// Numbas version: finer_feedback_settings
{"name": "Arithmetic operations", "metadata": {"description": "<p>Evaluating arithmetic operations, and the order of operations.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", ""], "variable_overrides": [[], [], []], "questions": [{"name": "Basic arithmetic operations: addition and subtraction", "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}, "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/"}], "type": "question", "statement": "<p>Calculate the following:</p>", "variablesTest": {"condition": "", "maxRuns": "100"}, "variables": {"pos": {"description": "<p>Random positive integers.</p>", "name": "pos", "group": "Ungrouped variables", "templateType": "anything", "definition": "repeat(random(1..300),5)"}, "neg": {"description": "<p>Random negative integers.</p>", "name": "neg", "group": "Ungrouped variables", "templateType": "anything", "definition": "repeat(random(-300..-1),8)"}, "dec": {"description": "<p>Random decimals.</p>", "name": "dec", "group": "Ungrouped variables", "templateType": "anything", "definition": "repeat(random(0..50 #0.01 except 0..50), 7)"}}, "functions": {}, "tags": ["addition", "Addition", "Decimals", "decimals", "subtraction", "taxonomy"], "variable_groups": [], "parts": [{"scripts": {}, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "maxValue": "pos[0]+pos[1]+pos[2]", "showFeedbackIcon": true, "minValue": "pos[0]+pos[1]+pos[2]", "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": "1", "showCorrectAnswer": true}], "showFeedbackIcon": true, "prompt": "<p style=\"padding-left: 30px;\">$\\var{pos[0]} + \\var{pos[1]} + \\var{pos[2]}=$ [[0]]</p>", "marks": 0}, {"scripts": {}, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "maxValue": "pos[3]+neg[0]", "showFeedbackIcon": true, "minValue": "pos[3]+neg[0]", "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": "1", "showCorrectAnswer": true}], "showFeedbackIcon": true, "prompt": "<p style=\"padding-left: 30px;\">$\\var{pos[3]}&nbsp;+(\\var{neg[0]})=$ [[0]]</p>", "marks": 0}, {"scripts": {}, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "maxValue": "dec[0] - dec[1]", "showFeedbackIcon": true, "minValue": "dec[0] - dec[1]", "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": "1", "showCorrectAnswer": true}], "showFeedbackIcon": true, "prompt": "<p style=\"padding-left: 30px;\">$\\var{dec[0]}&nbsp;- \\var{dec[1]}=$&nbsp;[[0]]</p>", "marks": 0}, {"scripts": {}, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "maxValue": "neg[1]-neg[2]", "showFeedbackIcon": true, "minValue": "neg[1]-neg[2]", "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": "1", "showCorrectAnswer": true}], "showFeedbackIcon": true, "prompt": "<p style=\"padding-left: 30px;\">$\\var{neg[1]}&nbsp;- (\\var{neg[2]})=$ [[0]]</p>", "marks": 0}, {"scripts": {}, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"correctAnswerFraction": false, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "maxValue": "neg[3]+dec[2]", "showFeedbackIcon": true, "minValue": "neg[3]+dec[2]", "correctAnswerStyle": "plain", "allowFractions": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "marks": "1", "showCorrectAnswer": true}], "showFeedbackIcon": true, "prompt": "<p style=\"padding-left: 30px;\">$\\var{neg[3]}&nbsp;+ \\var{dec[2]}=$&nbsp;[[0]]</p>", "marks": 0}], "ungrouped_variables": ["dec", "neg", "pos"], "rulesets": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Addition and subtraction of integers and decimals.