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Choose the correct symbols to describe the relations between each of these pairs of numbers.

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Random negative integers.

", "name": "neg", "group": "Ungrouped variables", "templateType": "anything", "definition": "repeat(random(-300..-1),8)"}, "c": {"description": "", "name": "c", "group": "Ungrouped variables", "templateType": "anything", "definition": "-b"}, "random": {"description": "", "name": "random", "group": "Ungrouped variables", "templateType": "anything", "definition": "repeat(random(0..0.01#0.001),3)"}, "d": {"description": "", "name": "d", "group": "Ungrouped variables", "templateType": "anything", "definition": "-a"}, "pos": {"description": "

Random positive integers.

", "name": "pos", "group": "Ungrouped variables", "templateType": "anything", "definition": "repeat(random(1..300),5)"}, "a": {"description": "", "name": "a", "group": "Ungrouped variables", "templateType": "anything", "definition": "neg[7] + random2"}, "b": {"description": "", "name": "b", "group": "Ungrouped variables", "templateType": "anything", "definition": "neg[7] + 0.9 + random[2]"}, "dec": {"description": "

Random decimals.

", "name": "dec", "group": "Ungrouped variables", "templateType": "anything", "definition": "repeat(random(0..50 #0.01 except 0..50), 7)"}, "random2": {"description": "", "name": "random2", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(0.5..0.8#0.001)"}}, "extensions": [], "functions": {}, "tags": ["inequality", "taxonomy"], "variable_groups": [], "parts": [{"scripts": {}, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"scripts": {}, "minMarks": 0, "distractors": ["", "", ""], "variableReplacementStrategy": "originalfirst", "displayType": "dropdownlist", "choices": ["

", "

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$\\var{dec[6] + 0.001 + random[0]}$ [[0]] $\\var{dec[6] - random[1]}$

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$\\var{neg[7] + random2}$ [[0]] $\\var{neg[7] + 0.9 + random[2]}$

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$(\\var{neg[3]}) \\times (\\var{neg[2]})$ [[0]] $\\var{-neg[3]*neg[2]}$

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Complete the inequality relationships by selecting the correct symbol from a drop down box

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\\[\\begin{align} \\text{Symbol }&\\lt \\text{ denotes \"less than\".} \\\\ \\text{Symbol }&\\gt \\text{denotes \"greater than\".} \\end{align}\\]

a)

$\\var{dec[6] + 0.001 + random[0]}$ is greater than $\\var{dec[6] - random[1]}$ so

\\[\\var{dec[6] + 0.001 + random[0]} \\gt \\var{dec[6] - random[1]} \\text{.} \\]

b)

When both of the numbers that you are comparing are negative, it may be tempting to ignore the negative signs and make an incorrect assumption. For example, when we have -5 and -4 we might ignore the signs and assume -5 is larger than -4 since +5 is larger than +4. This is however wrong, -5 < -4.

To understand this a bit better, look at the following number line:

Following the number line from left to right, we can see that $\\var{neg[7] + random2}$ is less than $\\var{neg[7] + 0.9 + random[2]}$, so

\\[\\var{neg[7] + random2} \\lt \\var{neg[7] + 0.9 + random[2]} \\text{.}\\]

c)

Multiplying two negative numbers results in a positive number. Therefore we can see without performing any calculation that $(\\var{neg[3]}) \\times (\\var{neg[2]}) \\gt \\var{-neg[3]*neg[2]}$ as positive numbers are always larger than negative numbers.

\\[(\\var{neg[3]} \\times \\var{neg[2]}) \\gt \\var{-neg[3]*neg[2]}\\]

\\[\\var{neg[3] * neg[2]} \\gt \\var{-neg[3]*neg[2]}\\]

", "contributors": [{"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}]}]}], "contributors": [{"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}]}