// Numbas version: exam_results_page_options
{"name": "Determining the resulting sign of an arithmetic operation", "extensions": [], "custom_part_types": [], "resources": [["question-resources/drawingresize_grbP9s8.svg", "/srv/numbas/media/question-resources/drawingresize_grbP9s8.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "variable_groups": [], "name": "Determining the resulting sign of an arithmetic operation", "functions": {}, "rulesets": {}, "ungrouped_variables": ["dec", "neg", "pos"], "metadata": {"description": "<p>Given an equation with an unknown, determine if the unknown is positive or negative.</p>\n<p>First part is the product of two numbers; second part is the product of three.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "advice": "<p>The following rules apply to <strong>multiplication and division</strong>.</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<th style=\"background-color: #d6d6d6;\">First sign</th>\n<th style=\"background-color: #d6d6d6;\">operation</th>\n<th style=\"background-color: #d6d6d6;\">Second sign</th>\n<th style=\"background-color: #d6d6d6;\">Resulting sign</th>\n<th style=\"background-color: #d6d6d6;\">Example</th>\n</tr>\n<tr>\n<td style=\"text-align: center; vertical-align: middle;\">$+$</td>\n<td style=\"text-align: center; vertical-align: middle;\">$\\times$ or $\\div$</td>\n<td style=\"text-align: center; vertical-align: middle;\">$+$</td>\n<td style=\"text-align: center; vertical-align: middle;\">$+$</td>\n<td style=\"text-align: left; vertical-align: middle;\">$3&nbsp;\\times 2 = 6$</td>\n</tr>\n<tr>\n<td style=\"text-align: center; vertical-align: middle;\">$+$</td>\n<td style=\"text-align: center; vertical-align: middle;\">$\\times$ or $\\div$</td>\n<td style=\"text-align: center; vertical-align: middle;\">$-$</td>\n<td style=\"text-align: center; vertical-align: middle;\">$-$</td>\n<td style=\"text-align: left; vertical-align: middle;\">$3&nbsp;\\times (-2) =&nbsp;-6$</td>\n</tr>\n<tr>\n<td style=\"text-align: center; vertical-align: middle;\">$-$</td>\n<td style=\"text-align: center; vertical-align: middle;\">$\\times$ or $\\div$</td>\n<td style=\"text-align: center; vertical-align: middle;\">$+$</td>\n<td style=\"text-align: center; vertical-align: middle;\">$-$</td>\n<td style=\"text-align: left; vertical-align: middle;\">$(-3)&nbsp;\\times 2 =&nbsp;-6$</td>\n</tr>\n<tr>\n<td style=\"text-align: center; vertical-align: middle;\">$-$</td>\n<td style=\"text-align: center; vertical-align: middle;\">$\\times$ or $\\div$</td>\n<td style=\"text-align: center; vertical-align: middle;\">$-$</td>\n<td style=\"text-align: center; vertical-align: middle;\">$+$</td>\n<td style=\"text-align: left; vertical-align: middle;\">$(-3)&nbsp;\\times (-2) = 6$</td>\n</tr>\n</tbody>\n</table>\n<h4>a)</h4>\n<p>$(\\var{neg[4]})&nbsp;\\times (\\var{neg[5]})$&nbsp;will be <strong>positive</strong>, as negative times negative gives us positive.</p>\n<h4>b)</h4>\n<p><strong></strong>$\\var{pos[4]}&nbsp;\\times (\\var{neg[6]})&nbsp;\\times \\var{dec[5]}$ will be <strong>negative</strong>, as positive times negative times positive gives us negative.</p>\n<p>To check these:</p>\n<p>\\[\\begin{align} a &amp;=(\\var{neg[4]})&nbsp;\\times (\\var{neg[5]}) \\\\&amp;= +&nbsp;\\var{neg[4]*neg[5]} \\text{ (positive),}&nbsp;\\\\ b&nbsp;&amp;=&nbsp;\\var{pos[4]}&nbsp;\\times (\\var{neg[6]})&nbsp;\\times \\var{dec[5]} \\\\&amp;= \\var{pos[4]*neg[6]*dec[5]} \\text{ (negative).}&nbsp;\\end{align} \\]</p>", "statement": "<p>Decide whether each of the following numbers is positive or negative.</p>", "preamble": {"js": "", "css": ""}, "variables": {"pos": {"name": "pos", "description": "<p>Random positive integers.</p>", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(1..300),5)"}, "dec": {"name": "dec", "description": "<p>Random decimals.</p>", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(0..50 #0.01 except 0..50), 7)"}, "neg": {"name": "neg", "description": "<p>Random negative integers.</p>", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(-300..-1),8)"}}, "parts": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p>$a = (\\var{neg[4]})&nbsp;\\times (\\var{neg[5]})$&nbsp;[[0]]</p>", "gaps": [{"variableReplacementStrategy": "originalfirst", "choices": ["<p>$a$ is positive</p>", "<p>$a$ is negative</p>"], "matrix": ["1", 0], "maxMarks": 0, "shuffleChoices": false, "variableReplacements": [], "type": "1_n_2", "displayColumns": 0, "marks": 0, "minMarks": 0, "displayType": "radiogroup", "showFeedbackIcon": true, "showCorrectAnswer": true, "distractors": ["", ""], "scripts": {}}], "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "type": "gapfill", "marks": 0, "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "prompt": "<p>$b = \\var{pos[4]}&nbsp;\\times (\\var{neg[6]})&nbsp;\\times \\var{dec[5]}$&nbsp;[[0]]</p>\n<p></p>", "gaps": [{"variableReplacementStrategy": "originalfirst", "choices": ["<p>$b$ is positive</p>", "<p>$b$ is negative</p>"], "matrix": [0, "1"], "maxMarks": 0, "shuffleChoices": false, "variableReplacements": [], "type": "1_n_2", "displayColumns": 0, "marks": 0, "minMarks": 0, "displayType": "radiogroup", "showFeedbackIcon": true, "showCorrectAnswer": true, "distractors": ["", ""], "scripts": {}}], "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "type": "gapfill", "marks": 0, "scripts": {}}], "tags": ["multiplication", "taxonomy"], "variablesTest": {"maxRuns": "100", "condition": ""}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}]}