</p>"}, "preamble": {"css": "", "js": ""}, "advice": "<p>A sign between numbers usually tells us whether to<strong>&nbsp;add</strong> or&nbsp;<strong>subtract</strong>. Sometimes, we can see two signs following each other.</p>\n<p>We&nbsp;need to remember that <strong>two different signs</strong> (+ and - in any order) become a&nbsp;<strong>minus (-)</strong>, while <strong>two same signs</strong> become a <strong>plus (+)</strong>.</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<th style=\"background-color: #d6d6d6;\">Operation</th>\n<th style=\"background-color: #d6d6d6;\">First sign</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;\">Resulting operation</th>\n<th style=\"background-color: #d6d6d6;\">Example</th>\n</tr>\n<tr>\n<td style=\"text-align: center; vertical-align: middle;\">Addition</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: center; vertical-align: middle;\">$+$</td>\n<td style=\"text-align: center; vertical-align: middle;\">Addition</td>\n<td>$3&nbsp;+ (+2) =&nbsp;3 + 2 =&nbsp;5$</td>\n</tr>\n<tr>\n<td style=\"text-align: center; vertical-align: middle;\">Addition</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: center; vertical-align: middle;\">$-$</td>\n<td style=\"text-align: center; vertical-align: middle;\">Subtraction</td>\n<td>$3&nbsp;+ (-2) =&nbsp;3 - 2 = 1$</td>\n</tr>\n<tr>\n<td style=\"text-align: center; vertical-align: middle;\">Subtraction</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: center; vertical-align: middle;\">$-$</td>\n<td style=\"text-align: center; vertical-align: middle;\">Subtraction</td>\n<td>$3&nbsp;- (+2) =&nbsp;3 - 2 = 1$</td>\n</tr>\n<tr>\n<td style=\"text-align: center; vertical-align: middle;\">Subtraction</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: center; vertical-align: middle;\">$+$</td>\n<td style=\"text-align: center; vertical-align: middle;\">Addition</td>\n<td>$3&nbsp;- (-2) =&nbsp;3&nbsp;+ 2 = 5$</td>\n</tr>\n</tbody>\n</table>\n<p>Another important thing to remember is to <strong>press AC</strong>&nbsp;on your calculator to clear it before you start&nbsp;the&nbsp;next&nbsp;calculation. If the following calculation starts with a minus, your calculator will assume you want to subtract something from your previous calculation, rather than start a new one.</p>"}, {"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}, "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/"}], "variable_groups": [], "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": ""}}, {"name": "Using BODMAS to evaluate arithmetic expressions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "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/"}], "variable_groups": [], "variables": {"int": {"templateType": "anything", "definition": "random(2..10 except sint)", "description": "<p>Random integer from 2 to 10.</p>", "name": "int", "group": "Ungrouped variables"}, "oint": {"templateType": "anything", "definition": "random(1..9 #2 except int except sint)", "description": "<p>Random odd integer from 1 to 9.</p>", "name": "oint", "group": "Ungrouped variables"}, "bint": {"templateType": "anything", "definition": "random(20..50)", "description": "<p>A random slightly&nbsp;bigger integer.</p>", "name": "bint", "group": "Ungrouped variables"}, "pint": {"templateType": "anything", "definition": "random(1..4 except 3)", "description": "<p>1, 2 or 4.