// Numbas version: exam_results_page_options {"name": "Addition", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Addition", "tags": ["adding", "Addition", "addition", "algorithms", "plus"], "metadata": {"description": "

Natural numbers addition algorithm. 2 and 3 digit numbers. Carrying.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Write the following questions down on paper and evaluate them without using a calculator.

\n

If you are unsure of how to do a question, click on Show steps to see the full working. Then, once you understand how to do the question, click on Try another question like this one to start again.

", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"chuncarry": {"name": "chuncarry", "group": "Ungrouped variables", "definition": "floor(chunsum/10)", "description": "", "templateType": "anything", "can_override": false}, "ctencarry": {"name": "ctencarry", "group": "Ungrouped variables", "definition": "floor(ctensum/10)", "description": "", "templateType": "anything", "can_override": false}, "bTenSum": {"name": "bTenSum", "group": "Ungrouped variables", "definition": "bdigs[1]+bdigs[3]+bunitsumtensdigit", "description": "", "templateType": "anything", "can_override": false}, "cunitsum": {"name": "cunitsum", "group": "Ungrouped variables", "definition": "cdigs[0]+cdigs[3]", "description": "", "templateType": "anything", "can_override": false}, "bUnitSumLastDigit": {"name": "bUnitSumLastDigit", "group": "Ungrouped variables", "definition": "mod(bunitsum,10)", "description": "", "templateType": "anything", "can_override": false}, "bunitsumtensdigit": {"name": "bunitsumtensdigit", "group": "Ungrouped variables", "definition": "floor((bunitsum)/10)", "description": "", "templateType": "anything", "can_override": false}, "bans": {"name": "bans", "group": "Ungrouped variables", "definition": "b2digit+b3digit", "description": "", "templateType": "anything", "can_override": false}, "btencarry": {"name": "btencarry", "group": "Ungrouped variables", "definition": "floor(btensum/10)", "description": "", "templateType": "anything", "can_override": false}, "bdigs": {"name": "bdigs", "group": "Ungrouped variables", "definition": "shuffle(1..9)[0..5]", "description": "", "templateType": "anything", "can_override": false}, "cunitcarry": {"name": "cunitcarry", "group": "Ungrouped variables", "definition": "floor(cunitsum/10)", "description": "", "templateType": "anything", "can_override": false}, "bunitsum": {"name": "bunitsum", "group": "Ungrouped variables", "definition": "bdigs[0]+bdigs[2]", "description": "", "templateType": "anything", "can_override": false}, "threedigit2": {"name": "threedigit2", "group": "Ungrouped variables", "definition": "cdigs[3]+cdigs[4]*10+cdigs[5]*100", "description": "", "templateType": "anything", "can_override": false}, "threedigit1": {"name": "threedigit1", "group": "Ungrouped variables", "definition": "cdigs[0]+cdigs[1]*10+cdigs[2]*100", "description": "", "templateType": "anything", "can_override": false}, "chunsumlastdigit": {"name": "chunsumlastdigit", "group": "Ungrouped variables", "definition": "mod(chunsum,10)", "description": "", "templateType": "anything", "can_override": false}, "cdigs": {"name": "cdigs", "group": "Ungrouped variables", "definition": "shuffle(3..9)", "description": "", "templateType": "anything", "can_override": false}, "b2digit": {"name": "b2digit", "group": "Ungrouped variables", "definition": "bdigs[0]+bdigs[1]*10", "description": "", "templateType": "anything", "can_override": false}, "cans": {"name": "cans", "group": "Ungrouped variables", "definition": "threedigit1+threedigit2", "description": "", "templateType": "anything", "can_override": false}, "cunitsumlastdigit": {"name": "cunitsumlastdigit", "group": "Ungrouped variables", "definition": "mod(cunitsum,10)", "description": "", "templateType": "anything", "can_override": false}, "b3digit": {"name": "b3digit", "group": "Ungrouped variables", "definition": "bdigs[2]+bdigs[3]*10+bdigs[4]*100", "description": "", "templateType": "anything", "can_override": false}, "ctensumlastdigit": {"name": "ctensumlastdigit", "group": "Ungrouped variables", "definition": "mod(ctensum,10)", "description": "", "templateType": "anything", "can_override": false}, "bsumhun": {"name": "bsumhun", "group": "Ungrouped variables", "definition": "bdigs[4]+btencarry", "description": "", "templateType": "anything", "can_override": false}, "bsumhunlastdigit": {"name": "bsumhunlastdigit", "group": "Ungrouped variables", "definition": "mod(bsumhun,10)", "description": "", "templateType": "anything", "can_override": false}, "bsumhuncarry": {"name": "bsumhuncarry", "group": "Ungrouped variables", "definition": "floor(bsumhun/10)", "description": "", "templateType": "anything", "can_override": false}, "ctensum": {"name": "ctensum", "group": "Ungrouped variables", "definition": "cdigs[1]+cdigs[4]+cunitcarry", "description": "", "templateType": "anything", "can_override": false}, "chunsum": {"name": "chunsum", "group": "Ungrouped variables", "definition": "ctencarry+cdigs[2]+cdigs[5]", "description": "", "templateType": "anything", "can_override": false}, "btensumlastdigit": {"name": "btensumlastdigit", "group": "Ungrouped variables", "definition": "mod(btensum,10)", "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": ["bdigs", "b2digit", "b3digit", "bunitsum", "bUnitSumLastDigit", "bunitsumtensdigit", "bTenSum", "btensumlastdigit", "btencarry", "bsumhun", "bsumhuncarry", "bsumhunlastdigit", "bans", "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": "

