// Numbas version: exam_results_page_options
{"name": "Merryn's copy of Subtraction", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Merryn's copy of Subtraction", "tags": ["algorithms", "minus", "subtracting", "subtraction", "take away"], "metadata": {"description": "<p>The subtraction algortihm using the borrow and pay back method with integers.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Write the following question down on paper and evaluate it without using a calculator using any method you choose.</p>\n<p>If you click on <em>Show steps</em> you will see full working using the standard algorithm. Click on <em>Try another question like this one</em> to get a new pair of numbers.</p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"newtopten": {"name": "newtopten", "group": "c", "definition": "if(unitdiff>=0,top[1],top[1]-1)", "description": "", "templateType": "anything", "can_override": false}, "ansunit": {"name": "ansunit", "group": "c", "definition": "mod(ans,10)", "description": "", "templateType": "anything", "can_override": false}, "hundiff": {"name": "hundiff", "group": "c", "definition": "if(tendiff>=0,top[2]-bot[2],top[2]-1-bot[2])", "description": "", "templateType": "anything", "can_override": false}, "botnum": {"name": "botnum", "group": "c", "definition": "bot[0]+bot[1]*10+bot[2]*100", "description": "", "templateType": "anything", "can_override": false}, "ansten": {"name": "ansten", "group": "c", "definition": "mod(floor(ans/10),10)", "description": "", "templateType": "anything", "can_override": false}, "tendiff": {"name": "tendiff", "group": "c", "definition": "if(unitdiff>=0,top[1]-bot[1],top[1]-1-bot[1])", "description": "", "templateType": "anything", "can_override": false}, "unitdiff": {"name": "unitdiff", "group": "c", "definition": "top[0]-bot[0]", "description": "", "templateType": "anything", "can_override": false}, "bot": {"name": "bot", "group": "c", "definition": "random(\nif(top[0]<9,[random(top[0]+1..9), random(top[1]..9), random(1..top[2]-1)],\n      if(top[1]<9,[random(top[0]..9), random(top[1]+1..9), random(1..top[2]-1)],\"error\")),\nif(top[1]<9,[random(0..top[0]), random(top[1]+1..9), random(1..top[2]-1)],\n      if(top[1]=9,[random(top[0]..9), random(0..9), random(1..top[2]-1)],\"error\"))\n)\n", "description": "<p>This should force some borrowing and <g class=\"gr_ gr_4 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar multiReplace\" id=\"4\" data-gr-id=\"4\">paying</g> back, and that the&nbsp;final answer&nbsp;is positive.</p>", "templateType": "anything", "can_override": false}, "newtophun": {"name": "newtophun", "group": "c", "definition": "if(tendiff>=0,top[2],top[2]-1)", "description": "", "templateType": "anything", "can_override": false}, "topnum": {"name": "topnum", "group": "c", "definition": "top[0]+top[1]*10+top[2]*100", "description": "", "templateType": "anything", "can_override": false}, "anshun": {"name": "anshun", "group": "c", "definition": "mod(floor(ans/100),10)", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "c", "definition": "topnum-botnum", "description": "", "templateType": "anything", "can_override": false}, "top": {"name": "top", "group": "c", "definition": "random([random(0..9),random(1..8),random(2..9)],[random(0..8),random(1..9),random(2..9)])", "description": "<p>Borrowing from the hundreds to do the units is not covered with this randomisation. We will do that in another part.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "c", "variables": ["top", "bot", "topnum", "botnum", "ans", "unitdiff", "tendiff", "hundiff", "ansunit", "ansten", "anshun", "newtopten", "newtophun"]}], "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{topnum}-\\var{botnum} = $&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&nbsp;we set up $\\var{topnum}-\\var{botnum}$&nbsp;with the <em>ones,&nbsp;</em><em>tens</em> and&nbsp;<em>hundreds</em>&nbsp;columns lined up vertically:</p>\n<table>\n<tbody>\n<tr>\n<td></td>\n<td>$\\var{top[2]}$</td>\n<td>$\\var{top[1]}$</td>\n<td>$\\var{top[0]}$</td>\n<td>$-$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td></td>\n<td>$\\var{bot[2]}$</td>\n<td>$\\var{bot[1]}$</td>\n<td>$\\var{bot[0]}$</td>\n<td></td>\n</tr>\n<tr>\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 try to subtract the digits in the <g class=\"gr_ gr_38 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar multiReplace\" id=\"38\" data-gr-id=\"38\">ones</g> column.</p>\n<p><span data-jme-visible=\"unitdiff&gt;=0\">Since this is $\\var{ansunit}$ we&nbsp;write $\\var{ansunit}$ under the line in the ones column.