</p>", "name": "pint", "group": "Ungrouped variables"}, "eint": {"templateType": "anything", "definition": "random(1..9 #2 except int except sint)", "description": "<p>Random even integer from 2 to 10.</p>", "name": "eint", "group": "Ungrouped variables"}, "sint": {"templateType": "anything", "definition": "random(2..6)", "description": "<p>Random integer from 1 to 5.</p>", "name": "sint", "group": "Ungrouped variables"}}, "type": "question", "parts": [{"maxMarks": 0, "type": "1_n_2", "showCorrectAnswer": true, "minMarks": 0, "distractors": ["", "", ""], "displayColumns": 0, "displayType": "radiogroup", "scripts": {}, "showFeedbackIcon": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "matrix": ["1", 0, 0], "choices": ["<p>{int*int}</p>", "<p>{int}</p>", "<p>1</p>"], "shuffleChoices": true, "variableReplacements": [], "prompt": "<p>$\\var{int*int} &divide;&nbsp;\\var{int}&nbsp;\\times&nbsp;\\var{int} =$&nbsp;&nbsp;$?$</p>"}, {"maxMarks": 0, "type": "1_n_2", "showCorrectAnswer": true, "minMarks": 0, "distractors": ["", "", ""], "displayColumns": 0, "displayType": "radiogroup", "scripts": {}, "showFeedbackIcon": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "matrix": ["1", 0, 0], "choices": ["<p>{eint*4}</p>", "<p>1</p>", "<p>{random(2..40 except eint*4)}</p>"], "shuffleChoices": true, "variableReplacements": [], "prompt": "<p>$\\var{eint*2} &divide; \\var{eint/2} \\times \\var{eint}=$&nbsp;&nbsp;$?$</p>"}, {"maxMarks": 0, "type": "1_n_2", "showCorrectAnswer": true, "minMarks": 0, "distractors": ["", "", ""], "displayColumns": 0, "displayType": "radiogroup", "scripts": {}, "showFeedbackIcon": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "matrix": [0, "1", 0], "choices": ["<p>{(sint + sint + 2)*sint}</p>", "<p>{sint + (sint + 2)*sint}</p>", "<p>{(((sint + sint + 2)*sint) + (sint + (sint + 2)*sint))/2}</p>"], "shuffleChoices": true, "variableReplacements": [], "prompt": "<p>$\\var{sint} + \\var{sint + 2}&nbsp;\\times&nbsp;\\var{sint}&nbsp;=$&nbsp;&nbsp;$?$</p>"}, {"maxMarks": 0, "type": "1_n_2", "showCorrectAnswer": true, "minMarks": 0, "distractors": ["", ""], "displayColumns": 0, "displayType": "radiogroup", "scripts": {}, "showFeedbackIcon": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "matrix": ["0", "1"], "choices": ["<p>1</p>", "<p>{bint - 14}</p>"], "shuffleChoices": false, "variableReplacements": [], "prompt": "<p>$\\var{bint - 15} - 1 \\times 0 + \\var{bint}\\div\\var{bint} =$ &nbsp;$?$</p>"}, {"showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "variableReplacements": [], "steps": [{"variableReplacementStrategy": "originalfirst", "type": "information", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true, "prompt": "<p>Root is another way of writing a power, e.g. $\\sqrt{4} = 4^{\\frac{1}{2}}$.</p>\n<p>Fraction means the numerator divided by the denominator, these two can be thought of as brackets while the fraction itself is a division.</p>\n<p>For example,</p>\n<p>\\begin{align} <br/>\\sqrt4&nbsp;+ \\frac{4+11}{5} &amp;= 4^{\\frac{1}{2}} + (4+11) \\div 5 \\\\ <br/>&amp;= 4^{\\frac{1}{2}} + 15 \\div 5 &amp; \\text{(BRACKETS)}\\\\<br/>&amp;= 2 + 15 \\div 5 &amp; \\text{(ORDINALS)} \\\\<br/>&amp;= 2 + 3 &amp; \\text{(DIVISION/multiplication)} \\\\<br/>&amp;= 5 \\text{ .