Solve (83.21/12+5.87/9+4.27/32-5.22/32)frac{22.4}{100}

$$( \frac { 83.21 } { 12 } + \frac { 5.87 } { 9 } + \frac { 4.27 } { 32 } - \frac { 5.22 } { 32 } ) \frac { 22.4 } { 100 }$$

Evaluate

$$\frac{1523431}{900000}\approx 1.692701111$$

Solution Steps

Expand \frac{83.21}{12} by multiplying both numerator and the denominator by 100.

$$\left(\frac{8321}{1200}+\frac{5.87}{9}+\frac{4.27}{32}-\frac{5.22}{32}\right)\times \frac{22.4}{100}$$

Expand \frac{5.87}{9} by multiplying both numerator and the denominator by 100.

$$\left(\frac{8321}{1200}+\frac{587}{900}+\frac{4.27}{32}-\frac{5.22}{32}\right)\times \frac{22.4}{100}$$

Least common multiple of 1200 and 900 is 3600. Convert \frac{8321}{1200} and \frac{587}{900} to fractions with denominator 3600.

$$\left(\frac{24963}{3600}+\frac{2348}{3600}+\frac{4.27}{32}-\frac{5.22}{32}\right)\times \frac{22.4}{100}$$

Since \frac{24963}{3600} and \frac{2348}{3600} have the same denominator, add them by adding their numerators.

$$\left(\frac{24963+2348}{3600}+\frac{4.27}{32}-\frac{5.22}{32}\right)\times \frac{22.4}{100}$$

Add 24963 and 2348 to get 27311.

$$\left(\frac{27311}{3600}+\frac{4.27}{32}-\frac{5.22}{32}\right)\times \frac{22.4}{100}$$

Expand \frac{4.27}{32} by multiplying both numerator and the denominator by 100.

$$\left(\frac{27311}{3600}+\frac{427}{3200}-\frac{5.22}{32}\right)\times \frac{22.4}{100}$$

Least common multiple of 3600 and 3200 is 28800. Convert \frac{27311}{3600} and \frac{427}{3200} to fractions with denominator 28800.

$$\left(\frac{218488}{28800}+\frac{3843}{28800}-\frac{5.22}{32}\right)\times \frac{22.4}{100}$$

Since \frac{218488}{28800} and \frac{3843}{28800} have the same denominator, add them by adding their numerators.

$$\left(\frac{218488+3843}{28800}-\frac{5.22}{32}\right)\times \frac{22.4}{100}$$

Add 218488 and 3843 to get 222331.

$$\left(\frac{222331}{28800}-\frac{5.22}{32}\right)\times \frac{22.4}{100}$$

Expand \frac{5.22}{32} by multiplying both numerator and the denominator by 100.

$$\left(\frac{222331}{28800}-\frac{522}{3200}\right)\times \frac{22.4}{100}$$

Reduce the fraction \frac{522}{3200} to lowest terms by extracting and canceling out 2.

$$\left(\frac{222331}{28800}-\frac{261}{1600}\right)\times \frac{22.4}{100}$$

Least common multiple of 28800 and 1600 is 28800. Convert \frac{222331}{28800} and \frac{261}{1600} to fractions with denominator 28800.

$$\left(\frac{222331}{28800}-\frac{4698}{28800}\right)\times \frac{22.4}{100}$$

Since \frac{222331}{28800} and \frac{4698}{28800} have the same denominator, subtract them by subtracting their numerators.

$$\frac{222331-4698}{28800}\times \frac{22.4}{100}$$

Subtract 4698 from 222331 to get 217633.

$$\frac{217633}{28800}\times \frac{22.4}{100}$$

Expand \frac{22.4}{100} by multiplying both numerator and the denominator by 10.

$$\frac{217633}{28800}\times \frac{224}{1000}$$

Reduce the fraction \frac{224}{1000} to lowest terms by extracting and canceling out 8.

$$\frac{217633}{28800}\times \frac{28}{125}$$

Multiply \frac{217633}{28800} times \frac{28}{125} by multiplying numerator times numerator and denominator times denominator.

$$\frac{217633\times 28}{28800\times 125}$$

Do the multiplications in the fraction \frac{217633\times 28}{28800\times 125}.

$$\frac{6093724}{3600000}$$

Reduce the fraction \frac{6093724}{3600000} to lowest terms by extracting and canceling out 4.

$$\frac{1523431}{900000}$$

Factor

$$\frac{7 \cdot 13 \cdot 16741}{2 ^ {5} \cdot 3 ^ {2} \cdot 5 ^ {5}} = 1\frac{623431}{900000} = 1.6927011111111112$$