Solve (3/10+4/5*35/100-4/10+frac{7}{2})divfrac{92}{100}-frac{1}{5}=

$$( \frac{ 3 }{ 10 } + \frac{ 4 }{ 5 } \times \frac{ 35 }{ 100 } - \frac{ 4 }{ 10 } + \frac{ 7 }{ 2 } ) \div \frac{ 92 }{ 100 } - \frac{ 1 }{ 5 } =$$

Evaluate

$$\frac{19}{5}=3.8$$

Solution Steps

Reduce the fraction \frac{35}{100} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{3}{10}+\frac{4}{5}\times \frac{7}{20}-\frac{4}{10}+\frac{7}{2}}{\frac{92}{100}}-\frac{1}{5}$$

Multiply \frac{4}{5} times \frac{7}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3}{10}+\frac{4\times 7}{5\times 20}-\frac{4}{10}+\frac{7}{2}}{\frac{92}{100}}-\frac{1}{5}$$

Do the multiplications in the fraction \frac{4\times 7}{5\times 20}.

$$\frac{\frac{3}{10}+\frac{28}{100}-\frac{4}{10}+\frac{7}{2}}{\frac{92}{100}}-\frac{1}{5}$$

Reduce the fraction \frac{28}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{3}{10}+\frac{7}{25}-\frac{4}{10}+\frac{7}{2}}{\frac{92}{100}}-\frac{1}{5}$$

Least common multiple of 10 and 25 is 50. Convert \frac{3}{10} and \frac{7}{25} to fractions with denominator 50.

$$\frac{\frac{15}{50}+\frac{14}{50}-\frac{4}{10}+\frac{7}{2}}{\frac{92}{100}}-\frac{1}{5}$$

Since \frac{15}{50} and \frac{14}{50} have the same denominator, add them by adding their numerators.

$$\frac{\frac{15+14}{50}-\frac{4}{10}+\frac{7}{2}}{\frac{92}{100}}-\frac{1}{5}$$

Add 15 and 14 to get 29.

$$\frac{\frac{29}{50}-\frac{4}{10}+\frac{7}{2}}{\frac{92}{100}}-\frac{1}{5}$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{29}{50}-\frac{2}{5}+\frac{7}{2}}{\frac{92}{100}}-\frac{1}{5}$$

Least common multiple of 50 and 5 is 50. Convert \frac{29}{50} and \frac{2}{5} to fractions with denominator 50.

$$\frac{\frac{29}{50}-\frac{20}{50}+\frac{7}{2}}{\frac{92}{100}}-\frac{1}{5}$$

Since \frac{29}{50} and \frac{20}{50} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{29-20}{50}+\frac{7}{2}}{\frac{92}{100}}-\frac{1}{5}$$

Subtract 20 from 29 to get 9.

$$\frac{\frac{9}{50}+\frac{7}{2}}{\frac{92}{100}}-\frac{1}{5}$$

Least common multiple of 50 and 2 is 50. Convert \frac{9}{50} and \frac{7}{2} to fractions with denominator 50.

$$\frac{\frac{9}{50}+\frac{175}{50}}{\frac{92}{100}}-\frac{1}{5}$$

Since \frac{9}{50} and \frac{175}{50} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9+175}{50}}{\frac{92}{100}}-\frac{1}{5}$$

Add 9 and 175 to get 184.

$$\frac{\frac{184}{50}}{\frac{92}{100}}-\frac{1}{5}$$

Reduce the fraction \frac{184}{50} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{92}{25}}{\frac{92}{100}}-\frac{1}{5}$$

Reduce the fraction \frac{92}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{92}{25}}{\frac{23}{25}}-\frac{1}{5}$$

Divide \frac{92}{25} by \frac{23}{25} by multiplying \frac{92}{25} by the reciprocal of \frac{23}{25}.

$$\frac{92}{25}\times \frac{25}{23}-\frac{1}{5}$$

Multiply \frac{92}{25} times \frac{25}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{92\times 25}{25\times 23}-\frac{1}{5}$$

Cancel out 25 in both numerator and denominator.

$$\frac{92}{23}-\frac{1}{5}$$

Divide 92 by 23 to get 4.

$$4-\frac{1}{5}$$

Convert 4 to fraction \frac{20}{5}.

$$\frac{20}{5}-\frac{1}{5}$$

Since \frac{20}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20-1}{5}$$

Subtract 1 from 20 to get 19.

$$\frac{19}{5}$$

Factor

$$\frac{19}{5} = 3\frac{4}{5} = 3.8$$