$\\var{b2digit}+\\var{b3digit} = $ [[0]]

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Generally, we set up $\\var{b2digit}+\\var{b3digit}$ with the ones and the tens columns lined up vertically:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\var{bdigs[1]}$$\\var{bdigs[0]}$$+$
$\\var{bdigs[4]}$$\\var{bdigs[3]}$$\\var{bdigs[2]}$
$\\phantom{0}$
\n

\n

Now we add the digits in the ones column.

\n

This results in $\\var{bunitsum}$ and so we place $\\var{bunitsumlastdigit}$ under the line in the ones column.

\n

This results in $\\var{bunitsum}$ and so we place $\\var{bunitsumlastdigit}$ under the line in the ones column and carry the $1$ into the tens column. 

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\overset{\\color{red}1}{\\var{bdigs[1]}}$ $\\overset{\\phantom{0}}{\\var{bdigs[1]}}$$\\overset{\\phantom{1}}{\\var{bdigs[0]}}$$+$
$\\var{bdigs[4]}$$\\var{bdigs[3]}$$\\var{bdigs[2]}$
$\\color{red}{\\var{bUnitSumLastDigit}}$
\n

\n

Now we add the digits in the tens column.

\n

This results in $\\var{bTenSum}$ and so we place $\\var{bTenSumlastdigit}$ under the line in the tens column.

\n

This results in $\\var{bTenSum}$ and so we place $\\var{bTenSumlastdigit}$ under the line in the tens column and carry the $1$ into the hundreds column.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
${\\overset{\\color{red}1}{\\phantom{0}}}$ $\\phantom{0}$$\\overset{1}{\\var{bdigs[1]}}$ $\\overset{\\phantom{0}}{\\var{bdigs[1]}}$$\\overset{\\phantom{1}}{\\var{bdigs[0]}}$$+$
$\\var{bdigs[4]}$$\\var{bdigs[3]}$$\\var{bdigs[2]}$
$\\color{red}{\\var{bTenSumlastdigit}}$${\\var{bUnitSumLastDigit}}$
\n

\n

Now we add the digits in the hundreds column.

\n

This is simply $\\var{bdigs[4]}$ so we place $\\var{bdigs[4]}$ under the line in the hundreds column.

\n

This is $\\var{bsumhun}$ so we place $\\var{bsumhun}$ under the line in the hundreds column.

