Solve 31,61+(100-31,61/126)*0,425=

$$31,61 + ( 100 - \frac { 31,61 } { 126 } ) \cdot 0,425 =$$

Evaluate

$$\frac{37297703}{504000}\approx 74,003378968$$

Solution Steps

Expand \frac{31,61}{126} by multiplying both numerator and the denominator by 100.

$$31,61+\left(100-\frac{3161}{12600}\right)\times 0,425$$

Convert 100 to fraction \frac{1260000}{12600}.

$$31,61+\left(\frac{1260000}{12600}-\frac{3161}{12600}\right)\times 0,425$$

Since \frac{1260000}{12600} and \frac{3161}{12600} have the same denominator, subtract them by subtracting their numerators.

$$31,61+\frac{1260000-3161}{12600}\times 0,425$$

Subtract 3161 from 1260000 to get 1256839.

$$31,61+\frac{1256839}{12600}\times 0,425$$

Convert decimal number 0,425 to fraction \frac{425}{1000}. Reduce the fraction \frac{425}{1000} to lowest terms by extracting and canceling out 25.

$$31,61+\frac{1256839}{12600}\times \frac{17}{40}$$

Multiply \frac{1256839}{12600} times \frac{17}{40} by multiplying numerator times numerator and denominator times denominator.

$$31,61+\frac{1256839\times 17}{12600\times 40}$$

Do the multiplications in the fraction \frac{1256839\times 17}{12600\times 40}.

$$31,61+\frac{21366263}{504000}$$

Convert decimal number 31,61 to fraction \frac{3161}{100}.

$$\frac{3161}{100}+\frac{21366263}{504000}$$

Least common multiple of 100 and 504000 is 504000. Convert \frac{3161}{100} and \frac{21366263}{504000} to fractions with denominator 504000.

$$\frac{15931440}{504000}+\frac{21366263}{504000}$$

Since \frac{15931440}{504000} and \frac{21366263}{504000} have the same denominator, add them by adding their numerators.

$$\frac{15931440+21366263}{504000}$$

Add 15931440 and 21366263 to get 37297703.

$$\frac{37297703}{504000}$$

Factor

$$\frac{19 \cdot 1963037}{7 \cdot 2 ^ {6} \cdot 3 ^ {2} \cdot 5 ^ {3}} = 74\frac{1703}{504000} = 74.00337896825397$$