// Numbas version: finer_feedback_settings
{"name": "Decimals: Addition", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Decimals: Addition", "tags": [], "metadata": {"description": "<p>Decimals addition algorithm. 2 and 3 digit numbers. Carrying.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Write the following question down on paper and evaluate&nbsp;it without using a calculator.</p>\n<p>If you are unsure of how to do&nbsp;a question, click on <em>Show steps</em> to see the full working. Then, once you understand how to do the question, click on <em>Try another question like this one</em> to start again.</p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"chunsumlastdigit": {"name": "chunsumlastdigit", "group": "Ungrouped variables", "definition": "mod(chunsum,10)", "description": "", "templateType": "anything", "can_override": false}, "threedigit1": {"name": "threedigit1", "group": "Ungrouped variables", "definition": "cdigs[0]/1000+cdigs[1]/100+cdigs[2]/10", "description": "", "templateType": "anything", "can_override": false}, "cunitsum": {"name": "cunitsum", "group": "Ungrouped variables", "definition": "cdigs[0]+cdigs[3]", "description": "", "templateType": "anything", "can_override": false}, "ctencarry": {"name": "ctencarry", "group": "Ungrouped variables", "definition": "floor(ctensum/10)", "description": "", "templateType": "anything", "can_override": false}, "cunitsumlastdigit": {"name": "cunitsumlastdigit", "group": "Ungrouped variables", "definition": "mod(cunitsum,10)", "description": "", "templateType": "anything", "can_override": false}, "cunitcarry": {"name": "cunitcarry", "group": "Ungrouped variables", "definition": "floor(cunitsum/10)", "description": "", "templateType": "anything", "can_override": false}, "chunsum": {"name": "chunsum", "group": "Ungrouped variables", "definition": "ctencarry+cdigs[2]+cdigs[5]", "description": "", "templateType": "anything", "can_override": false}, "ctensum": {"name": "ctensum", "group": "Ungrouped variables", "definition": "cdigs[1]+cdigs[4]+cunitcarry", "description": "", "templateType": "anything", "can_override": false}, "threedigit2": {"name": "threedigit2", "group": "Ungrouped variables", "definition": "cdigs[3]/1000+cdigs[4]/100+cdigs[5]/10", "description": "", "templateType": "anything", "can_override": false}, "ctensumlastdigit": {"name": "ctensumlastdigit", "group": "Ungrouped variables", "definition": "mod(ctensum,10)", "description": "", "templateType": "anything", "can_override": false}, "chuncarry": {"name": "chuncarry", "group": "Ungrouped variables", "definition": "floor(chunsum/10)", "description": "", "templateType": "anything", "can_override": false}, "cans": {"name": "cans", "group": "Ungrouped variables", "definition": "threedigit1+threedigit2", "description": "", "templateType": "anything", "can_override": false}, "cdigs": {"name": "cdigs", "group": "Ungrouped variables", "definition": "[0]+shuffle(3..9)", "description": "", "templateType": "anything", "can_override": false}, "cunitsumtensdigit": {"name": "cunitsumtensdigit", "group": "Ungrouped variables", "definition": "0.1*(cunitsum-cunitsumlastdigit)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["cdigs", "threedigit1", "threedigit2", "cans", "cunitsum", "cunitsumlastdigit", "cunitcarry", "ctensum", "ctensumlastdigit", "ctencarry", "chunsum", "chunsumlastdigit", "chuncarry", "cunitsumtensdigit"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "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>$\\var{threedigit1}+\\var{threedigit2} = $&nbsp;[[0]]</p>", "stepsPenalty": "1", "steps": [{"type": "information", "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>Generally, we set up $\\var{threedigit1}+\\var{threedigit2}$ with the decimal points lined up vertically so that the columns with the same place value are also lined up vertically:</p>\n<table>\n<tbody>\n<tr>\n<td>$0$</td>\n<td>.