Solve (3/4+2/1)div(3/1-13/8)-(-frac{11}{6}-(frac{2}{7}+frac{1}{1})div(-frac{5}{14})+frac{1}{30})-(-frac{1}{4})

$$( \frac{ 3 }{ 4 } + \frac{ 2 }{ 1 } ) \div ( \frac{ 3 }{ 1 } - \frac{ 13 }{ 8 } )-(- \frac{ 11 }{ 6 } -( \frac{ 2 }{ 7 } + \frac{ 1 }{ 1 } ) \div (- \frac{ 5 }{ 14 } )+ \frac{ 1 }{ 30 } )-(- \frac{ 1 }{ 4 } )$$

Evaluate

$$\frac{9}{20}=0.45$$

Solution Steps

Divide 1 by 1 to get 1.

$$\frac{\frac{3}{4}+\frac{2}{1}}{\frac{3}{1}-\frac{13}{8}}-\left(-\frac{11}{6}-\frac{\frac{2}{7}+1}{-\frac{5}{14}}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Anything divided by one gives itself.

$$\frac{\frac{3}{4}+2}{\frac{3}{1}-\frac{13}{8}}-\left(-\frac{11}{6}-\frac{\frac{2}{7}+1}{-\frac{5}{14}}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Convert 2 to fraction \frac{8}{4}.

$$\frac{\frac{3}{4}+\frac{8}{4}}{\frac{3}{1}-\frac{13}{8}}-\left(-\frac{11}{6}-\frac{\frac{2}{7}+1}{-\frac{5}{14}}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Since \frac{3}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+8}{4}}{\frac{3}{1}-\frac{13}{8}}-\left(-\frac{11}{6}-\frac{\frac{2}{7}+1}{-\frac{5}{14}}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Add 3 and 8 to get 11.

$$\frac{\frac{11}{4}}{\frac{3}{1}-\frac{13}{8}}-\left(-\frac{11}{6}-\frac{\frac{2}{7}+1}{-\frac{5}{14}}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Anything divided by one gives itself.

$$\frac{\frac{11}{4}}{3-\frac{13}{8}}-\left(-\frac{11}{6}-\frac{\frac{2}{7}+1}{-\frac{5}{14}}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Convert 3 to fraction \frac{24}{8}.

$$\frac{\frac{11}{4}}{\frac{24}{8}-\frac{13}{8}}-\left(-\frac{11}{6}-\frac{\frac{2}{7}+1}{-\frac{5}{14}}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Since \frac{24}{8} and \frac{13}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{11}{4}}{\frac{24-13}{8}}-\left(-\frac{11}{6}-\frac{\frac{2}{7}+1}{-\frac{5}{14}}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Subtract 13 from 24 to get 11.

$$\frac{\frac{11}{4}}{\frac{11}{8}}-\left(-\frac{11}{6}-\frac{\frac{2}{7}+1}{-\frac{5}{14}}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Divide \frac{11}{4} by \frac{11}{8} by multiplying \frac{11}{4} by the reciprocal of \frac{11}{8}.

$$\frac{11}{4}\times \frac{8}{11}-\left(-\frac{11}{6}-\frac{\frac{2}{7}+1}{-\frac{5}{14}}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Multiply \frac{11}{4} times \frac{8}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 8}{4\times 11}-\left(-\frac{11}{6}-\frac{\frac{2}{7}+1}{-\frac{5}{14}}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Cancel out 11 in both numerator and denominator.

$$\frac{8}{4}-\left(-\frac{11}{6}-\frac{\frac{2}{7}+1}{-\frac{5}{14}}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Divide 8 by 4 to get 2.

$$2-\left(-\frac{11}{6}-\frac{\frac{2}{7}+1}{-\frac{5}{14}}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Convert 1 to fraction \frac{7}{7}.

$$2-\left(-\frac{11}{6}-\frac{\frac{2}{7}+\frac{7}{7}}{-\frac{5}{14}}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Since \frac{2}{7} and \frac{7}{7} have the same denominator, add them by adding their numerators.

$$2-\left(-\frac{11}{6}-\frac{\frac{2+7}{7}}{-\frac{5}{14}}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Add 2 and 7 to get 9.

$$2-\left(-\frac{11}{6}-\frac{\frac{9}{7}}{-\frac{5}{14}}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Divide \frac{9}{7} by -\frac{5}{14} by multiplying \frac{9}{7} by the reciprocal of -\frac{5}{14}.

$$2-\left(-\frac{11}{6}-\frac{9}{7}\left(-\frac{14}{5}\right)+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Multiply \frac{9}{7} times -\frac{14}{5} by multiplying numerator times numerator and denominator times denominator.

$$2-\left(-\frac{11}{6}-\frac{9\left(-14\right)}{7\times 5}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Do the multiplications in the fraction \frac{9\left(-14\right)}{7\times 5}.

$$2-\left(-\frac{11}{6}-\frac{-126}{35}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Reduce the fraction \frac{-126}{35} to lowest terms by extracting and canceling out 7.

$$2-\left(-\frac{11}{6}-\left(-\frac{18}{5}\right)+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

The opposite of -\frac{18}{5} is \frac{18}{5}.

$$2-\left(-\frac{11}{6}+\frac{18}{5}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Least common multiple of 6 and 5 is 30. Convert -\frac{11}{6} and \frac{18}{5} to fractions with denominator 30.

$$2-\left(-\frac{55}{30}+\frac{108}{30}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Since -\frac{55}{30} and \frac{108}{30} have the same denominator, add them by adding their numerators.

$$2-\left(\frac{-55+108}{30}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Add -55 and 108 to get 53.

$$2-\left(\frac{53}{30}+\frac{1}{30}\right)-\left(-\frac{1}{4}\right)$$

Since \frac{53}{30} and \frac{1}{30} have the same denominator, add them by adding their numerators.

$$2-\frac{53+1}{30}-\left(-\frac{1}{4}\right)$$

Add 53 and 1 to get 54.

$$2-\frac{54}{30}-\left(-\frac{1}{4}\right)$$

Reduce the fraction \frac{54}{30} to lowest terms by extracting and canceling out 6.

$$2-\frac{9}{5}-\left(-\frac{1}{4}\right)$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{10}{5}-\frac{9}{5}-\left(-\frac{1}{4}\right)$$

Since \frac{10}{5} and \frac{9}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-9}{5}-\left(-\frac{1}{4}\right)$$

Subtract 9 from 10 to get 1.

$$\frac{1}{5}-\left(-\frac{1}{4}\right)$$

The opposite of -\frac{1}{4} is \frac{1}{4}.

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

Least common multiple of 5 and 4 is 20. Convert \frac{1}{5} and \frac{1}{4} to fractions with denominator 20.

$$\frac{4}{20}+\frac{5}{20}$$

Since \frac{4}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$\frac{4+5}{20}$$

Add 4 and 5 to get 9.

$$\frac{9}{20}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {2} \cdot 5} = 0.45$$