// Numbas version: exam_results_page_options {"name": "Simon's copy of Q4 & 5 Arithmetic", "extensions": [], "custom_part_types": [], "resources": [["question-resources/bodmas.png", "/srv/numbas/media/question-resources/bodmas.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "

Arithmetic

\n

rebelmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "variables": {"e7": {"definition": "pos()", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "e7"}, "ans5e": {"definition": "ans5a * ans5b", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "ans5e"}, "ans5a": {"definition": "e2 * e5", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "ans5a"}, "e5": {"definition": "pos()", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "e5"}, "ans22": {"definition": "abs(ans2a)-(ans2b*abs(ans2))", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "ans22"}, "e8": {"definition": "pos()", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "e8"}, "c4": {"definition": "random(2..5)+c7", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": 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"random(1..{d5}-1)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "d6"}, "ans4d": {"definition": "ans4a*d2", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "ans4d"}, "b5": {"definition": "pos()", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "b5"}, "b4": {"definition": "random(2..5)+b7", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "b4"}, "ans44": {"definition": "abs(ans4c)-(ans4d*abs(ans4))", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "ans44"}, "ans666": {"definition": "floor(ans6/ans6a)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "ans666"}, "d5": {"definition": "pos()", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "d5"}, "ans4c": {"definition": "(((d2*d1)+d3))* ans4b", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "ans4c"}, "ans3": {"definition": "floor(ans3d/ans3c)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "ans3"}, "f5": {"definition": "pos()", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "f5"}, "d3": {"definition": "random(1..{d2}-1)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "d3"}, "b1": {"definition": "pos()", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "b1"}, "D2": {"definition": "pos()", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "D2"}, "ans11": {"definition": "ans1a-(ans1b*ans1)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "ans11"}, "d7": {"definition": "pos()", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "d7"}, 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When adding and/or subtracting fractions, do the following;

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First convert any mixed numbers to improper fractions e.g. $1\\frac{2}{3} = \\frac{5}{3}$

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Find the lowest common multiple of the denominators i.e. $\\frac{5}{3} + \\frac{1}{2} = \\frac{}{6}$

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Next, transform each fraction into an equivalent fraction with the denominator equal to this LCM i.e. $\\frac{5}{3} + \\frac{1}{2} = \\frac{10}{6} + \\frac{3}{6}$

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Add/subtract the numbers above the denominator i.e. $\\frac{10}{6} + \\frac{3}{6} = \\frac{10 + 3}{6} = \\frac{13}{6} = 2\\frac{1}{6}$

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When multiplying fractions, multiply the numbers above the line by each other and then the numbers below the line by each other i.e.

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$\\frac{5}{3} \\times \\frac{1}{4} = \\frac{5}{12}$

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If possible simplify the answer i.e.

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$\\frac{5}{3} \\times \\frac{1}{5} = \\frac{5}{15} = \\frac{1}{3}$

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If there are more than 2 fractions, follow the same rules:

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i.e. $\\frac{5}{3} \\times \\frac{1}{4} \\times \\frac{2}{5} \\times \\frac{3}{2} = \\frac{30}{120} = \\frac{1}{4}$

\n

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When dividing fractions, flip the SECOND fraction upside down and then follow the rules for multiplying fractions i.e.

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$\\frac{5}{3} \\div \\frac{3}{4} = \\frac{5}{3} \\times \\frac{4}{3} = \\frac{20}{9}$

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If possible simplify the answer i.e.

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$\\frac{5}{3} \\div \\frac{4}{21} = \\frac{5}{3} \\times \\frac{21}{4} = \\frac{105}{12} = \\frac{35}{4} = 8\\frac{3}{4}$

\n

\n

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Evaluate the following without using a calculator:

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Answer in whole number and/or fraction!!

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Remember the BODMAS rule

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N.B. 

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Give your answers as mixed fractions, writing the whole number part in the first box, and the fraction part in the second box.

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If there is no whole number part, place 0 in the first box.

