Question 980537
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Using given method:
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{{{x/12.6=(83+2/3)/100}}} 
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Convert mixed fractions and decimals to improper fractions.
12.6 = 12 6/10 = 126/10 This denominator from tenths in the decimal.
83 2/3 = 251/3 This denominator from thirds in the percent.
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{{{x/(126/10)=(251/3)/100}}} Cross multiply
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{{{100x=(126/10)(251/3)}}}
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{{{100x=31626/30}}} Divide each side by 100.
{{{x=31626/3000}}} Convert right side to thousands,
multiply by {{{(1/3)/(1/3)}}} (equivalent to 1) to make it easier
to convert to decimal.
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{{{x=10542/1000}}}
{{{x=10.542}}}
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Even by hand (without calculator), I find it quicker to use:
{{{(.8367)(12.6)=10.542}}}
though the first method avoids any error from rounding.