Solve 2-frac{1/frac{3{2}-1/3}}{2/3*frac{1/3-frac{2}{5}}{frac{1}{15}}}

$$\frac { 2 - \frac { 1 } { \frac { 3 } { 2 } - \frac { 1 } { 3 } } } { \frac { 2 } { 3 } * \frac { \frac { 1 } { 3 } - \frac { 2 } { 5 } } { \frac { 1 } { 15 } } }$$

Evaluate

$$-\frac{12}{7}\approx -1.714285714$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{2-\frac{1}{\frac{9}{6}-\frac{2}{6}}}{\frac{2}{3}\times \frac{\frac{1}{3}-\frac{2}{5}}{\frac{1}{15}}}$$

Since \frac{9}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-\frac{1}{\frac{9-2}{6}}}{\frac{2}{3}\times \frac{\frac{1}{3}-\frac{2}{5}}{\frac{1}{15}}}$$

Subtract 2 from 9 to get 7.

$$\frac{2-\frac{1}{\frac{7}{6}}}{\frac{2}{3}\times \frac{\frac{1}{3}-\frac{2}{5}}{\frac{1}{15}}}$$

Divide 1 by \frac{7}{6} by multiplying 1 by the reciprocal of \frac{7}{6}.

$$\frac{2-1\times \frac{6}{7}}{\frac{2}{3}\times \frac{\frac{1}{3}-\frac{2}{5}}{\frac{1}{15}}}$$

Multiply 1 and \frac{6}{7} to get \frac{6}{7}.

$$\frac{2-\frac{6}{7}}{\frac{2}{3}\times \frac{\frac{1}{3}-\frac{2}{5}}{\frac{1}{15}}}$$

Convert 2 to fraction \frac{14}{7}.

$$\frac{\frac{14}{7}-\frac{6}{7}}{\frac{2}{3}\times \frac{\frac{1}{3}-\frac{2}{5}}{\frac{1}{15}}}$$

Since \frac{14}{7} and \frac{6}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{14-6}{7}}{\frac{2}{3}\times \frac{\frac{1}{3}-\frac{2}{5}}{\frac{1}{15}}}$$

Subtract 6 from 14 to get 8.

$$\frac{\frac{8}{7}}{\frac{2}{3}\times \frac{\frac{1}{3}-\frac{2}{5}}{\frac{1}{15}}}$$

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{2}{5} to fractions with denominator 15.

$$\frac{\frac{8}{7}}{\frac{2}{3}\times \frac{\frac{5}{15}-\frac{6}{15}}{\frac{1}{15}}}$$

Since \frac{5}{15} and \frac{6}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{8}{7}}{\frac{2}{3}\times \frac{\frac{5-6}{15}}{\frac{1}{15}}}$$

Subtract 6 from 5 to get -1.

$$\frac{\frac{8}{7}}{\frac{2}{3}\times \frac{-\frac{1}{15}}{\frac{1}{15}}}$$

Divide -\frac{1}{15} by \frac{1}{15} to get -1.

$$\frac{\frac{8}{7}}{\frac{2}{3}\left(-1\right)}$$

Multiply \frac{2}{3} and -1 to get -\frac{2}{3}.

$$\frac{\frac{8}{7}}{-\frac{2}{3}}$$

Divide \frac{8}{7} by -\frac{2}{3} by multiplying \frac{8}{7} by the reciprocal of -\frac{2}{3}.

$$\frac{8}{7}\left(-\frac{3}{2}\right)$$

Multiply \frac{8}{7} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\left(-3\right)}{7\times 2}$$

Do the multiplications in the fraction \frac{8\left(-3\right)}{7\times 2}.

$$\frac{-24}{14}$$

Reduce the fraction \frac{-24}{14} to lowest terms by extracting and canceling out 2.

$$-\frac{12}{7}$$

Factor

$$-\frac{12}{7} = -1\frac{5}{7} = -1.7142857142857142$$