// Numbas version: finer_feedback_settings
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sometimes easier to work out $(\\var{a5}+\\var{b5}) \\bmod{X}$ and $(\\var{g5}+\\var{h5}) \\bmod{X}$ separately, giving two numbers in the range $[0 \\dots X-1]$, and then to multiply them together.</p>\n<p>For example, working $\\bmod{9}$ we have:</p>\n<p>\\begin{align}<br/>\\var{a5}+\\var{b5}&amp;\\equiv \\var{mod(a5+b5,9)} \\bmod{9}, \\\\<br/> \\var{g5}+\\var{h5}&amp;\\equiv \\var{mod(g5+h5,9)} \\bmod{9}. \\\\ \\\\ <br/>(\\var{a5}+\\var{b5})\\times (\\var{g5}+\\var{h5}) &amp;\\equiv \\var{s5} \\times \\var{t5} \\bmod{9} \\\\ <br/>&amp;\\equiv \\var{mod(ans5,9)} \\bmod{9}<br/>\\end{align}</p>", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "parts": [{"prompt": "\n  \n  \n  <p>Perform the following calculations in $\\mathbb{Z}_{2},\\;\\;\\mathbb{Z}_{9},\\;\\;\\mathbb{Z}_{10}$.</p>\n  \n  \n  \n  <table border=\"1\">\n  \n  <tr>\n  \n  <th></th>\n  \n  <th>$\\mathbb{Z}_{2}$</th>\n  \n  <th>$\\mathbb{Z}_{9}$</th>\n  \n  <th>$\\mathbb{Z}_{10}$</th>\n  \n  </tr>\n  \n  <tr>\n  \n  <td>$\\var{a1}+\\var{b1}$</td>\n  \n  <td>[[0]]</td>\n  \n  <td>[[1]]</td>\n  \n  <td>[[2]]</td>\n  \n  </tr>\n  \n  <tr>\n  \n  <td>$\\var{a2}\\times\\var{b2}$</td>\n  \n  <td>[[3]]</td>\n  \n  <td>[[4]]</td>\n  \n  <td>[[5]]</td>\n  \n  </tr>\n  \n  <tr>\n  \n  <td>$\\var{a3}\\times(\\var{b3}+\\var{g3})$</td>\n  \n  <td>[[6]]</td>\n  \n  <td>[[7]]</td>\n  \n  <td>[[8]]</td>\n  \n  </tr>\n  \n  <tr>\n  \n  <td>$\\var{a4}\\times\\var{b4}$</td>\n  \n  <td>[[9]]</td>\n  \n  <td>[[10]]</td>\n  \n  <td>[[11]]</td>\n  \n  </tr>\n  \n  <tr>\n  \n  <td>$(\\var{a5}+\\var{b5})\\times (\\var{g5}+\\var{h5})$</td>\n  \n  <td>[[12]]</td>\n  \n  <td>[[13]]</td>\n  \n  <td>[[14]]</td>\n  \n  </tr>\n  \n  </table>\n  \n  ", "marks": 0, "gaps": [{"allowFractions": false, "scripts": {}, "maxValue": "{mod(ans1,2)}", "minValue": "{mod(ans1,2)}", "correctAnswerFraction": false, "showCorrectAnswer": true, "marks": 0.2, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "scripts": {}, "maxValue": "{mod(ans1,9)}", "minValue": "{mod(ans1,9)}", "correctAnswerFraction": false, "showCorrectAnswer": true, "marks": 0.2, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "scripts": {}, "maxValue": "{mod(ans1,10)}", "minValue": "{mod(ans1,10)}", "correctAnswerFraction": false, "showCorrectAnswer": true, "marks": 0.2, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "scripts": {}, "maxValue": "{mod(ans2,2)}", "minValue": "{mod(ans2,2)}", "correctAnswerFraction": false, "showCorrectAnswer": true, "marks": 0.2, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "scripts": {}, "maxValue": "{mod(ans2,9)}", "minValue": "{mod(ans2,9)}", "correctAnswerFraction": false, "showCorrectAnswer": true, "marks": 0.2, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "scripts": {}, "maxValue": "{mod(ans2,10)}", 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"type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "scripts": {}, "maxValue": "{mod(ans4,9)}", "minValue": "{mod(ans4,9)}", "correctAnswerFraction": false, "showCorrectAnswer": true, "marks": 0.2, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "scripts": {}, "maxValue": "{mod(ans4,10)}", "minValue": "{mod(ans4,10)}", "correctAnswerFraction": false, "showCorrectAnswer": true, "marks": 0.2, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "scripts": {}, "maxValue": "{mod(ans5,2)}", "minValue": "{mod(ans5,2)}", "correctAnswerFraction": false, "showCorrectAnswer": true, "marks": 0.2, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "scripts": {}, "maxValue": "{mod(ans5,9)}", "minValue": "{mod(ans5,9)}", "correctAnswerFraction": false, "showCorrectAnswer": true, "marks": 0.2, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "scripts": {}, 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"random(5..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "b5", "description": ""}, "a3": {"definition": "random(3..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "a5": {"definition": "random(5..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a5", "description": ""}, "b1": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "b2": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "description": ""}, "b3": {"definition": "random(3..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "b3", "description": ""}, "a4": {"definition": "random(6..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}}, "metadata": {"notes": "<p><strong>16/08/2012:</strong></p>\n                <p><strong><br /></strong>Added tags.</p>\n                <p>Added description. &nbsp; &nbsp;</p>", "description": "<p>Calculations in $\\mathbb{Z_n}$ for three values of $n$. &nbsp; &nbsp;&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Factorise four numbers", "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": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}], "parts": 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"variableReplacements": [], "marks": "0.25"}], "type": "gapfill", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "sortAnswers": false}, {"customName": "", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "useCustomName": false, "prompt": "<p>$\\var{numbers[3]} =$ [[0]]</p>", "unitTests": [], "showFeedbackIcon": true, "scripts": {}, "gaps": [{"answer": "{numbers[3]}", "showCorrectAnswer": true, "customMarkingAlgorithm": "", "checkingType": "absdiff", "vsetRangePoints": 5, "failureRate": 1, "customName": "", "checkVariableNames": false, "unitTests": [], "valuegenerators": [], "vsetRange": [0, 1], "showFeedbackIcon": true, "scripts": {"constructor": {"script": "question.createFactorisePart(this);", "order": "after"}, "mark": {"script": "question.markFactorisePart(this);", "order": "instead"}}, "extendBaseMarkingAlgorithm": true, "type": "jme", "variableReplacementStrategy": "originalfirst", 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