</td>\n<td>$\\var{cdigs[2]}$</td>\n<td>$\\var{cdigs[1]}$</td>\n<td></td>\n<td>$+$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td>$0$</td>\n<td>.</td>\n<td>$\\var{cdigs[5]}$</td>\n<td>$\\var{cdigs[4]}$</td>\n<td>$\\var{cdigs[3]}$</td>\n<td></td>\n</tr>\n<tr>\n<td></td>\n<td></td>\n<td></td>\n<td>$\\phantom{0}$</td>\n<td></td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>Note that we can <em>pad out</em> the decimal with zeros if we prefer:</p>\n<table>\n<tbody>\n<tr>\n<td>$0$</td>\n<td>.</td>\n<td>$\\var{cdigs[2]}$</td>\n<td>$\\var{cdigs[1]}$</td>\n<td>$\\color{red}{\\var{cdigs[0]}}$</td>\n<td>$+$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td>$0$</td>\n<td>.</td>\n<td>$\\var{cdigs[5]}$</td>\n<td>$\\var{cdigs[4]}$</td>\n<td>$\\var{cdigs[3]}$</td>\n<td></td>\n</tr>\n<tr>\n<td></td>\n<td></td>\n<td></td>\n<td>$\\phantom{0}$</td>\n<td></td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>Now&nbsp;we add the digits in the column to the far right (in this case, the <em>thousandths</em> column).</p>\n<p><span data-jme-visible=\"cunitsumtensdigit=0\">This results in&nbsp;$\\var{cunitsum}$ and so&nbsp;we place $\\var{cunitsumlastdigit}$ under the line in this column. </span></p>\n<p><span data-jme-visible=\"cunitsumtensdigit=1\">This results in&nbsp;$\\var{cunitsum}$ and so&nbsp;we place $\\var{cunitsumlastdigit}$ under the line in this column and carry the $1$ into the&nbsp;next column to the left.&nbsp;</span></p>\n<table>\n<tbody>\n<tr>\n<td>$\\overset{\\phantom{1}}{0}$</td>\n<td>.</td>\n<td>$\\overset{\\phantom{1}}{\\var{cdigs[2]}}$</td>\n<td><span data-jme-visible=\"cunitcarry=1\">$\\overset{\\color{red}1}{\\var{cdigs[1]}}$</span> <span data-jme-visible=\"cunitcarry=0\">$\\overset{\\phantom{0}}{\\var{cdigs[1]}}$</span></td>\n<td>$\\color{green}{\\overset{\\phantom{1}}{\\var{cdigs[0]}}}$</td>\n<td>$+$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td>$0$</td>\n<td>.</td>\n<td>$\\var{cdigs[5]}$</td>\n<td>$\\var{cdigs[4]}$</td>\n<td>$\\color{green}{\\var{cdigs[3]}}$</td>\n<td></td>\n</tr>\n<tr>\n<td></td>\n<td></td>\n<td></td>\n<td></td>\n<td>$\\color{red}{\\var{cunitSumLastDigit}}$</td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>Now we add the digits in the&nbsp;next&nbsp;column to the left (in this case, the <em>hundredths</em> column).</p>\n<p><span data-jme-visible=\"ctencarry=0\">This results in&nbsp;$\\var{ctenSum}$ and so we place $\\var{ctenSumlastdigit}$ under the line in&nbsp;this column.</span></p>\n<p><span data-jme-visible=\"ctencarry=1\">This results in&nbsp;$\\var{ctenSum}$ and so we place $\\var{ctenSumlastdigit}$ under the line in this column and carry the $1$ into the next column to the left.</span></p>\n<table>\n<tbody>\n<tr>\n<td>$\\overset{\\phantom{1}}{0}$</td>\n<td>.</td>\n<td><span data-jme-visible=\"ctencarry=1\">$\\overset{\\color{red}{1}}{\\var{cdigs[2]}}$</span> <span data-jme-visible=\"ctencarry=0\">$\\overset{\\phantom{1}}{\\var{cdigs[2]}}$</span></td>\n<td><span data-jme-visible=\"cunitcarry=1\">$\\color{green}{\\overset{1}{\\var{cdigs[1]}}}$</span> <span data-jme-visible=\"cunitcarry=0\">$\\color{green}{\\overset{\\phantom{0}}{\\var{cdigs[1]}}}$</span></td>\n<td>$\\overset{\\phantom{1}}{\\var{cdigs[0]}}$</td>\n<td>$+$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td>$0$</td>\n<td>.