// Numbas version: finer_feedback_settings
{"name": "Musa's copy of Fractions are division", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Musa's copy of Fractions are division", "tags": [], "metadata": {"description": "<p>Divisor is single digit. There is&nbsp;a remainder which we express as a decimal by continuing the long division process.&nbsp;Rounding is required to one decimal place.&nbsp;The working suggests determining the second decimal place&nbsp;so the student knows whether to round up or down.</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&nbsp;<em>Show steps</em>&nbsp;to see the full working. Then, once you understand how to do the question, click on&nbsp;<em>Try another question like this one</em>&nbsp;to start again.</p>", "advice": "", "rulesets": {}, "extensions": [], "variables": {"prod0": {"name": "prod0", "group": "Ungrouped variables", "definition": "divisor1*qd0", "description": "", "templateType": "anything"}, "diff1": {"name": "diff1", "group": "Ungrouped variables", "definition": "b1-prod1", "description": "", "templateType": "anything"}, "b1": {"name": "b1", "group": "Ungrouped variables", "definition": "10*diff2+dd1", "description": "", "templateType": "anything"}, "diff0": {"name": "diff0", "group": "Ungrouped variables", "definition": "b0-prod0", "description": "", "templateType": "anything"}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "precround(quotient1,1)", "description": "", "templateType": "anything"}, "dd2": {"name": "dd2", "group": "Ungrouped variables", "definition": "mod(floor(dividend1),10)", "description": "", "templateType": "anything"}, "b2": {"name": "b2", "group": "Ungrouped variables", "definition": "10*diff3+dd2", "description": "", "templateType": "anything"}, "remainder": {"name": "remainder", "group": "Ungrouped variables", "definition": "mod(dividend1,divisor1)", "description": "", "templateType": "anything"}, "dividend1": {"name": "dividend1", "group": "Ungrouped variables", "definition": "random(25..99 except list(divisor1/2..99#divisor1/2))\n//divisor1*quotient1+remainder/100", "description": "", "templateType": "anything"}, "diff3": {"name": "diff3", "group": "Ungrouped variables", "definition": "dd3-prod3", "description": "", "templateType": "anything"}, "qd0": {"name": "qd0", "group": "Ungrouped variables", "definition": "mod(floor(quotient1*100),10)", "description": "", "templateType": "anything"}, "divisor1": {"name": "divisor1", "group": "Ungrouped variables", "definition": "random(3..9 except 5)", "description": "<p>excluded 5 so that the decimal part is longer than 1 place.