} &amp;&nbsp;\\text{(ADDITION/subtraction)}<br/>\\end{align}</p>"}], "gaps": [{"correctAnswerFraction": false, "mustBeReduced": false, "type": "numberentry", "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "mustBeReducedPC": "50", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "scripts": {}, "minValue": "{(oint*oint + sqrt(eint*eint))/2 + 8/pint}", "maxValue": "{(oint*oint + sqrt(eint*eint))/2 + 8/pint}", "marks": "3", "variableReplacements": []}], "prompt": "<p>$\\displaystyle \\frac{\\var{oint}^2+ \\sqrt{\\var{eint*eint}}}{3 \\times 2 - 2 \\times 2} +&nbsp;(10 - 2)&nbsp;\\div&nbsp;\\var{pint}&nbsp; =$ &nbsp;[[0]]&nbsp;</p>", "stepsPenalty": "1"}], "advice": "<p>The correct order of carrying out operations can be remembered by the mnemonic BODMAS:</p>\n<blockquote>\n<p style=\"padding-left: 30px;\"><strong>B</strong>rackets&nbsp;&rArr;&nbsp;<strong>O</strong>rdinals &rArr;&nbsp;<strong>D</strong>ivision/<strong>M</strong>ultiplication &rArr;&nbsp;<strong>A</strong>ddition/<strong>S</strong>ubtraction</p>\n</blockquote>\n<p>It is important to notice that division and multiplication have the same priority&nbsp;- division does <span style=\"text-decoration: underline;\">not</span> have a priority over multiplication. Similarly, adition and subtraction also have the same priority. When the order is unclear, we work from left to right.</p>\n<p>Note that brackets have the highest&nbsp;priority, but when we&nbsp;evaluate them, we&nbsp;still need to follow BODMAS inside them.</p>\n<p>Sometimes, an alternative acronym <em>BIDMAS</em> (Brackets, Indices, ...) is also used.</p>\n<p><strong>a) </strong></p>\n<p>Division and multiplication have the same priority, so we just work from left to right. $\\var{int*int} &divide;&nbsp;\\var{int}&nbsp; = \\var{int}$ and hence</p>\n<p style=\"padding-left: 30px;\">\\[\\begin{align}&nbsp;\\var{int*int} &divide;&nbsp;\\var{int}&nbsp;\\times&nbsp;\\var{int} &amp;= \\var{int} \\times \\var{int} \\\\&amp;= \\var{int*int} \\text{.}&nbsp;&nbsp; \\end{align}\\]</p>\n<p style=\"padding-left: 30px;\"></p>\n<p><strong>b) </strong></p>\n<p>Similarly, $\\var{eint*2} &divide;&nbsp;\\var{eint/2}&nbsp; = 4&nbsp;$ and hence</p>\n<p style=\"padding-left: 30px;\">\\[\\begin{align} \\var{eint*2} &divide; \\var{eint/2} \\times \\var{eint} &amp;= 4 \\times \\var{eint} \\\\&amp;= \\var{4*eint}\\text{.} \\end{align}\\]</p>\n<p style=\"padding-left: 30px;\"></p>\n<p><strong>c) </strong></p>\n<p>Applying BODMAS, multiplication has a priority over addition. $\\var{sint + 2} \\times \\var{sint} = \\var{(sint + 2)*sint}$ and hence</p>\n<p style=\"padding-left: 30px;\">\\[\\begin{align} \\var{sint} + \\var{sint + 2}&nbsp;\\times&nbsp;\\var{sint}&nbsp;&amp;= \\var{sint} + \\var{(sint + 2)*sint} \\\\&amp;= \\var{sint + (sint + 2)*sint}\\text{.} \\end{align}\\]</p>\n<p style=\"padding-left: 30px;\"></p>\n<p><strong>d)</strong></p>\n<p>Applying BODMAS, multiplication and division have priority over addition and subtraction. $1 \\times 0 = 0$&nbsp;and&nbsp;$\\var{bint}\\div\\var{bint} = 1$&nbsp;so</p>\n<p style=\"padding-left: 30px;\">\\[\\begin{align} \\var{bint - 15} - 1 \\times 0 + \\var{bint}\\div\\var{bint} &amp;= \\var{bint - 15} - 0 + 1 \\\\&amp;= \\var{bint - 14}\\text{.} \\end{align}\\]</p>\n<p style=\"padding-left: 30px;\"></p>\n<p><strong>e)</strong></p>\n<p>Roots can be considered as powers, while fractions can be considered as a bracket divided by a bracket.