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

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

Evaluate

$$\frac{2183}{460}\approx 4.745652174$$

Solution Steps

Least common multiple of 10 and 5 is 10. Convert \frac{3}{10} and \frac{4}{5} to fractions with denominator 10.

$$\frac{\frac{3}{10}+\frac{8}{10}+\frac{35}{100}-\frac{4}{10}+\frac{7}{2}}{\frac{92}{100}}-\frac{1}{5}$$

Since \frac{3}{10} and \frac{8}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+8}{10}+\frac{35}{100}-\frac{4}{10}+\frac{7}{2}}{\frac{92}{100}}-\frac{1}{5}$$

Add 3 and 8 to get 11.

$$\frac{\frac{11}{10}+\frac{35}{100}-\frac{4}{10}+\frac{7}{2}}{\frac{92}{100}}-\frac{1}{5}$$

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

$$\frac{\frac{11}{10}+\frac{7}{20}-\frac{4}{10}+\frac{7}{2}}{\frac{92}{100}}-\frac{1}{5}$$

Least common multiple of 10 and 20 is 20. Convert \frac{11}{10} and \frac{7}{20} to fractions with denominator 20.

$$\frac{\frac{22}{20}+\frac{7}{20}-\frac{4}{10}+\frac{7}{2}}{\frac{92}{100}}-\frac{1}{5}$$

Since \frac{22}{20} and \frac{7}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{22+7}{20}-\frac{4}{10}+\frac{7}{2}}{\frac{92}{100}}-\frac{1}{5}$$

Add 22 and 7 to get 29.

$$\frac{\frac{29}{20}-\frac{4}{10}+\frac{7}{2}}{\frac{92}{100}}-\frac{1}{5}$$

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

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

Least common multiple of 20 and 5 is 20. Convert \frac{29}{20} and \frac{2}{5} to fractions with denominator 20.

$$\frac{\frac{29}{20}-\frac{8}{20}+\frac{7}{2}}{\frac{92}{100}}-\frac{1}{5}$$

Since \frac{29}{20} and \frac{8}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{29-8}{20}+\frac{7}{2}}{\frac{92}{100}}-\frac{1}{5}$$

Subtract 8 from 29 to get 21.

$$\frac{\frac{21}{20}+\frac{7}{2}}{\frac{92}{100}}-\frac{1}{5}$$

Least common multiple of 20 and 2 is 20. Convert \frac{21}{20} and \frac{7}{2} to fractions with denominator 20.

$$\frac{\frac{21}{20}+\frac{70}{20}}{\frac{92}{100}}-\frac{1}{5}$$

Since \frac{21}{20} and \frac{70}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{21+70}{20}}{\frac{92}{100}}-\frac{1}{5}$$

Add 21 and 70 to get 91.

$$\frac{\frac{91}{20}}{\frac{92}{100}}-\frac{1}{5}$$

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

$$\frac{\frac{91}{20}}{\frac{23}{25}}-\frac{1}{5}$$

Divide \frac{91}{20} by \frac{23}{25} by multiplying \frac{91}{20} by the reciprocal of \frac{23}{25}.

$$\frac{91}{20}\times \frac{25}{23}-\frac{1}{5}$$

Multiply \frac{91}{20} times \frac{25}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{91\times 25}{20\times 23}-\frac{1}{5}$$

Do the multiplications in the fraction \frac{91\times 25}{20\times 23}.

$$\frac{2275}{460}-\frac{1}{5}$$

Reduce the fraction \frac{2275}{460} to lowest terms by extracting and canceling out 5.

$$\frac{455}{92}-\frac{1}{5}$$

Least common multiple of 92 and 5 is 460. Convert \frac{455}{92} and \frac{1}{5} to fractions with denominator 460.

$$\frac{2275}{460}-\frac{92}{460}$$

Since \frac{2275}{460} and \frac{92}{460} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2275-92}{460}$$

Subtract 92 from 2275 to get 2183.

$$\frac{2183}{460}$$

Factor

$$\frac{37 \cdot 59}{2 ^ {2} \cdot 5 \cdot 23} = 4\frac{343}{460} = 4.745652173913044$$