</p>", "templateType": "anything"}, "prod1": {"name": "prod1", "group": "Ungrouped variables", "definition": "divisor1*qd1", "description": "", "templateType": "anything"}, "dd3": {"name": "dd3", "group": "Ungrouped variables", "definition": "mod(floor(dividend1/10),10)", "description": "", "templateType": "anything"}, "qd3": {"name": "qd3", "group": "Ungrouped variables", "definition": "mod(floor(quotient1/10),10)", "description": "", "templateType": "anything"}, "diff2": {"name": "diff2", "group": "Ungrouped variables", "definition": "b2-prod2", "description": "", "templateType": "anything"}, "b0": {"name": "b0", "group": "Ungrouped variables", "definition": "10*diff1+dd0", "description": "", "templateType": "anything"}, "prod3": {"name": "prod3", "group": "Ungrouped variables", "definition": "divisor1*qd3", "description": "", "templateType": "anything"}, "quotient1": {"name": "quotient1", "group": "Ungrouped variables", "definition": "dividend1/divisor1\n//random(ceil(1001/divisor1)..floor(9999/divisor1) except list(100..10000#10))/100", "description": "", "templateType": "anything"}, "qd1": {"name": "qd1", "group": "Ungrouped variables", "definition": "mod(floor(quotient1*10),10)", "description": "", "templateType": "anything"}, "dd0": {"name": "dd0", "group": "Ungrouped variables", "definition": "mod(dividend1*100,10)", "description": "", "templateType": "anything"}, "dd1": {"name": "dd1", "group": "Ungrouped variables", "definition": "mod(floor(dividend1*10),10)", "description": "", "templateType": "anything"}, "prod2": {"name": "prod2", "group": "Ungrouped variables", "definition": "divisor1*qd2", "description": "", "templateType": "anything"}, "qd2": {"name": "qd2", "group": "Ungrouped variables", "definition": "mod(floor(quotient1),10)", "description": "<p>qd2</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["divisor1", "remainder", "quotient1", "dividend1", "dd0", "dd1", "dd2", "dd3", "qd3", "qd2", "qd1", "qd0", "prod3", "prod2", "prod1", "prod0", "diff3", "b2", "diff2", "b1", "diff1", "b0", "diff0", "ans"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>$\\displaystyle\\frac{\\var{dividend1}}{\\var{divisor1}}=$[[0]]&nbsp;(1 decimal place)&nbsp;</p>\n<p></p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>We want to calculate&nbsp;$\\frac{\\var{dividend1}}{\\var{divisor1}}$,&nbsp;which is just the same as $\\var{dividend1}\\div\\var{divisor1}$, since both of these expressions mean \"how many $\\var{divisor1}$s go into $\\var{dividend1}$?\"</p>\n<p></p>\n<p>The long division algorithm allows you to work&nbsp;this out by working from the left to the right of $\\var{dividend1}$ whilst respecting place value. We normally set up the division in the following way:</p>\n<p style=\"text-align: left;\">$\\var{divisor1} \\strut \\overline{\\smash{\\raise.09ex{)}}\\var{dividend1}}$</p>\n<p>Note the positions of the numbers!</p>\n<p>Actually, since we want the answer to <strong>one decimal place</strong>&nbsp;we add as many zeroes after the decimal place to ensure we have <strong>two decimal places!&nbsp;</strong></p>\n<p style=\"text-align: left;\">$\\var{divisor1} \\strut \\overline{\\smash{\\raise.09ex{)}}{\\var{dd3}}\\var{dd2}.\\!\\var{dd1}\\var{dd0}}$</p>\n<p>Why two? We use&nbsp;that extra digit to determine whether to round up or down.