</td>\n<td>$\\var{cdigs[5]}$</td>\n<td>$\\color{green}{\\var{cdigs[4]}}$</td>\n<td>$\\var{cdigs[3]}$</td>\n<td></td>\n</tr>\n<tr>\n<td></td>\n<td></td>\n<td></td>\n<td>$\\color{red}{\\var{ctenSumlastdigit}}$</td>\n<td>${\\var{cunitSumLastDigit}}$</td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p></p>\n<p>Now we add the digits in the&nbsp;next&nbsp;column to the left (in this case, the&nbsp;<em>tenths</em>&nbsp;column).</p>\n<p><span data-jme-visible=\"cans&lt;1\">This is $\\var{chunsum}$ so we place&nbsp;$\\var{chunsum}$ under the line in&nbsp;this column.</span></p>\n<p><span data-jme-visible=\"cans&gt;0.999\">This is $\\var{chunsum}$ so we place&nbsp;$\\var{chunsumlastdigit}$ under the line in this column and carry $\\var{chuncarry}$ into the next column to the left (which in this case is the ones column on the other side of the decimal point).</span></p>\n<table>\n<tbody>\n<tr>\n<td><span data-jme-visible=\"chuncarry&gt;0\">$\\overset{\\color{red}1}{0}$</span> <span data-jme-visible=\"chuncarry=0\">$\\overset{\\phantom{1}}{0}$</span></td>\n<td>.</td>\n<td><span data-jme-visible=\"ctencarry=1\">$\\color{green}{\\overset{1}{\\var{cdigs[2]}}}$</span> <span data-jme-visible=\"ctencarry=0\">$\\color{green}{\\overset{\\phantom{1}}{\\var{cdigs[2]}}}$</span></td>\n<td><span data-jme-visible=\"cunitcarry=1\">$\\overset{1}{\\var{cdigs[1]}}$</span> <span data-jme-visible=\"cunitcarry=0\">$\\overset{\\phantom{0}}{\\var{cdigs[1]}}$</span></td>\n<td>$\\overset{\\phantom{1}}{\\var{cdigs[0]}}$</td>\n<td>$+$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td>$0$</td>\n<td>.</td>\n<td>$\\color{green}{\\var{cdigs[5]}}$</td>\n<td>$\\var{cdigs[4]}$</td>\n<td>$\\var{cdigs[3]}$</td>\n<td></td>\n</tr>\n<tr>\n<td></td>\n<td>.</td>\n<td>$\\color{red}{\\var{chunsumlastdigit}}$</td>\n<td>$\\var{ctenSumlastdigit}$</td>\n<td>${\\var{cunitSumLastDigit}}$</td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>Now we add the digits in the&nbsp;next&nbsp;column to the left (in this case, the&nbsp;<em>ones</em>&nbsp;column).</p>\n<p><span data-jme-visible=\"cans&lt;1\">This is&nbsp;just $0$ so we place&nbsp;$0$ under the line in&nbsp;this column.</span></p>\n<p><span data-jme-visible=\"cans&gt;0.999\">This is just $\\var{chuncarry}$ so we place&nbsp;$\\var{chuncarry}$ under the line in this column.</span></p>\n<table>\n<tbody>\n<tr>\n<td><span data-jme-visible=\"chuncarry&gt;0\">$\\color{green}{\\overset{1}{0}}$</span> <span data-jme-visible=\"chuncarry=0\">$\\color{green}{\\overset{\\phantom{1}}{0}}$</span></td>\n<td>.</td>\n<td><span data-jme-visible=\"ctencarry=1\">$\\overset{1}{\\var{cdigs[2]}}$</span> <span data-jme-visible=\"ctencarry=0\">$\\overset{\\phantom{1}}{\\var{cdigs[2]}}$</span></td>\n<td><span data-jme-visible=\"cunitcarry=1\">$\\overset{1}{\\var{cdigs[1]}}$</span> <span data-jme-visible=\"cunitcarry=0\">$\\overset{\\phantom{0}}{\\var{cdigs[1]}}$</span></td>\n<td>$\\overset{\\phantom{1}}{\\var{cdigs[0]}}$</td>\n<td>$+$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td>$\\color{green}{0}$</td>\n<td>.</td>\n<td>$\\var{cdigs[5]}$</td>\n<td>$\\var{cdigs[4]}$</td>\n<td>$\\var{cdigs[3]}$</td>\n<td></td>\n</tr>\n<tr>\n<td>$\\color{red}{\\var{chuncarry}}$</td>\n<td>.</td>\n<td>$\\var{chunsumlastdigit}$</td>\n<td>$\\var{ctenSumlastdigit}$</td>\n<td>${\\var{cunitSumLastDigit}}$</td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p>The answer is therefore $\\var{cans}$.</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "cans", "maxValue": "cans", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "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/"}]}