Solve -0,5-((11/15-14/15*1/7):(-19/20-frac{9}{20}:1,8)):(-frac{1}{3})

$$- 0,5 - ( ( \frac { 11 } { 15 } - \frac { 14 } { 15 } \cdot \frac { 1 } { 7 } ) : ( - \frac { 19 } { 20 } - \frac { 9 } { 20 } : 1,8 ) ) : ( - \frac { 1 } { 3 } )$$

Evaluate

$$-2$$

Solution Steps

Divide \frac{\frac{11}{15}-\frac{14}{15}\times \frac{1}{7}}{-\frac{19}{20}-\frac{\frac{9}{20}}{1,8}} by -\frac{1}{3} by multiplying \frac{\frac{11}{15}-\frac{14}{15}\times \frac{1}{7}}{-\frac{19}{20}-\frac{\frac{9}{20}}{1,8}} by the reciprocal of -\frac{1}{3}.

$$-0,5-\frac{\left(\frac{11}{15}-\frac{14}{15}\times \frac{1}{7}\right)\times 3}{\left(-\frac{19}{20}-\frac{\frac{9}{20}}{1,8}\right)\left(-1\right)}$$

Multiply \frac{14}{15} times \frac{1}{7} by multiplying numerator times numerator and denominator times denominator.

$$-0,5-\frac{\left(\frac{11}{15}-\frac{14\times 1}{15\times 7}\right)\times 3}{\left(-\frac{19}{20}-\frac{\frac{9}{20}}{1,8}\right)\left(-1\right)}$$

Do the multiplications in the fraction \frac{14\times 1}{15\times 7}.

$$-0,5-\frac{\left(\frac{11}{15}-\frac{14}{105}\right)\times 3}{\left(-\frac{19}{20}-\frac{\frac{9}{20}}{1,8}\right)\left(-1\right)}$$

Reduce the fraction \frac{14}{105} to lowest terms by extracting and canceling out 7.

$$-0,5-\frac{\left(\frac{11}{15}-\frac{2}{15}\right)\times 3}{\left(-\frac{19}{20}-\frac{\frac{9}{20}}{1,8}\right)\left(-1\right)}$$

Since \frac{11}{15} and \frac{2}{15} have the same denominator, subtract them by subtracting their numerators.

$$-0,5-\frac{\frac{11-2}{15}\times 3}{\left(-\frac{19}{20}-\frac{\frac{9}{20}}{1,8}\right)\left(-1\right)}$$

Subtract 2 from 11 to get 9.

$$-0,5-\frac{\frac{9}{15}\times 3}{\left(-\frac{19}{20}-\frac{\frac{9}{20}}{1,8}\right)\left(-1\right)}$$

Reduce the fraction \frac{9}{15} to lowest terms by extracting and canceling out 3.

$$-0,5-\frac{\frac{3}{5}\times 3}{\left(-\frac{19}{20}-\frac{\frac{9}{20}}{1,8}\right)\left(-1\right)}$$

Express \frac{3}{5}\times 3 as a single fraction.

$$-0,5-\frac{\frac{3\times 3}{5}}{\left(-\frac{19}{20}-\frac{\frac{9}{20}}{1,8}\right)\left(-1\right)}$$

Multiply 3 and 3 to get 9.

$$-0,5-\frac{\frac{9}{5}}{\left(-\frac{19}{20}-\frac{\frac{9}{20}}{1,8}\right)\left(-1\right)}$$

Express \frac{\frac{9}{20}}{1,8} as a single fraction.

$$-0,5-\frac{\frac{9}{5}}{\left(-\frac{19}{20}-\frac{9}{20\times 1,8}\right)\left(-1\right)}$$

Multiply 20 and 1,8 to get 36.

$$-0,5-\frac{\frac{9}{5}}{\left(-\frac{19}{20}-\frac{9}{36}\right)\left(-1\right)}$$

Reduce the fraction \frac{9}{36} to lowest terms by extracting and canceling out 9.

$$-0,5-\frac{\frac{9}{5}}{\left(-\frac{19}{20}-\frac{1}{4}\right)\left(-1\right)}$$

Least common multiple of 20 and 4 is 20. Convert -\frac{19}{20} and \frac{1}{4} to fractions with denominator 20.

$$-0,5-\frac{\frac{9}{5}}{\left(-\frac{19}{20}-\frac{5}{20}\right)\left(-1\right)}$$

Since -\frac{19}{20} and \frac{5}{20} have the same denominator, subtract them by subtracting their numerators.

$$-0,5-\frac{\frac{9}{5}}{\frac{-19-5}{20}\left(-1\right)}$$

Subtract 5 from -19 to get -24.

$$-0,5-\frac{\frac{9}{5}}{\frac{-24}{20}\left(-1\right)}$$

Reduce the fraction \frac{-24}{20} to lowest terms by extracting and canceling out 4.

$$-0,5-\frac{\frac{9}{5}}{-\frac{6}{5}\left(-1\right)}$$

Multiply -\frac{6}{5} and -1 to get \frac{6}{5}.

$$-0,5-\frac{\frac{9}{5}}{\frac{6}{5}}$$

Divide \frac{9}{5} by \frac{6}{5} by multiplying \frac{9}{5} by the reciprocal of \frac{6}{5}.

$$-0,5-\frac{9}{5}\times \frac{5}{6}$$

Multiply \frac{9}{5} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$-0,5-\frac{9\times 5}{5\times 6}$$

Cancel out 5 in both numerator and denominator.

$$-0,5-\frac{9}{6}$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$-0,5-\frac{3}{2}$$

Convert decimal number -0,5 to fraction -\frac{5}{10}. Reduce the fraction -\frac{5}{10} to lowest terms by extracting and canceling out 5.

$$-\frac{1}{2}-\frac{3}{2}$$

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

$$\frac{-1-3}{2}$$

Subtract 3 from -1 to get -4.

$$\frac{-4}{2}$$

Divide -4 by 2 to get -2.

$$-2$$

Factor

$$-2$$