</p>\n<p>The algorithm (or procedure) seems complicated at first but you might find a&nbsp;mnemonic helps to remember the steps. We work left to right doing the following steps</p>\n<ol>\n<li>Divide</li>\n<li>Multiply</li>\n<li>Subtract</li>\n<li>Bring down&nbsp;</li>\n</ol>\n<p>and repeating until we run out of digits. The steps form the acronym <strong>DMSB</strong>. Popular&nbsp;mnemonics include \"Does McDonalds Sell Burgers?\", \"Dracula Must Suck Blood\" and \"Dead Mice Smell Bad\".</p>\n<p></p>\n<p>We need to know the $\\var{divisor1}$ times tables or write the $\\var{divisor1}$ times tables out (be repeatedly adding $\\var{divisor1}$) so that we can refer to them.</p>\n<p>\\[\\boxed{\\begin{align}1\\times\\var{divisor1}&amp;=\\var{divisor1}\\\\2\\times\\var{divisor1}&amp;=\\var{2*divisor1}\\\\3\\times\\var{divisor1}&amp;=\\var{3*divisor1}\\\\4\\times\\var{divisor1}&amp;=\\var{4*divisor1}\\\\5\\times\\var{divisor1}&amp;=\\var{5*divisor1}\\\\6\\times\\var{divisor1}&amp;=\\var{6*divisor1}\\\\7\\times\\var{divisor1}&amp;=\\var{7*divisor1}\\\\8\\times\\var{divisor1}&amp;=\\var{8*divisor1}\\\\9\\times\\var{divisor1}&amp;=\\var{9*divisor1}\\end{align}}\\]</p>\n<p style=\"text-align: left;\"><strong></strong></p>\n<p style=\"text-align: left;\"><strong>The&nbsp;tens column</strong></p>\n<p><strong>D:</strong> The first thing we ask ourselves is, \"How many $\\color{green}{\\var{divisor1}}$s go into $\\color{green}{\\var{dd3}}$?\" (note this&nbsp;$\\var{dd3}$ actually represents&nbsp;$\\var{dd3*10}$ since it is in the tens column)&nbsp;</p>\n<p><span data-jme-visible=\"qd3=0\">Well, none!&nbsp;$\\var{divisor1}$ is too big to fit into $\\var{dd3}$. So we write $\\color{red}0$ above the $\\var{dd3}$ in the&nbsp;tens column:</span> <span data-jme-visible=\"qd3&gt;1\">Well, $\\var{qd3}\\times \\var{divisor1}=\\var{prod3}$ so $\\var{qd3}$ fit&nbsp;and we write&nbsp;$\\color{red}{\\var{qd3}}$ above&nbsp;the $\\var{dd3}$ in the&nbsp;tens column:&nbsp;</span> <span data-jme-visible=\"qd3=1\">Well, $\\var{qd3}\\times \\var{divisor1}=\\var{prod3}$ so $\\var{qd3}$ fits&nbsp;and we write&nbsp;$\\color{red}{\\var{qd3}}$ above&nbsp;the $\\var{dd3}$ in the tens column:&nbsp;</span></p>\n<p>$\\begin{array}{r} \\color{red}{\\var{qd3}\\phantom{\\var{qd2}.\\!\\var{qd1}\\var{qd0}}} \\\\[-.5cm] \\color{green}{\\var{divisor1}} \\strut \\overline{\\smash{\\raise.09ex{)}}\\color{green}{\\var{dd3}}\\var{dd2}.\\!\\var{dd1}\\var{dd0}} \\end{array}$</p>\n<p><strong>M:</strong> Now since $\\color{green}{\\var{qd3}}\\times \\color{green}{\\var{divisor1}}=\\var{prod3}$ we write&nbsp;$\\color{red}{\\var{prod3}}$ underneath in the&nbsp;tens column:</p>\n<p>&nbsp;$\\begin{array}{r} \\color{green}{\\var{qd3}\\phantom{\\var{qd2}.\\!\\var{qd1}\\var{qd0}}} \\\\[-.5cm] \\color{green}{\\var{divisor1}} \\strut \\overline{\\smash{\\raise.09ex{)}}{\\var{dd3}}\\var{dd2}.\\!\\var{dd1}\\var{dd0}} \\\\[-.5cm] \\color{red}{\\var{prod3}}\\phantom{5.55}\\end{array}$</p>\n<p><strong>S:</strong> We now do&nbsp;the subtraction, $\\color{green}{\\var{dd3}-\\var{prod3}}$, to determine the <em>remainder</em> (what remains to be divided) in the&nbsp;tens column.