\n

This is $\\var{bsumhun}$ so we place $\\var{bsumhun}$ under the line so that its rightmost digit is in the hundreds column.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\overset{1}{\\phantom{0}}$ $\\phantom{0}$$\\overset{1}{\\var{bdigs[1]}}$ $\\overset{\\phantom{0}}{\\var{bdigs[1]}}$$\\overset{\\phantom{1}}{\\var{bdigs[0]}}$$+$
$\\var{bdigs[4]}$$\\var{bdigs[3]}$$\\var{bdigs[2]}$
$\\phantom{\\var{bsumhuncarry}}$ $\\color{red}{\\var{bsumhuncarry}}$$\\color{red}{\\var{bsumhunlastdigit}}$$\\var{bTenSumlastdigit}$${\\var{bUnitSumLastDigit}}$
\n

\n

\n

The answer is therefore $\\var{bans}$.

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$\\var{threedigit1}+\\var{threedigit2} = $ [[0]]

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Generally we set up $\\var{threedigit1}+\\var{threedigit2}$ with the ones, tens and hundreds columns lined up vertically:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\var{cdigs[2]}$$\\var{cdigs[1]}$$\\var{cdigs[0]}$$+$
$\\var{cdigs[5]}$$\\var{cdigs[4]}$$\\var{cdigs[3]}$
$\\phantom{0}$
\n

\n

Now we add the digits in the ones column.

\n

This results in $\\var{cunitsum}$ and so we place $\\var{cunitsumlastdigit}$ under the line in the ones column.

\n

This results in $\\var{cunitsum}$ and so we place $\\var{cunitsumlastdigit}$ under the line in the ones column and carry the $1$ into the tens column. 

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\overset{\\phantom{1}}{\\var{cdigs[2]}}$$\\overset{\\color{red}1}{\\var{cdigs[1]}}$ $\\overset{\\phantom{0}}{\\var{cdigs[1]}}$$\\overset{\\phantom{1}}{\\var{cdigs[0]}}$$+$
$\\var{cdigs[5]}$$\\var{cdigs[4]}$$\\var{cdigs[3]}$
$\\color{red}{\\var{cunitSumLastDigit}}$
\n

\n

Now we add the digits in the tens column.

\n

This results in $\\var{ctenSum}$ and so we place $\\var{ctenSumlastdigit}$ under the line in the tens column.

\n

This results in $\\var{ctenSum}$ and so we place $\\var{ctenSumlastdigit}$ under the line in the tens column and carry the $1$ into the hundreds column.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
${\\overset{\\color{red}1}{\\var{cdigs[2]}}}$ $\\overset{\\phantom{1}}{\\var{cdigs[2]}}$$\\overset{1}{\\var{cdigs[1]}}$ $\\overset{\\phantom{0}}{\\var{cdigs[1]}}$$\\overset{\\phantom{1}}{\\var{cdigs[0]}}$$+$
$\\var{cdigs[5]}$$\\var{cdigs[4]}$$\\var{cdigs[3]}$
$\\color{red}{\\var{ctenSumlastdigit}}$${\\var{cunitSumLastDigit}}$
\n

\n

Now we add the digits in the hundreds column.

\n

This is $\\var{chunsum}$ so we place $\\var{chunsum}$ under the line in the hundreds column.

\n

This is $\\var{chunsum}$ so we place $\\var{chunsum}$ under the line so that its rightmost digit is in the hundreds column.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\overset{1}{\\var{cdigs[2]}}$ $\\overset{\\phantom{1}}{\\var{cdigs[2]}}$$\\overset{1}{\\var{cdigs[1]}}$ $\\overset{\\phantom{0}}{\\var{cdigs[1]}}$$\\overset{\\phantom{1}}{\\var{cdigs[0]}}$$+$
$\\var{cdigs[5]}$$\\var{cdigs[4]}$$\\var{cdigs[3]}$
$\\phantom{\\var{chuncarry}}$ $\\color{red}{\\var{chuncarry}}$$\\color{red}{\\var{chunsumlastdigit}}$$\\var{ctenSumlastdigit}$${\\var{cunitSumLastDigit}}$
\n

\n

\n

The answer is therefore $\\var{cans}$.

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