</span></p>\n<p><span data-jme-visible=\"unitdiff&lt;0\">Since we can't&nbsp;take $\\var{bot[0]}$ away from $\\var{top[0]}$ (without using negative numbers) we <em>borrow</em>&nbsp;a ten from the tens column. This means we cross out the $\\var{top[1]}$ in the tens column&nbsp;and replace it with a $\\var{top[1]-1}$, and the $\\var{top[0]}$ becomes a $\\var{10+top[0]}$. Now we can do&nbsp;$\\var{10+top[0]}-\\var{bot[0]}$, and write the result, $\\var{ansunit}$, under the line in the ones column.</span>&nbsp;</p>\n<table>\n<tbody>\n<tr>\n<td></td>\n<td>$\\overset{\\phantom{1}}{\\var{top[2]}}$</td>\n<td><span data-jme-visible=\"unitdiff&lt;0\">$\\overset{\\color{red}{\\var{newtopten}}}{\\var{top[1]}\\mkern-7.5mu\\color{red}/}$</span> <span data-jme-visible=\"unitdiff&gt;=0\">$\\overset{\\phantom{1}}{\\var{top[1]}}$</span></td>\n<td><span data-jme-visible=\"unitdiff&lt;0\">$\\color{red}{^1}\\overset{\\phantom{1}}{\\var{top[0]}}$</span> <span data-jme-visible=\"unitdiff&gt;=0\">$\\overset{\\phantom{1}}{\\var{top[0]}}$</span></td>\n<td>$-$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td></td>\n<td>$\\var{bot[2]}$</td>\n<td>$\\var{bot[1]}$</td>\n<td>$\\var{bot[0]}$</td>\n<td></td>\n</tr>\n<tr>\n<td></td>\n<td></td>\n<td></td>\n<td>$\\color{red}{\\var{ansunit}}$</td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>Now we&nbsp;try to subtract the digits in the tens column.</p>\n<p><span data-jme-visible=\"tendiff&gt;=0\">Since this is $\\var{ansten}$ we&nbsp;write $\\var{ansten}$ under the line in the tens column.</span></p>\n<p><span data-jme-visible=\"tendiff&lt;0\">Since we can't&nbsp;take $\\var{bot[1]}$ away from $\\var{newtopten}$ (without using negative numbers) we <em>borrow</em>&nbsp;a hundred from the hundred column. This means we cross out the $\\var{top[2]}$ in the hundreds column&nbsp;and replace it with a $\\var{top[2]-1}$, and the $\\var{newtopten}$ in the tens column becomes a $\\var{10+newtopten}$. Now we can do&nbsp;$\\var{10+newtopten}-\\var{bot[1]}$, and write the result, $\\var{ansten}$, under the line in the tens column.</span>&nbsp;</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td></td>\n<td>\n<p><span data-jme-visible=\"tendiff&lt;0\">$\\overset{\\color{red}{\\var{newtophun}}}{\\var{top[2]}\\mkern-7.5mu\\color{red}{/}}$</span> <span data-jme-visible=\"tendiff&gt;=0\">$\\overset{\\phantom{1}}{\\var{top[2]}}$</span></p>\n</td>\n<td>\n<p><span data-jme-visible=\"unitdiff&lt;0 and tendiff&lt;0\">$\\overset{\\color{red}{1}\\var{newtopten}}{\\var{top[1]}\\mkern-7.5mu/}$</span> <span data-jme-visible=\"unitdiff&lt;0 and tendiff&gt;=0\">$\\overset{\\var{newtopten}}{\\var{top[1]}\\mkern-7.5mu/}$</span> <span data-jme-visible=\"unitdiff&gt;=0 and tendiff&lt;0\">$\\color{red}{^1}\\overset{\\phantom{1}}{\\var{top[1]}}$</span> <span data-jme-visible=\"unitdiff&gt;=0 and tendiff&gt;=0\">$\\overset{\\phantom{1}}{\\var{top[1]}}$</span></p>\n</td>\n<td><span data-jme-visible=\"unitdiff&lt;0\">${^1}\\overset{\\phantom{1}}{\\var{top[0]}}$</span> <span data-jme-visible=\"unitdiff&gt;=0\">$\\overset{\\phantom{1}}{\\var{top[0]}}$</span></td>\n<td>$-$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td></td>\n<td>$\\var{bot[2]}$</td>\n<td>$\\var{bot[1]}$</td>\n<td>$\\var{bot[0]}$</td>\n<td></td>\n</tr>\n<tr>\n<td></td>\n<td></td>\n<td>$\\color{red}{\\var{ansten}}$</td>\n<td>$\\var{ansunit}$</td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>Now we&nbsp;try to subtract the digits in the hundreds column.</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td></td>\n<td>\n<p><span data-jme-visible=\"tendiff&lt;0\">$\\overset{\\var{newtophun}}{\\var{top[2]}\\mkern-7.5mu/}$</span> <span data-jme-visible=\"tendiff&gt;=0\">$\\overset{\\phantom{1}}{\\var{top[2]}}$</span></p>\n</td>\n<td>\n<p><span data-jme-visible=\"unitdiff&lt;0 and tendiff&lt;0\">$\\overset{{1}\\var{newtopten}}{\\var{top[1]}\\mkern-7.5mu/}$</span> <span data-jme-visible=\"unitdiff&lt;0 and tendiff&gt;=0\">$\\overset{\\var{newtopten}}{\\var{top[1]}\\mkern-7.5mu/}$</span> <span data-jme-visible=\"unitdiff&gt;=0 and tendiff&lt;0\">${^1}\\overset{\\phantom{1}}{\\var{top[1]}}$</span> <span data-jme-visible=\"unitdiff&gt;=0 and tendiff&gt;=0\">$\\overset{\\phantom{1}}{\\var{top[1]}}$</span></p>\n</td>\n<td><span data-jme-visible=\"unitdiff&lt;0\">${^1}\\overset{\\phantom{1}}{\\var{top[0]}}$</span> <span data-jme-visible=\"unitdiff&gt;=0\">$\\overset{\\phantom{1}}{\\var{top[0]}}$</span></td>\n<td>$-$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td></td>\n<td>$\\var{bot[2]}$</td>\n<td>$\\var{bot[1]}$</td>\n<td>$\\var{bot[0]}$</td>\n<td></td>\n</tr>\n<tr>\n<td></td>\n<td>$\\color{red}{\\var{anshun}}$</td>\n<td>$\\var{ansten}$</td>\n<td>$\\var{ansunit}$</td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>The answer is therefore $\\var{ans}$.</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": "ans", "maxValue": "ans", "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", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}