&nbsp;</p>\n<p>$\\begin{array}{r} {\\var{qd3}\\phantom{\\var{qd2}.\\!\\var{qd1}\\var{qd0}}} \\\\[-.7cm] {\\var{divisor1}} \\strut \\overline{\\smash{\\raise.09ex{)}}\\color{green}{\\var{dd3}}\\var{dd2}.\\!\\var{dd1}\\var{dd0}} \\\\[-0.5cm]&nbsp;\\underline{\\color{green}{\\var{prod3}}}\\phantom{5.55}\\\\[-.7cm]\\color{red}{\\var{diff3}}\\phantom{5.55}\\end{array}$</p>\n<p><strong>B:</strong> Now we bring the $\\color{green}{\\var{dd2}}$ in the&nbsp;ones column down next to the&nbsp;remainder so that&nbsp;it forms $\\var{diff3}\\var{dd2}$.</p>\n<p>$\\begin{array}{r} {\\var{qd3}\\phantom{\\var{qd2}.\\!\\var{qd1}\\var{qd0}}} \\\\[-.7cm] {\\var{divisor1}} \\strut \\overline{\\smash{\\raise.09ex{)}}{\\var{dd3}}\\color{green}{\\var{dd2}}.\\!\\var{dd1}\\var{dd0}} \\\\[-0.5cm]&nbsp;\\underline{{\\var{prod3}}}\\phantom{5.55}\\\\[-.7cm]{\\var{diff3}}\\color{red}{\\var{dd2}}\\phantom{.55}\\end{array}$</p>\n<p></p>\n<p style=\"text-align: left;\"><strong>The&nbsp;ones column</strong></p>\n<p><strong>D:</strong>&nbsp;Now we ask ourselves, \"How many $\\color{green}{\\var{divisor1}}$s go into $\\color{green}{\\var{b2}}$?\" (note this&nbsp;$\\var{b2}$ does actually represent $\\var{b2}$ since it is in the ones column)</p>\n<p><span data-jme-visible=\"qd2=0\">Well, none!&nbsp;$\\var{divisor1}$ is too big to fit into $\\var{b2}$. So we write $\\color{red}0$ above the $\\var{dd2}$ in the&nbsp;ones column:</span> <span data-jme-visible=\"qd2&gt;1\">Well, $\\var{qd2}\\times \\var{divisor1}=\\var{prod2}$ so $\\var{qd2}$ fit&nbsp;and we write&nbsp;$\\color{red}{\\var{qd2}}$ above&nbsp;the $\\var{dd2}$ in the&nbsp;ones column:&nbsp;</span> <span data-jme-visible=\"qd2=1\">Well, $\\var{qd2}\\times \\var{divisor1}=\\var{prod2}$ so $\\var{qd2}$ fits&nbsp;and we write&nbsp;$\\color{red}{\\var{qd2}}$ above&nbsp;the $\\var{dd2}$ in the&nbsp;ones column:&nbsp;</span></p>\n<p>$\\begin{array}{r} {\\var{qd3}\\color{red}{\\var{qd2}}\\phantom{.\\!\\var{qd1}\\var{qd0}}} \\\\[-.7cm] \\color{green}{\\var{divisor1}} \\strut \\overline{\\smash{\\raise.09ex{)}}{\\var{dd3}}{\\var{dd2}}.\\!\\var{dd1}\\var{dd0}} \\\\[-0.5cm]&nbsp;\\underline{{\\var{prod3}}}\\phantom{5.55}\\\\[-.7cm]\\color{green}{\\var{diff3}\\var{dd2}}\\phantom{.55}\\end{array}$</p>\n<p><strong>M:</strong> Now since $\\color{green}{\\var{qd2}}\\times \\color{green}{\\var{divisor1}}=\\var{prod2}$ we write&nbsp;$\\color{red}{\\var{prod2}}$ underneath in the ones&nbsp;column:</p>\n<p>$\\begin{array}{r} {\\var{qd3}\\color{green}{\\var{qd2}}\\phantom{.\\!\\var{qd1}\\var{qd0}}} \\\\[-.7cm] \\color{green}{\\var{divisor1}} \\strut \\overline{\\smash{\\raise.09ex{)}}{\\var{dd3}}{\\var{dd2}}.\\!\\var{dd1}\\var{dd0}} \\\\[-0.5cm]&nbsp;\\underline{{\\var{prod3}}}\\phantom{5.55}\\\\[-.7cm]{\\var{diff3}\\var{dd2}}\\phantom{.55}\\\\[-0.5cm]\\color{red}{\\var{prod2}}\\phantom{.55}\\end{array}$</p>\n<p><strong>S:</strong> We now do&nbsp;the subtraction, $\\color{green}{\\var{b2}-\\var{prod2}}$, to determine the <em>remainder</em> (what remains to be divided) in the&nbsp;ones column.