// Numbas version: exam_results_page_options
{"name": "Decimals: Subtraction", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Decimals: Subtraction", "tags": [], "metadata": {"description": "<p>Subtracting a decimal with 3 decimal places from a decimal with 2 or 3 decimal places. borrowing is necessary. This was modified from a subtraction question using integers with each number divided by 1000 so the variables have names referring to ones, tens, hundreds etc.</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": "<p class=\"p1\">Write the following question down on paper and evaluate&nbsp;it without using a calculator.</p>\n<p class=\"p1\">If you are unsure of how to do&nbsp;a question, click on&nbsp;<i>Show steps</i>&nbsp;to see the full working. Then, once you understand how to do the question, click on&nbsp;<i>Try another question like this one</i>&nbsp;to start again.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"tendiff": {"name": "tendiff", "group": "c", "definition": "if(unitdiff>=0,top[1]-bot[1],top[1]-1-bot[1])", "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}, "newtopten": {"name": "newtopten", "group": "c", "definition": "if(unitdiff>=0,top[1],top[1]-1)", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "c", "definition": "topnum-botnum", "description": "", "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}, "anshun": {"name": "anshun", "group": "c", "definition": "mod(floor(ans*10),10)", "description": "", "templateType": "anything", "can_override": false}, "topnum": {"name": "topnum", "group": "c", "definition": "top[0]/1000+top[1]/100+top[2]/10", "description": "", "templateType": "anything", "can_override": false}, "ansunit": {"name": "ansunit", "group": "c", "definition": "mod(ans*1000,10)", "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": "if(top[0]<>0, \n  random(\n    [0, random(top[1]+1..9), random(1..top[2]-1)],\n    [random(top[0]+1..9), random(0..9), random(1..top[2]-1)]), \n [random(1..9), random(2..9), 1])\n\n//original \n//random(\n//if(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\"),\n//if(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\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}, "top": {"name": "top", "group": "c", "definition": "random([random(1..8),random(1..8),random(2..9)],[0,random(1..9),random(2..9)])", "description": "<p>the digits of a 2 or 3 decimal place number</p>", "templateType": "anything", "can_override": false}, "botnum": {"name": "botnum", "group": "c", "definition": "bot[0]/1000+bot[1]/100+bot[2]/10", "description": "", "templateType": "anything", "can_override": false}, "ansten": {"name": "ansten", "group": "c", "definition": "mod(floor(ans*100),10)", "description": "", "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 $\\var{topnum}-\\var{botnum}$ with the decimal points lined up vertically so that the columns with the same place value are also lined up vertically. <span data-jme-visible=\"top[0]=0 or bot[0]=0\">We also&nbsp;<em>pad out</em> the decimals with zeros:</span></p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td>$0$</td>\n<td>.</td>\n<td>$\\var{top[2]}$</td>\n<td>$\\var{top[1]}$</td>\n<td><span data-jme-visible=\"top[0]=0\">$\\color{red}{\\var{top[0]}}$</span> <span data-jme-visible=\"top[0]&lt;&gt;0\">$\\var{top[0]}$</span></td>\n<td>$-$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td>$0$</td>\n<td>.</td>\n<td>$\\var{bot[2]}$</td>\n<td>$\\var{bot[1]}$</td>\n<td><span data-jme-visible=\"bot[0]=0\">$\\color{red}{\\var{bot[0]}}$</span> <span data-jme-visible=\"bot[0]&lt;&gt;0\">$\\var{bot[0]}$</span></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 try to subtract the digits in the column to the far right (in this case, the&nbsp;<em>thousandths</em>&nbsp;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&nbsp;this 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;from the next column to the left (in this case, the <em>hundredths</em> column). This means we cross out the $\\var{top[1]}$ in the&nbsp;hundredths 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 thousandths column.</span>&nbsp;</p>\n<table>\n<tbody>\n<tr>\n<td>$\\overset{\\phantom{1}}{0}$</td>\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\">$\\color{red}{^1}\\overset{\\phantom{1}}{\\color{green}{\\var{top[0]}}}$</span> <span data-jme-visible=\"unitdiff&gt;=0\">$\\overset{\\phantom{1}}{\\color{green}{\\var{top[0]}}}$</span></td>\n<td>$-$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td>$0$</td>\n<td>.</td>\n<td>$\\var{bot[2]}$</td>\n<td>$\\var{bot[1]}$</td>\n<td>$\\color{green}{\\var{bot[0]}}$</td>\n<td></td>\n</tr>\n<tr>\n<td></td>\n<td>.</td>\n<td></td>\n<td></td>\n<td>$\\color{red}{\\var{ansunit}}$</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 hundredths 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&nbsp;this 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;from the next column to the left (in this case, the <em>tenths</em> column). This means we cross out the $\\var{top[2]}$ in the&nbsp;tenths column&nbsp;and replace it with a $\\var{top[2]-1}$, and the $\\var{newtopten}$ in the&nbsp;hundredths 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 hundredths.</span>&nbsp;</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td>$\\overset{\\phantom{1}}{0}$</td>\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\">$\\overset{\\color{red}{1}\\color{green}{\\var{newtopten}}}{\\var{top[1]}\\mkern-7.5mu/}$</span> <span data-jme-visible=\"unitdiff&lt;0 and tendiff&gt;=0\">$\\overset{\\color{green}{\\var{newtopten}}}{\\var{top[1]}\\mkern-7.5mu/}$</span> <span data-jme-visible=\"unitdiff&gt;=0 and tendiff&lt;0\">$\\color{red}{^1}\\overset{\\phantom{1}}{\\color{green}{\\var{top[1]}}}$</span> <span data-jme-visible=\"unitdiff&gt;=0 and tendiff&gt;=0\">$\\overset{\\phantom{1}}{\\color{green}{\\var{top[1]}}}$</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>$0$</td>\n<td>.</td>\n<td>$\\var{bot[2]}$</td>\n<td>$\\color{green}{\\var{bot[1]}}$</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>$\\color{red}{\\var{ansten}}$</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&nbsp;tenths column and&nbsp;then subtract the digits in the ones column.</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td>$\\overset{\\phantom{1}}{\\color{green}{0}}$</td>\n<td>.</td>\n<td>\n<p><span data-jme-visible=\"tendiff&lt;0\">$\\overset{\\color{green}{\\var{newtophun}}}{\\var{top[2]}\\mkern-7.5mu/}$</span> <span data-jme-visible=\"tendiff&gt;=0\">$\\overset{\\phantom{1}}{\\color{green}{\\var{top[2]}}}$</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>$\\color{green}0$</td>\n<td>.</td>\n<td>$\\color{green}{\\var{bot[2]}}$</td>\n<td>$\\var{bot[1]}$</td>\n<td>$\\var{bot[0]}$</td>\n<td></td>\n</tr>\n<tr>\n<td>$\\color{red}0$</td>\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></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/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}