// Numbas version: exam_results_page_options
{"name": "Ben's copy of Subtraction", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "tags": [], "extensions": [], "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>", "parts": [{"steps": [{"unitTests": [], "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>", "customMarkingAlgorithm": "", "customName": "", "showFeedbackIcon": true, "variableReplacements": [], "type": "information", "marks": 0, "extendBaseMarkingAlgorithm": true, "useCustomName": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true}], "unitTests": [], "prompt": "<p>$\\var{topnum}-\\var{botnum} = $&nbsp;[[0]]</p>\n<p>$\\var{topnum}-\\var{botnum} = $&nbsp;[[0]]</p>", "customMarkingAlgorithm": "", "customName": "", "stepsPenalty": "1", "showFeedbackIcon": true, "variableReplacements": [], "type": "gapfill", "sortAnswers": false, "marks": 0, "extendBaseMarkingAlgorithm": true, "useCustomName": false, "gaps": [{"maxValue": "ans", "showFractionHint": true, "unitTests": [], "customMarkingAlgorithm": "", "customName": "", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "variableReplacements": [], "allowFractions": false, "mustBeReduced": false, "type": "numberentry", "correctAnswerFraction": false, "correctAnswerStyle": "plain", "marks": 1, "extendBaseMarkingAlgorithm": true, "useCustomName": false, "minValue": "ans", "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true}], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true}], "advice": "", "functions": {}, "variables": {"bot": {"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", "group": "c", "definition": "random(\nif(top[0]<9,[random(top[0]+1..9), random(top[1]..9), random(1..top[2]-1)],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)],if(top[1]=9,[random(top[0]..9), random(0..9), random(1..top[2]-1)]),\"error\")\n)\n", "name": "bot"}, "botnum": {"description": "", "templateType": "anything", "group": "c", "definition": "bot[0]+bot[1]*10+bot[2]*100", "name": "botnum"}, "tendiff": {"description": "", "templateType": "anything", "group": "c", "definition": "if(unitdiff>=0,top[1]-bot[1],top[1]-1-bot[1])", "name": "tendiff"}, "top": {"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", "group": "c", "definition": "random([random(0..9),random(1..8),random(2..9)],[random(0..8),random(1..9),random(2..9)])", "name": "top"}, "ansten": {"description": "", "templateType": "anything", "group": "c", "definition": "mod(floor(ans/10),10)", "name": "ansten"}, "newtophun": {"description": "", "templateType": "anything", "group": "c", "definition": "if(tendiff>=0,top[2],top[2]-1)", "name": "newtophun"}, "ansunit": {"description": "", "templateType": "anything", "group": "c", "definition": "mod(ans,10)", "name": "ansunit"}, "topnum": {"description": "", "templateType": "anything", "group": "c", "definition": "top[0]+top[1]*10+top[2]*100", "name": "topnum"}, "newtopten": {"description": "", "templateType": "anything", "group": "c", "definition": "if(unitdiff>=0,top[1],top[1]-1)", "name": "newtopten"}, "ans": {"description": "", "templateType": "anything", "group": "c", "definition": "topnum-botnum", "name": "ans"}, "unitdiff": {"description": "", "templateType": "anything", "group": "c", "definition": "top[0]-bot[0]", "name": "unitdiff"}, "anshun": {"description": "", "templateType": "anything", "group": "c", "definition": "mod(floor(ans/100),10)", "name": "anshun"}, "hundiff": {"description": "", "templateType": "anything", "group": "c", "definition": "if(tendiff>=0,top[2]-bot[2],top[2]-1-bot[2])", "name": "hundiff"}}, "preamble": {"js": "", "css": ""}, "ungrouped_variables": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variable_groups": [{"name": "c", "variables": ["top", "bot", "topnum", "botnum", "ans", "tendiff", "hundiff", "ansunit", "ansten", "anshun", "unitdiff", "newtopten", "newtophun"]}], "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"}, "name": "Ben's copy of Subtraction", "type": "question", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Ben George", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3372/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Ben George", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3372/"}]}