&nbsp;</p>\n<p>$\\begin{array}{r} {\\var{qd3}{\\var{qd2}}\\phantom{.\\!\\var{qd1}\\var{qd0}}} \\\\[-.7cm] {\\var{divisor1}} \\strut \\overline{\\smash{\\raise.09ex{)}}{\\var{dd3}}{\\var{dd2}}.\\!\\var{dd1}\\var{dd0}} \\\\[-0.5cm]&nbsp;\\underline{{\\var{prod3}}}\\phantom{5.55}\\\\[-.7cm]\\color{green}{\\var{diff3}\\var{dd2}}\\phantom{.55}\\\\[-0.5cm]\\underline{\\color{green}{\\var{prod2}}}\\phantom{.55}\\\\[-0.5cm]\\color{red}{\\var{diff2}}\\phantom{.55}\\end{array}$</p>\n<p><strong>B:</strong> Now we bring the $\\color{green}{\\var{dd1}}$ in the&nbsp;tenths column down next to the&nbsp;remainder so that&nbsp;it forms $\\var{diff2}\\var{dd1}$.</p>\n<p>$\\begin{array}{r} {\\var{qd3}{\\var{qd2}}\\phantom{.\\!\\var{qd1}\\var{qd0}}} \\\\[-.7cm] {\\var{divisor1}} \\strut \\overline{\\smash{\\raise.09ex{)}}{\\var{dd3}}{\\var{dd2}}.\\!\\color{green}{\\var{dd1}}\\var{dd0}} \\\\[-0.5cm]&nbsp;\\underline{{\\var{prod3}}}\\phantom{5.55}\\\\[-.7cm]{\\var{diff3}\\var{dd2}}\\phantom{.55}\\\\[-0.5cm]\\underline{{\\var{prod2}}}\\phantom{.55}\\\\[-0.5cm]\\var{diff2}\\phantom{.}\\color{red}{\\var{dd1}}\\phantom{5}\\end{array}$</p>\n<p></p>\n<p style=\"text-align: left;\"><strong>The tenths column</strong></p>\n<p><strong>D:</strong>&nbsp;Now we ask ourselves, \"How many $\\color{green}{\\var{divisor1}}$s go into $\\color{green}{\\var{b1}}$?\" (note this&nbsp;$\\var{b1}$ actually represents&nbsp;$\\var{b1/10}$ since it is in the tenths column)</p>\n<p><span data-jme-visible=\"qd1=0\">Well, none!&nbsp;$\\var{divisor1}$ is too big to fit into $\\var{b1}$. So we write $\\color{red}0$ above the $\\var{dd1}$ in the tenths column:</span> <span data-jme-visible=\"qd1&gt;1\">Well, $\\var{qd1}\\times \\var{divisor1}=\\var{prod1}$ so $\\var{qd1}$ fit&nbsp;and we write&nbsp;$\\color{red}{\\var{qd1}}$ above&nbsp;the $\\var{dd1}$ in the tenths column:&nbsp;</span> <span data-jme-visible=\"qd1=1\">Well, $\\var{qd1}\\times \\var{divisor1}=\\var{prod1}$ so $\\var{qd1}$ fits&nbsp;and we write&nbsp;$\\color{red}{\\var{qd1}}$ above&nbsp;the $\\var{dd1}$ in the tenths column:&nbsp;</span></p>\n<p>$\\begin{array}{r} {\\var{qd3}{\\var{qd2}}.\\!\\color{red}{\\var{qd1}}\\phantom{\\var{qd0}}} \\\\[-.7cm] \\color{green}{\\var{divisor1}} \\strut \\overline{\\smash{\\raise.09ex{)}}{\\var{dd3}}{\\var{dd2}}.\\!{\\var{dd1}}\\var{dd0}} \\\\[-0.5cm]&nbsp;\\underline{{\\var{prod3}}}\\phantom{5.55}\\\\[-.7cm]{\\var{diff3}\\var{dd2}}\\phantom{.55}\\\\[-0.5cm]\\underline{{\\var{prod2}}}\\phantom{.55}\\\\[-0.5cm]\\color{green}{\\var{diff2}\\phantom{.}\\var{dd1}}\\phantom{5}\\end{array}$</p>\n<p><strong>M:</strong> Now since $\\color{green}{\\var{qd1}}\\times \\color{green}{\\var{divisor1}}=\\var{prod1}$ we write&nbsp;$\\color{red}{\\var{prod1}}$ underneath in the tenths&nbsp;column:</p>\n<p>$\\begin{array}{r} {\\var{qd3}{\\var{qd2}}.