Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions.
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\n\\[\\displaystyle \\text{Numerator is considered as a bracket } (\\var{oint}^2+ \\sqrt{\\var{eint*eint}}) \\text{ and the denominator as } (3 \\times 2 - 2 \\times 2)\\text{.}\\]
\nBefore we evaluate numerator, we calculate powers:
\n\\[\\begin{align} \\sqrt{\\var{eint*eint}} &= \\var{eint} \\text{,}
\\\\\\var{oint}^2 &= \\var{oint*oint} \\text{.} \\end{align}\\]
Before we evaluate denominator we calculate multiplications:
\n\\[\\begin{align} 3 \\times 2 &= 6 \\text{ and } \\\\ 2 \\times 2 &= 4\\text{.} \\end{align}\\]
\nPerforming addition/subtraction as the last step in evaluating numerator/denominator we get:
\n\\[ \\begin{align} (\\var{oint}^2+ \\sqrt{\\var{eint*eint}}) &= \\var{oint*oint} + \\var{eint}
\\\\&= \\var{oint*oint + eint}
\\\\\\text{and}
\\\\(3 \\times 2 - 2 \\times 2) &= 6 - 4
\\\\&= 2 \\end{align} \\]
So the fraction
\n\\[\\begin{align} \\displaystyle \\frac{(\\var{oint}^2+ \\var{eint})}{(3 \\times 2 - 2 \\times 2)} &= \\frac{\\var{(oint*oint + eint)}}{2}\\text{.} \\end{align}\\]
\nEvaluating the final bracket we get:
\n\\[(10 - 2) = 8\\text{.}\\]
\nAs we evaluated all brackets, we can continue with:
\n\\[\\displaystyle \\frac{\\var{oint}^2+ \\sqrt{\\var{eint*eint}}}{3 \\times 2 - 2 \\times 2} + (10 - 2) \\div \\var{pint} = \\frac{\\var{(oint*oint + eint)}}{2} + 8 \\div \\var{pint} \\]
\nNow, division has a priority over addition so since $\\frac{\\var{(oint*oint + eint)}}{2} = \\var{(oint*oint + eint)/2}$ and $8 \\div \\var{pint} = \\var{8/pint}$:
\n\\[\\begin{align} \\frac{\\var{(oint*oint + eint)}}{2} + 8 \\div \\var{pint} &= \\var{(oint*oint + eint)/2} + \\var{8/pint} \\\\&= \\var{(oint*oint + eint)/2 + 8/pint}\\text{.} \\end{align}\\]
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", "templateType": "anything", "can_override": false}, "oint": {"name": "oint", "group": "Ungrouped variables", "definition": "random(1..9 #2 except int except sint)", "description": "Random odd integer from 1 to 9.
", "templateType": "anything", "can_override": false}, "bint": {"name": "bint", "group": "Ungrouped variables", "definition": "random(20..50)", "description": "A random slightly bigger integer.
", "templateType": "anything", "can_override": false}, "pint": {"name": "pint", "group": "Ungrouped variables", "definition": "random(1..4 except 3)", "description": "1, 2 or 4.
", "templateType": "anything", "can_override": false}, "eint": {"name": "eint", "group": "Ungrouped variables", "definition": "random(1..9 #2 except int except sint)", "description": "Random even integer from 2 to 10.
", "templateType": "anything", "can_override": false}, "sint": {"name": "sint", "group": "Ungrouped variables", "definition": "random(2..6)", "description": "Random integer from 1 to 5.
", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["int", "sint", "eint", "oint", "pint", "bint"], "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": "$\\displaystyle \\frac{\\var{oint}^2+ \\sqrt{\\var{eint*eint}}}{3 \\times 2 - 2 \\times 2} + (10 - 2) \\div \\var{pint} =$ [[0]]
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\nFraction means the numerator divided by the denominator, these two can be thought of as brackets while the fraction itself is a division.
\nFor example,
\n\\begin{align}
\\sqrt4 + \\frac{4+11}{5} &= 4^{\\frac{1}{2}} + (4+11) \\div 5 \\\\
&= 4^{\\frac{1}{2}} + 15 \\div 5 & \\text{(BRACKETS)}\\\\
&= 2 + 15 \\div 5 & \\text{(ORDINALS)} \\\\
&= 2 + 3 & \\text{(DIVISION/multiplication)} \\\\
&= 5 \\text{ .} & \\text{(ADDITION/subtraction)}
\\end{align}