Solve (-1/5*(3/2+1)+3/2)div5/4+(3-frac{2}{3})*(-frac{1}{5}-frac{2}{7})divfrac{4}{3}-frac{1}{12}=

$$(- \frac{ 1 }{ 5 } \times ( \frac{ 3 }{ 2 } +1)+ \frac{ 3 }{ 2 } ) \div \frac{ 5 }{ 4 } +(3- \frac{ 2 }{ 3 } ) \times (- \frac{ 1 }{ 5 } - \frac{ 2 }{ 7 } ) \div \frac{ 4 }{ 3 } - \frac{ 1 }{ 12 } =$$

Evaluate

$$-\frac{2}{15}\approx -0.133333333$$

Solution Steps

Convert 1 to fraction \frac{2}{2}.

$$\frac{-\frac{1}{5}\left(\frac{3}{2}+\frac{2}{2}\right)+\frac{3}{2}}{\frac{5}{4}}+\frac{\left(3-\frac{2}{3}\right)\left(-\frac{1}{5}-\frac{2}{7}\right)}{\frac{4}{3}}-\frac{1}{12}$$

Since \frac{3}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{1}{5}\times \frac{3+2}{2}+\frac{3}{2}}{\frac{5}{4}}+\frac{\left(3-\frac{2}{3}\right)\left(-\frac{1}{5}-\frac{2}{7}\right)}{\frac{4}{3}}-\frac{1}{12}$$

Add 3 and 2 to get 5.

$$\frac{-\frac{1}{5}\times \frac{5}{2}+\frac{3}{2}}{\frac{5}{4}}+\frac{\left(3-\frac{2}{3}\right)\left(-\frac{1}{5}-\frac{2}{7}\right)}{\frac{4}{3}}-\frac{1}{12}$$

Multiply -\frac{1}{5} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-5}{5\times 2}+\frac{3}{2}}{\frac{5}{4}}+\frac{\left(3-\frac{2}{3}\right)\left(-\frac{1}{5}-\frac{2}{7}\right)}{\frac{4}{3}}-\frac{1}{12}$$

Cancel out 5 in both numerator and denominator.

$$\frac{\frac{-1}{2}+\frac{3}{2}}{\frac{5}{4}}+\frac{\left(3-\frac{2}{3}\right)\left(-\frac{1}{5}-\frac{2}{7}\right)}{\frac{4}{3}}-\frac{1}{12}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$\frac{-\frac{1}{2}+\frac{3}{2}}{\frac{5}{4}}+\frac{\left(3-\frac{2}{3}\right)\left(-\frac{1}{5}-\frac{2}{7}\right)}{\frac{4}{3}}-\frac{1}{12}$$

Since -\frac{1}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-1+3}{2}}{\frac{5}{4}}+\frac{\left(3-\frac{2}{3}\right)\left(-\frac{1}{5}-\frac{2}{7}\right)}{\frac{4}{3}}-\frac{1}{12}$$

Add -1 and 3 to get 2.

$$\frac{\frac{2}{2}}{\frac{5}{4}}+\frac{\left(3-\frac{2}{3}\right)\left(-\frac{1}{5}-\frac{2}{7}\right)}{\frac{4}{3}}-\frac{1}{12}$$

Divide 2 by 2 to get 1.

$$\frac{1}{\frac{5}{4}}+\frac{\left(3-\frac{2}{3}\right)\left(-\frac{1}{5}-\frac{2}{7}\right)}{\frac{4}{3}}-\frac{1}{12}$$

Divide 1 by \frac{5}{4} by multiplying 1 by the reciprocal of \frac{5}{4}.

$$1\times \frac{4}{5}+\frac{\left(3-\frac{2}{3}\right)\left(-\frac{1}{5}-\frac{2}{7}\right)}{\frac{4}{3}}-\frac{1}{12}$$

Multiply 1 and \frac{4}{5} to get \frac{4}{5}.