\\!\\color{green}{\\var{qd1}}\\phantom{\\var{qd0}}} \\\\[-.7cm] \\color{green}{\\var{divisor1}} \\strut \\overline{\\smash{\\raise.09ex{)}}{\\var{dd3}}{\\var{dd2}}.\\!{\\var{dd1}}\\var{dd0}} \\\\[-0.5cm]&nbsp;\\underline{{\\var{prod3}}}\\phantom{5.55}\\\\[-.7cm]{\\var{diff3}\\var{dd2}}\\phantom{.55}\\\\[-0.5cm]\\underline{{\\var{prod2}}}\\phantom{.55}\\\\[-0.5cm]{\\var{diff2}\\phantom{.}\\var{dd1}}\\phantom{5}\\\\[-0.5cm]\\color{red}{\\var{prod1}}\\phantom{5}\\end{array}$</p>\n<p><strong>S:</strong> We now do&nbsp;the subtraction, $\\color{green}{\\var{b1}-\\var{prod1}}$, to determine the <em>remainder</em> (what remains to be divided) in the&nbsp;tenths column.&nbsp;</p>\n<p>$\\begin{array}{r} {\\var{qd3}{\\var{qd2}}.\\!{\\var{qd1}}\\phantom{\\var{qd0}}} \\\\[-.7cm] {\\var{divisor1}} \\strut \\overline{\\smash{\\raise.09ex{)}}{\\var{dd3}}{\\var{dd2}}.\\!{\\var{dd1}}\\var{dd0}} \\\\[-0.5cm]&nbsp;\\underline{{\\var{prod3}}}\\phantom{5.55}\\\\[-.7cm]{\\var{diff3}\\var{dd2}}\\phantom{.55}\\\\[-0.5cm]\\underline{{\\var{prod2}}}\\phantom{.55}\\\\[-0.5cm]\\color{green}{\\var{diff2}\\phantom{.}\\var{dd1}}\\phantom{5}\\\\[-0.5cm]\\underline{\\color{green}{\\var{prod1}}}\\phantom{5}\\\\[-0.5cm] \\color{red}{\\var{diff1}}\\phantom{5}\\end{array}$</p>\n<p><strong>B:</strong> Now we bring the $\\color{green}{\\var{dd0}}$ in the&nbsp;hundredths column down next to the&nbsp;remainder so that&nbsp;it forms $\\var{diff1}\\var{dd0}$.</p>\n<p>$\\begin{array}{r} {\\var{qd3}{\\var{qd2}}.\\!{\\var{qd1}}\\phantom{\\var{qd0}}} \\\\[-.7cm] {\\var{divisor1}} \\strut \\overline{\\smash{\\raise.09ex{)}}{\\var{dd3}}{\\var{dd2}}.\\!{\\var{dd1}}\\color{green}{\\var{dd0}}} \\\\[-0.5cm]&nbsp;\\underline{{\\var{prod3}}}\\phantom{5.55}\\\\[-.7cm]{\\var{diff3}\\var{dd2}}\\phantom{.55}\\\\[-0.5cm]\\underline{{\\var{prod2}}}\\phantom{.55}\\\\[-0.5cm]{\\var{diff2}\\phantom{.}\\var{dd1}}\\phantom{5}\\\\[-0.5cm]\\underline{{\\var{prod1}}}\\phantom{5}\\\\[-0.5cm] {\\var{diff1}}\\color{red}{\\var{dd0}}\\end{array}$</p>\n<p></p>\n<p style=\"text-align: left;\"><strong>The&nbsp;hundredths column</strong></p>\n<p><strong>D:</strong>&nbsp;Now we ask ourselves, \"How many $\\color{green}{\\var{divisor1}}$s go into $\\color{green}{\\var{b0}}$?\"&nbsp;(note this&nbsp;$\\var{b0}$ actually represents&nbsp;$\\var{b0/100}$ since it is in the hundredths column)</p>\n<p><span data-jme-visible=\"qd0=0\">Well, none!&nbsp;$\\var{divisor1}$ is too big to fit into $\\var{b0}$. So we write $\\color{red}0$ above the $\\var{dd0}$ in the hundredths&nbsp;column:</span> <span data-jme-visible=\"qd0&gt;1\">Well, $\\var{qd0}\\times \\var{divisor1}=\\var{prod0}$ so $\\var{qd0}$ fit&nbsp;and we write&nbsp;$\\color{red}{\\var{qd0}}$ above&nbsp;the $\\var{dd0}$ in the&nbsp;hundredths column:&nbsp;</span> <span data-jme-visible=\"qd0=1\">Well, $\\var{qd0}\\times \\var{divisor1}=\\var{prod0}$ so $\\var{qd0}$ fits&nbsp;and we write&nbsp;$\\color{red}{\\var{qd0}}$ above&nbsp;the $\\var{dd0}$ in the hundredths column:&nbsp;</span></p>\n<p>$\\begin{array}{r} {\\var{qd3}{\\var{qd2}}.