "all-ordered", "pickQuestions": 0, "name": "", "questions": []}], "showQuestionGroupNames": false, "contributors": [{"name": "Johan Maertens", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1301/"}]}]}], "contributors": [{"name": "Johan Maertens", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1301/"}]}