// Numbas version: exam_results_page_options {"name": "Determining the resulting sign of an arithmetic operation", "extensions": [], "custom_part_types": [], "resources": [["question-resources/drawingresize_grbP9s8.svg", "/srv/numbas/media/question-resources/drawingresize_grbP9s8.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "variable_groups": [], "name": "Determining the resulting sign of an arithmetic operation", "functions": {}, "rulesets": {}, "ungrouped_variables": ["dec", "neg", "pos"], "metadata": {"description": "

Given an equation with an unknown, determine if the unknown is positive or negative.

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First part is the product of two numbers; second part is the product of three.

", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "advice": "

The following rules apply to multiplication and division.

\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\n\n\n\n\n\n\n\n\n\n\n\n\n\n
First signoperationSecond signResulting signExample
$+$$\\times or \\div$$+$$+$$3 \\times 2 = 6$
$+$$\\times or \\div$$-$$-$$3 \\times (-2) = -6$
$-$$\\times or \\div$$+$$-$$(-3) \\times 2 = -6$
$-$$\\times or \\div$$-$$+$$(-3) \\times (-2) = 6$
\n

#### a)

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$(\\var{neg[4]}) \\times (\\var{neg[5]})$ will be positive, as negative times negative gives us positive.

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#### b)

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$\\var{pos[4]} \\times (\\var{neg[6]}) \\times \\var{dec[5]}$ will be negative, as positive times negative times positive gives us negative.

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To check these:

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\\\begin{align} a &=(\\var{neg[4]}) \\times (\\var{neg[5]}) \\\\&= + \\var{neg[4]*neg[5]} \\text{ (positive),} \\\\ b &= \\var{pos[4]} \\times (\\var{neg[6]}) \\times \\var{dec[5]} \\\\&= \\var{pos[4]*neg[6]*dec[5]} \\text{ (negative).} \\end{align} \

", "statement": "

Decide whether each of the following numbers is positive or negative.

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Random positive integers.

", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(1..300),5)"}, "dec": {"name": "dec", "description": "

Random decimals.

", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(0..50 #0.01 except 0..50), 7)"}, "neg": {"name": "neg", "description": "

Random negative integers.

", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(-300..-1),8)"}}, "parts": [{"variableReplacementStrategy": "originalfirst", "prompt": "

$a = (\\var{neg[4]}) \\times (\\var{neg[5]})$ [[0]]

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$a$ is positive

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$a$ is negative

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$b = \\var{pos[4]} \\times (\\var{neg[6]}) \\times \\var{dec[5]}$ [[0]]

\n

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$b$ is positive

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$b$ is negative

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