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E.g. $\\frac{7}{2} = 3\\frac{1}{2} =>  $ first box $ =3 $, second box$ =\\frac{1}{2}$

\n

E.g. $\\frac{1}{3} => $ first box $ =0 $, second box$  =\\frac{1}{3}$

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$\\simplify{{a2}/{a1}} + \\simplify{{a4}/{a3}} - \\simplify{{a6}/{a5}}$

\n

[[0]][[1]]

\n

\n

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$\\var{b1}\\simplify{{b3}/{b2}} + \\var{b4}\\simplify{{b6}/{b5}}  - \\var{b7}\\simplify{{b9}/{b8}} $

\n

[[0]][[1]]

", "customMarkingAlgorithm": "", "gaps": [{"type": "numberentry", "marks": 1, "unitTests": [], "variableReplacementStrategy": "originalfirst", "maxValue": "{ans2}", "showCorrectAnswer": true, "showFeedbackIcon": true, "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "minValue": "{ans2}", "mustBeReduced": false, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true, "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "allowFractions": true}, {"type": "numberentry", "marks": 1, "unitTests": [], "variableReplacementStrategy": "originalfirst", "maxValue": "{ans22}/{ans2b}", "showCorrectAnswer": true, "showFeedbackIcon": true, "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "minValue": "{ans22}/{ans2b}", "mustBeReduced": false, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true, "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "allowFractions": true}], "sortAnswers": false, "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true}, {"type": "gapfill", "marks": 0, "unitTests": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "

$\\var{c1}\\simplify{{c3}/{c2}} \\times \\var{c4}\\simplify{{c6}/{c5}} - \\var{c7}\\simplify{{c9}/{c8}} $

\n

[[0]][[1]]

", "customMarkingAlgorithm": "", "gaps": [{"type": "numberentry", "marks": 1, "unitTests": [], "variableReplacementStrategy": "originalfirst", "maxValue": "{ans3}", "showCorrectAnswer": true, "showFeedbackIcon": true, "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "minValue": "{ans3}", "mustBeReduced": false, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true, "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "allowFractions": true}, {"type": "numberentry", "marks": 1, "unitTests": [], "variableReplacementStrategy": "originalfirst", "maxValue": "{ans33}/{ans3c}", "showCorrectAnswer": true, "showFeedbackIcon": true, "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "minValue": "{ans33}/{ans3c}", "mustBeReduced": false, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true, "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "allowFractions": true}], "sortAnswers": false, "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true}, {"type": "gapfill", "marks": 0, "unitTests": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "

$\\var{d1}\\simplify{{d3}/{d2}} \\div (\\var{d4}\\simplify{{d6}/{d5}} \\times \\var{d7}\\simplify{{d9}/{d8}}) $

\n

[[0]][[1]]

", "customMarkingAlgorithm": "", "gaps": [{"type": "numberentry", "marks": 1, "unitTests": [], "variableReplacementStrategy": "originalfirst", "maxValue": "{ans4}", "showCorrectAnswer": true, "showFeedbackIcon": true, "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "minValue": "{ans4}", "mustBeReduced": false, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true, "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "allowFractions": true}, {"type": "numberentry", "marks": 1, "unitTests": [], "variableReplacementStrategy": "originalfirst", "maxValue": "{ans44}/{ans4d}", "showCorrectAnswer": true, "showFeedbackIcon": true, "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "minValue": "{ans44}/{ans4d}", "mustBeReduced": false, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true, "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "allowFractions": true}], "sortAnswers": false, "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true}, {"type": "gapfill", "marks": 0, "unitTests": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "

$\\frac{\\var{e1}\\simplify{{e3}/{e2}} \\times \\var{e4}\\simplify{{e6}/{e5}}}{\\var{e7}\\simplify{{e9}/{e8}} \\times \\var{e10}\\simplify{{e12}/{e11}}}$

\n

[[0]][[1]]

", "customMarkingAlgorithm": "", "gaps": [{"type": "numberentry", "marks": 1, "unitTests": [], "variableReplacementStrategy": "originalfirst", "maxValue": "{ans555}", "showCorrectAnswer": true, "showFeedbackIcon": true, "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "minValue": "{ans555}", "mustBeReduced": false, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true, "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "allowFractions": true}, {"type": "numberentry", "marks": 1, "unitTests": [], "variableReplacementStrategy": "originalfirst", "maxValue": "{ans55}/{ans5e}", "showCorrectAnswer": true, "showFeedbackIcon": true, "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "minValue": "{ans55}/{ans5e}", "mustBeReduced": false, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true, "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "allowFractions": true}], "sortAnswers": false, "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true}, {"type": "gapfill", "marks": 0, "unitTests": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "

$\\var{f1}\\simplify{{f3}/{f2}} \\div \\var{f4}\\simplify{{f6}/{f5}}$ 

\n

[[0]][[1]]

\n

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