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83.3 recurring divided by 1.3 recurring

 Oct 13, 2017
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83.3 recurring is the same as \(83\frac{1}{3}\)

1.3 recurring is the same as \(1\frac{1}{3}\)

So your problem is equivalent to \(\frac{83\frac{1}{3}}{1\frac{1}{3}}\)

To be clearer, make them both into improper fractions.

Multiply the whole number by the denominator and add it to the numerator.

For the top, 83*3=249

Adding that to the numerator gives 250.

For the bottom, 1*3=3

Adding that to the numerator gives 4.

\(\frac{\frac{250}{3}}{\frac{4}{3}}\)

Anything divided by a fraction is the same as it multiplied by the fraction's reciprocal.

\(\frac{250}{3}*\frac{3}{4}\)

250*3=750

3*4=12

\(\frac{750}{12}\)

Simplify

\(\frac{750}{12}=\frac{375}{6}\)

That is as far as that fraction can be simplified, but it is equivalent to 62.5

\(\frac{750}{12}=\frac{375}{6}=62.5\)

.
 Oct 13, 2017

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