</p>\n<p>\\[\\displaystyle \\text{Numerator is considered as a bracket } (\\var{oint}^2+ \\sqrt{\\var{eint*eint}}) \\text{ and the denominator as&nbsp;} (3 \\times 2 - 2 \\times 2)\\text{.}\\]</p>\n<p>Before we&nbsp;evaluate numerator, we calculate powers:</p>\n<p style=\"padding-left: 30px;\">\\[\\begin{align} \\sqrt{\\var{eint*eint}} &amp;= \\var{eint} \\text{,}<br/>\\\\\\var{oint}^2 &amp;= \\var{oint*oint}&nbsp;\\text{.} \\end{align}\\]</p>\n<p>Before we evaluate denominator&nbsp;we calculate multiplications:</p>\n<p style=\"padding-left: 30px;\">\\[\\begin{align}&nbsp;3 \\times 2 &amp;= 6&nbsp;\\text{ and&nbsp;} \\\\&nbsp;2 \\times 2 &amp;= 4\\text{.} \\end{align}\\]</p>\n<p>Performing addition/subtraction as the last step in evaluating numerator/denominator we get:</p>\n<p style=\"padding-left: 30px;\">\\[ \\begin{align} (\\var{oint}^2+ \\sqrt{\\var{eint*eint}})&nbsp;&amp;= \\var{oint*oint} + \\var{eint}<br/>\\\\&amp;= \\var{oint*oint + eint}<br/>\\\\\\text{and}<br/>\\\\(3 \\times 2 - 2 \\times 2) &amp;= 6 - 4<br/>\\\\&amp;= 2&nbsp;\\end{align} \\]</p>\n<p>So the fraction</p>\n<p style=\"padding-left: 30px;\">\\[\\begin{align} \\displaystyle \\frac{(\\var{oint}^2+ \\var{eint})}{(3 \\times 2 - 2 \\times 2)} &amp;= \\frac{\\var{(oint*oint + eint)}}{2}\\text{.} \\end{align}\\]</p>\n<p>Evaluating the final bracket we get:</p>\n<p style=\"padding-left: 30px;\">\\[(10 - 2) = 8\\text{.}\\]</p>\n<p>As we evaluated all brackets, we can continue with:</p>\n<p style=\"padding-left: 30px;\">\\[\\displaystyle \\frac{\\var{oint}^2+ \\sqrt{\\var{eint*eint}}}{3 \\times 2 - 2 \\times 2} +&nbsp;(10 - 2)&nbsp;\\div&nbsp;\\var{pint} = \\frac{\\var{(oint*oint + eint)}}{2} +&nbsp;8&nbsp;\\div&nbsp;\\var{pint} \\]</p>\n<p>Now, division has a priority over addition so since $\\frac{\\var{(oint*oint + eint)}}{2} = \\var{(oint*oint + eint)/2}$ and $8 \\div \\var{pint} = \\var{8/pint}$:</p>\n<p style=\"padding-left: 30px;\">\\[\\begin{align} \\frac{\\var{(oint*oint + eint)}}{2} +&nbsp;8&nbsp;\\div&nbsp;\\var{pint} &amp;= \\var{(oint*oint + eint)/2} + \\var{8/pint} \\\\&amp;= \\var{(oint*oint + eint)/2 + 8/pint}\\text{.} \\end{align}\\]</p>\n<p></p>", "tags": ["BODMAS", "bodmas", "taxonomy"], "preamble": {"js": "", "css": ""}, "rulesets": {}, "functions": {}, "ungrouped_variables": ["int", "sint", "eint", "oint", "pint", "bint"], "statement": "<p>Wrong order of solving operations can often lead to incorrect answers.&nbsp; Therefore, the&nbsp;order in which we carry out a calculation is important.</p>\n<p><em>BODMAS</em> is a&nbsp;mnemonic which tells us the correct order in which operations should be carried out:</p>\n<blockquote>\n<p><strong>B</strong>rackets&nbsp;&rArr;&nbsp;<strong>O</strong>rdinals &rArr;&nbsp;<strong>D</strong>ivision/<strong>M</strong>ultiplication &rArr;&nbsp;<strong>A</strong>ddition/<strong>S</strong>ubtraction</p>\n</blockquote>\n<p>Apply BODMAS and&nbsp;try to solve these&nbsp;calculations.</p>", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions.&nbsp;</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "end_message": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": [], "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "inreview"}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "type": "exam", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "extensions": [], "custom_part_types": [], "resources": [["question-resources/drawingresize_grbP9s8.svg", "/srv/numbas/media/question-resources/drawingresize_grbP9s8.svg"]]}