// Numbas version: finer_feedback_settings
{"name": "LD01 Commutativity, Associativity and Distributive", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "LD01 Commutativity, Associativity and Distributive", "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "<p><strong>Commutative</strong></p>\n<p>The definition of commutativity can be written in the following way:</p>\n<p>$$<br/>a \\times b = b \\times a.<br/>$$</p>\n<p>There are varying degress of technical detail that can be included in this definition depending on what area you are studying. The key idea is that an operation is said to be commutative if the order in which you write the two elements being operated on does not matter. Multiplication of real numbers is commutative because as we know $2 \\times 3 = 3 \\times 2 = 6$ for example. The most common example of something being non-commutative is multiplication for matrices. In general for two matrices $A$ and $B$, $AB \\neq BA$ (in fact sometimes one of these things can be calculated and the other does not even exist).</p>\n<p><strong>Assosciative</strong></p>\n<p>The definition of associativity can be written in the following way:</p>\n<p>$$<br/>(ab)c = a(bc).<br/>$$</p>\n<p>In other words it doesn't matter if you first work out $a$ times $b$ and then take the result and times it by $c$, or if you first work out $b$ times $c$ and then pre-multiply the result by $a$.</p>\n<p><strong>Distributive</strong></p>\n<p>The definition of distributive can be written in the following way:</p>\n<p>$$<br/>a \\times (b + c) = a \\times b + a \\times c.<br/>$$</p>\n<p>As with the others there are increasing levels of detail that can be put into this definition (such as including ideas such as right-distributive and left-distributive) but the key idea is that you can \"expand brackets\" as you can in elementary algebra, if an operator is distributive.</p>\n<p><a href=\"https://math.libretexts.org/Bookshelves/Applied_Mathematics/Developmental_Math_(NROC)/09%3A_Real_Numbers/9.03%3A_Properties_of_Real_Numbers/9.3.01%3A_Associative_Commutative_and_Distributive_Properties\" target=\"_blank\" rel=\"noopener\" title=\"definitions of the three properties\">For more reading on this try (for example) this link.</a></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "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>Match the word to its correct definition</p>", "minMarks": 0, "maxMarks": "3", "minAnswers": 0, "maxAnswers": "3", "shuffleChoices": true, "shuffleAnswers": false, "displayType": "checkbox", "warningType": "warn", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["$a,b \\in S \\Rightarrow ab = ba$", "$a,b,c \\in S \\Rightarrow (ab)c = a(bc)$", "$a,b,c \\in S \\Rightarrow a(b+c)=ab+ac$", "If $a,b \\in S$, and $ab = ba = I$ then $b = a^{-1}$&nbsp;", "$a,b,c \\in S$ and $a+b = b+c \\Rightarrow a = c$"], "matrix": [["1", "0", "0"], ["0", "1", 0], ["0", "0", "1"], [0, 0, 0], [0, 0, 0]], "layout": {"type": "all", "expression": ""}, "answers": ["Commutative", "Associative", "Distributive"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Poppy Jeffries", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21275/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "resources": []}]}], "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Poppy Jeffries", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21275/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}]}