$$\frac{4}{5}+\frac{\left(3-\frac{2}{3}\right)\left(-\frac{1}{5}-\frac{2}{7}\right)}{\frac{4}{3}}-\frac{1}{12}$$

Convert 3 to fraction \frac{9}{3}.

$$\frac{4}{5}+\frac{\left(\frac{9}{3}-\frac{2}{3}\right)\left(-\frac{1}{5}-\frac{2}{7}\right)}{\frac{4}{3}}-\frac{1}{12}$$

Since \frac{9}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{5}+\frac{\frac{9-2}{3}\left(-\frac{1}{5}-\frac{2}{7}\right)}{\frac{4}{3}}-\frac{1}{12}$$

Subtract 2 from 9 to get 7.

$$\frac{4}{5}+\frac{\frac{7}{3}\left(-\frac{1}{5}-\frac{2}{7}\right)}{\frac{4}{3}}-\frac{1}{12}$$

Least common multiple of 5 and 7 is 35. Convert -\frac{1}{5} and \frac{2}{7} to fractions with denominator 35.

$$\frac{4}{5}+\frac{\frac{7}{3}\left(-\frac{7}{35}-\frac{10}{35}\right)}{\frac{4}{3}}-\frac{1}{12}$$

Since -\frac{7}{35} and \frac{10}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{5}+\frac{\frac{7}{3}\times \frac{-7-10}{35}}{\frac{4}{3}}-\frac{1}{12}$$

Subtract 10 from -7 to get -17.

$$\frac{4}{5}+\frac{\frac{7}{3}\left(-\frac{17}{35}\right)}{\frac{4}{3}}-\frac{1}{12}$$

Multiply \frac{7}{3} times -\frac{17}{35} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{5}+\frac{\frac{7\left(-17\right)}{3\times 35}}{\frac{4}{3}}-\frac{1}{12}$$

Do the multiplications in the fraction \frac{7\left(-17\right)}{3\times 35}.

$$\frac{4}{5}+\frac{\frac{-119}{105}}{\frac{4}{3}}-\frac{1}{12}$$

Reduce the fraction \frac{-119}{105} to lowest terms by extracting and canceling out 7.

$$\frac{4}{5}+\frac{-\frac{17}{15}}{\frac{4}{3}}-\frac{1}{12}$$

Divide -\frac{17}{15} by \frac{4}{3} by multiplying -\frac{17}{15} by the reciprocal of \frac{4}{3}.

$$\frac{4}{5}-\frac{17}{15}\times \frac{3}{4}-\frac{1}{12}$$

Multiply -\frac{17}{15} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{5}+\frac{-17\times 3}{15\times 4}-\frac{1}{12}$$

Do the multiplications in the fraction \frac{-17\times 3}{15\times 4}.

$$\frac{4}{5}+\frac{-51}{60}-\frac{1}{12}$$

Reduce the fraction \frac{-51}{60} to lowest terms by extracting and canceling out 3.

$$\frac{4}{5}-\frac{17}{20}-\frac{1}{12}$$

Least common multiple of 5 and 20 is 20. Convert \frac{4}{5} and \frac{17}{20} to fractions with denominator 20.

$$\frac{16}{20}-\frac{17}{20}-\frac{1}{12}$$

Since \frac{16}{20} and \frac{17}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-17}{20}-\frac{1}{12}$$

Subtract 17 from 16 to get -1.

$$-\frac{1}{20}-\frac{1}{12}$$

Least common multiple of 20 and 12 is 60. Convert -\frac{1}{20} and \frac{1}{12} to fractions with denominator 60.

$$-\frac{3}{60}-\frac{5}{60}$$

Since -\frac{3}{60} and \frac{5}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-3-5}{60}$$

Subtract 5 from -3 to get -8.

$$\frac{-8}{60}$$

Reduce the fraction \frac{-8}{60} to lowest terms by extracting and canceling out 4.

$$-\frac{2}{15}$$

Factor

$$-\frac{2}{15} = -0.13333333333333333$$