// Numbas version: finer_feedback_settings
{"name": "Solving linear equations: one step: multiplying or dividing ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "g", "f", "ans3", "h", "j", "ans4"], "name": "Solving linear equations: one step: multiplying or dividing ", "tags": ["algebra", "balancing equations", "Linear equations", "linear equations", "one step equations", "rearranging equations", "solving equations", "Solving equations"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "1", "prompt": "<p>Given $\\var{a}x=\\var{b}$, we can rearrange the equation to that find $x=$&nbsp;[[0]].</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{b}/{a}", "minValue": "{b}/{a}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>Given $\\var{a}x=\\var{b}$, we divide both sides by $\\var{a}$ to get $x$ by itself.</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\var{a}x$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{b}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{\\var{a}x}{\\var{a}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\frac{\\var{b}}{\\var{a}}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$x$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\simplify{{b}/{a}}}$</td>\n</tr>\n</tbody>\n</table>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>Given $\\var{c}y=\\var{d}$, &nbsp;$y=$&nbsp;[[0]].</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{d}/{c}", "minValue": "{d}/{c}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>Given $\\var{c}y=\\var{d}$, we divide both sides by $\\var{c}$ to get $y$ by itself.</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\var{c}y$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{d}$</td>\n</tr>\n<tr>\n<td></td>\n<td></td>\n<td>&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{\\var{c}y}{\\var{c}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\frac{\\var{d}}{\\var{c}}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$y$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\simplify{{d}/{c}}}$</td>\n</tr>\n</tbody>\n</table>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>Rearrange $\\displaystyle{\\frac{z}{\\var{f}}}=\\var{g}$ to determine the value of $z$.</p>\n<p>$z=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans3}", "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>Given $\\displaystyle{\\frac{z}{\\var{f}}}=\\var{g}$, we multiply both sides by $\\var{f}$ to get $z$ by itself.</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{z}{\\var{f}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{g}$</td>\n</tr>\n<tr>\n<td></td>\n<td></td>\n<td>&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{z}{\\var{f}}}\\times \\var{f}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{g}\\times\\var{f}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$z$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{ans3}$</td>\n</tr>\n</tbody>\n</table>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>Solve $\\displaystyle{\\var{h}=-\\frac{a}{\\var{j}}}$ for $a$.</p>\n<p>$a=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans4}", "minValue": "{ans4}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>Given $\\displaystyle{\\var{h}=-\\frac{a}{\\var{j}}}$, we multiply both sides by $-\\var{j}$ to get $a$ by itself.</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\var{h}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{-\\frac{a}{\\var{j}}}$</td>\n</tr>\n<tr>\n<td></td>\n<td></td>\n<td>&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{h}\\times(-\\var{j})$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{-\\frac{a}{\\var{j}}\\times(-\\var{j})}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{ans4}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$a$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$a$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\var{ans4}$</td>\n</tr>\n</tbody>\n</table>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": "100", "condition": ""}, "variables": {"a": {"definition": "random(2..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(-2..-40)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(-40..40 except [0,a,1])", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(-12..12 except [0,c,1])", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(-12..12 except [0,1])", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(list(2..12)+[20,50,100,200] except [g])", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "random(-12..12 except [0,1])", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "ans3": {"definition": "g*f", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "ans4": {"definition": "-h*j", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4", "description": ""}, "j": {"definition": "random(2..12 except [h])", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "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/"}]}