Solve 1:{2/19*|(3/2+27/5):3/5-(frac{11}{6}-frac{7}{4})|:frac{5}{6}}

$$1 : \{ \frac { 2 } { 19 } \times | ( \frac { 3 } { 2 } + \frac { 27 } { 5 } ) : \frac { 3 } { 5 } - ( \frac { 11 } { 6 } - \frac { 7 } { 4 } ) | : \frac { 5 } { 6 } \}$$

Evaluate

$$\frac{95}{137}\approx 0.693430657$$

Solution Steps

Divide 1 by \frac{\frac{2}{19}|\frac{\frac{3}{2}+\frac{27}{5}}{\frac{3}{5}}-\left(\frac{11}{6}-\frac{7}{4}\right)|}{\frac{5}{6}} by multiplying 1 by the reciprocal of \frac{\frac{2}{19}|\frac{\frac{3}{2}+\frac{27}{5}}{\frac{3}{5}}-\left(\frac{11}{6}-\frac{7}{4}\right)|}{\frac{5}{6}}.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{\frac{3}{2}+\frac{27}{5}}{\frac{3}{5}}-\left(\frac{11}{6}-\frac{7}{4}\right)|}$$

Least common multiple of 2 and 5 is 10. Convert \frac{3}{2} and \frac{27}{5} to fractions with denominator 10.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{\frac{15}{10}+\frac{54}{10}}{\frac{3}{5}}-\left(\frac{11}{6}-\frac{7}{4}\right)|}$$

Since \frac{15}{10} and \frac{54}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{\frac{15+54}{10}}{\frac{3}{5}}-\left(\frac{11}{6}-\frac{7}{4}\right)|}$$

Add 15 and 54 to get 69.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{\frac{69}{10}}{\frac{3}{5}}-\left(\frac{11}{6}-\frac{7}{4}\right)|}$$

Divide \frac{69}{10} by \frac{3}{5} by multiplying \frac{69}{10} by the reciprocal of \frac{3}{5}.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{69}{10}\times \frac{5}{3}-\left(\frac{11}{6}-\frac{7}{4}\right)|}$$

Multiply \frac{69}{10} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{69\times 5}{10\times 3}-\left(\frac{11}{6}-\frac{7}{4}\right)|}$$

Do the multiplications in the fraction \frac{69\times 5}{10\times 3}.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{345}{30}-\left(\frac{11}{6}-\frac{7}{4}\right)|}$$

Reduce the fraction \frac{345}{30} to lowest terms by extracting and canceling out 15.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{23}{2}-\left(\frac{11}{6}-\frac{7}{4}\right)|}$$

Least common multiple of 6 and 4 is 12. Convert \frac{11}{6} and \frac{7}{4} to fractions with denominator 12.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{23}{2}-\left(\frac{22}{12}-\frac{21}{12}\right)|}$$

Since \frac{22}{12} and \frac{21}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{23}{2}-\frac{22-21}{12}|}$$

Subtract 21 from 22 to get 1.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{23}{2}-\frac{1}{12}|}$$

Least common multiple of 2 and 12 is 12. Convert \frac{23}{2} and \frac{1}{12} to fractions with denominator 12.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{138}{12}-\frac{1}{12}|}$$

Since \frac{138}{12} and \frac{1}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{138-1}{12}|}$$

Subtract 1 from 138 to get 137.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{137}{12}|}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{137}{12} is \frac{137}{12}.

$$\frac{\frac{5}{6}}{\frac{2}{19}\times \frac{137}{12}}$$

Multiply \frac{2}{19} times \frac{137}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{6}}{\frac{2\times 137}{19\times 12}}$$

Do the multiplications in the fraction \frac{2\times 137}{19\times 12}.

$$\frac{\frac{5}{6}}{\frac{274}{228}}$$

Reduce the fraction \frac{274}{228} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{5}{6}}{\frac{137}{114}}$$

Divide \frac{5}{6} by \frac{137}{114} by multiplying \frac{5}{6} by the reciprocal of \frac{137}{114}.

$$\frac{5}{6}\times \frac{114}{137}$$

Multiply \frac{5}{6} times \frac{114}{137} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 114}{6\times 137}$$

Do the multiplications in the fraction \frac{5\times 114}{6\times 137}.

$$\frac{570}{822}$$

Reduce the fraction \frac{570}{822} to lowest terms by extracting and canceling out 6.

$$\frac{95}{137}$$

Factor

$$\frac{5 \cdot 19}{137} = 0.6934306569343066$$