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Recall the following:
\nThe above gives us (amoung other things) that
\n$\\displaystyle \\var{c}\\times \\frac{\\var{a}}{\\var{b}}$ | \n$=\\displaystyle\\var{c}\\times\\var{a}\\div\\var{b}$ | \n
\n | $=\\displaystyle\\frac{\\var{a}}{\\var{b}}\\times\\var{c}$ | \n
\n | $=\\displaystyle(\\var{a}\\div\\var{b})\\times\\var{c}$ | \n
\n | $=\\displaystyle\\frac{\\var{a}}{\\var{b}}\\times\\frac{\\var{c}}{1}$ | \n
\n | $=\\displaystyle\\frac{\\var{a}\\times\\var{c}}{\\var{b}}$ | \n
\n | $=\\displaystyle\\frac{\\var{c}\\times\\var{a}}{\\var{b}}$ | \n
\n | $=\\displaystyle\\frac{\\var{c}}{\\var{b}}\\times\\var{a}$ | \n
\n | $=\\displaystyle\\var{c}\\div\\var{b}\\times\\var{a}$ | \n
\n | $=\\displaystyle\\var{a}\\times\\frac{\\var{c}}{\\var{b}}$ | \n
\n | $=\\displaystyle\\var{a}\\times\\var{c}\\div\\var{b}$ | \n
\n | $=\\displaystyle\\var{a}\\times\\var{c}\\times\\frac{1}{\\var{b}}$ | \n
Students seem to not realise that $\\frac{a}{b}\\times c=c\\times\\frac{a}{b}=\\frac{a\\times c}{b}=\\frac{c\\times a}{b}=a\\times c \\div b=a\\div b\\times c=c\\div b \\times a \\ne c \\div (b\\times a)\\ldots $ etc. This question is my attempt to help rectify this.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "Without the use of a calculator and without actually calculating the values of each answer, which of the following are equal to $\\displaystyle \\var{c}\\times \\frac{\\var{a}}{\\var{b}}$?
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