\\!{\\var{qd1}}\\color{red}{\\var{qd0}}} \\\\[-.7cm] \\color{green}{\\var{divisor1}} \\strut \\overline{\\smash{\\raise.09ex{)}}{\\var{dd3}}{\\var{dd2}}.\\!{\\var{dd1}}{\\var{dd0}}} \\\\[-0.5cm]&nbsp;\\underline{{\\var{prod3}}}\\phantom{5.55}\\\\[-.7cm]{\\var{diff3}\\var{dd2}}\\phantom{.55}\\\\[-0.5cm]\\underline{{\\var{prod2}}}\\phantom{.55}\\\\[-0.5cm]{\\var{diff2}\\phantom{.}\\var{dd1}}\\phantom{5}\\\\[-0.5cm]\\underline{{\\var{prod1}}}\\phantom{5}\\\\[-0.5cm] \\color{green}{\\var{diff1}\\var{dd0}}\\end{array}$</p>\n<p><strong>M:</strong> Now since $\\color{green}{\\var{qd0}}\\times \\color{green}{\\var{divisor1}}=\\var{prod0}$ we write&nbsp;$\\color{red}{\\var{prod0}}$ underneath in the&nbsp;hundredths column:</p>\n<p>$\\begin{array}{r} {\\var{qd3}{\\var{qd2}}.\\!{\\var{qd1}}\\color{green}{\\var{qd0}}} \\\\[-.7cm] \\color{green}{\\var{divisor1}} \\strut \\overline{\\smash{\\raise.09ex{)}}{\\var{dd3}}{\\var{dd2}}.\\!{\\var{dd1}}{\\var{dd0}}} \\\\[-0.5cm]&nbsp;\\underline{{\\var{prod3}}}\\phantom{5.55}\\\\[-.7cm]{\\var{diff3}\\var{dd2}}\\phantom{.55}\\\\[-0.5cm]\\underline{{\\var{prod2}}}\\phantom{.55}\\\\[-0.5cm]{\\var{diff2}\\phantom{.}\\var{dd1}}\\phantom{5}\\\\[-0.5cm]\\underline{{\\var{prod1}}}\\phantom{5}\\\\[-0.5cm]{\\var{diff1}\\var{dd0}}\\\\[-0.5cm]\\color{red}{\\var{prod0}}\\end{array}$</p>\n<p><strong>S:</strong> We now do&nbsp;the subtraction, $\\color{green}{\\var{b0}-\\var{prod0}}$, to determine the <em>remainder</em> (what remains to be divided) in the&nbsp;hundredths&nbsp;column.&nbsp;</p>\n<p>$\\begin{array}{r} {\\var{qd3}{\\var{qd2}}.\\!{\\var{qd1}}{\\var{qd0}}} \\\\[-.7cm] {\\var{divisor1}} \\strut \\overline{\\smash{\\raise.09ex{)}}{\\var{dd3}}{\\var{dd2}}.\\!{\\var{dd1}}{\\var{dd0}}} \\\\[-0.5cm]&nbsp;\\underline{{\\var{prod3}}}\\phantom{5.55}\\\\[-.7cm]{\\var{diff3}\\var{dd2}}\\phantom{.55}\\\\[-0.5cm]\\underline{{\\var{prod2}}}\\phantom{.55}\\\\[-0.5cm]{\\var{diff2}\\phantom{.}\\var{dd1}}\\phantom{5}\\\\[-0.5cm]\\underline{{\\var{prod1}}}\\phantom{5}\\\\[-0.5cm]\\color{green}{\\var{diff1}\\var{dd0}}\\\\[-0.5cm]\\underline{\\color{green}{\\var{prod0}}}\\\\[-0.5cm]\\color{red}{\\var{diff0}}\\end{array}$</p>\n<p><br/><strong></strong></p>\n<p>Now we could keep adding zeros and continue the procedure but we only needed&nbsp;to determine&nbsp;the second decimal place in order to correctly round to one decimal place and so we now stop the procedure.</p>\n<p>Since the second decimal place was $\\var{qd0}$ we round <span data-jme-visible=\"qd0&gt;=5\">up</span>&nbsp;<span data-jme-visible=\"qd0&lt;5\">down</span> to $\\var{ans}$.&nbsp;Therefore, $\\frac{\\var{dividend1}}{\\var{divisor1}}=\\var{ans}$ (1 dec. pl.).</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "ans", "maxValue": "ans", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "type": "question", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}]}