Solve (1/2-3/5*1/3/frac{1{6}-frac{2}{3}})*(frac{(2-frac{1}{3})*3}{frac{1}{3}-1})

$$( \frac { \frac { 1 } { 2 } - \frac { 3 } { 5 } \cdot \frac { 1 } { 3 } } { \frac { 1 } { 6 } - \frac { 2 } { 3 } } ) \cdot ( \frac { ( 2 - \frac { 1 } { 3 } ) \cdot 3 } { \frac { 1 } { 3 } - 1 } )$$

Evaluate

$$\frac{9}{2}=4.5$$

Solution Steps

Multiply \frac{3}{5} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{2}-\frac{3\times 1}{5\times 3}}{\frac{1}{6}-\frac{2}{3}}\times \frac{\left(2-\frac{1}{3}\right)\times 3}{\frac{1}{3}-1}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{1}{2}-\frac{1}{5}}{\frac{1}{6}-\frac{2}{3}}\times \frac{\left(2-\frac{1}{3}\right)\times 3}{\frac{1}{3}-1}$$

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{1}{5} to fractions with denominator 10.

$$\frac{\frac{5}{10}-\frac{2}{10}}{\frac{1}{6}-\frac{2}{3}}\times \frac{\left(2-\frac{1}{3}\right)\times 3}{\frac{1}{3}-1}$$

Since \frac{5}{10} and \frac{2}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5-2}{10}}{\frac{1}{6}-\frac{2}{3}}\times \frac{\left(2-\frac{1}{3}\right)\times 3}{\frac{1}{3}-1}$$

Subtract 2 from 5 to get 3.

$$\frac{\frac{3}{10}}{\frac{1}{6}-\frac{2}{3}}\times \frac{\left(2-\frac{1}{3}\right)\times 3}{\frac{1}{3}-1}$$

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

$$\frac{\frac{3}{10}}{\frac{1}{6}-\frac{4}{6}}\times \frac{\left(2-\frac{1}{3}\right)\times 3}{\frac{1}{3}-1}$$

Since \frac{1}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{10}}{\frac{1-4}{6}}\times \frac{\left(2-\frac{1}{3}\right)\times 3}{\frac{1}{3}-1}$$

Subtract 4 from 1 to get -3.

$$\frac{\frac{3}{10}}{\frac{-3}{6}}\times \frac{\left(2-\frac{1}{3}\right)\times 3}{\frac{1}{3}-1}$$

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

$$\frac{\frac{3}{10}}{-\frac{1}{2}}\times \frac{\left(2-\frac{1}{3}\right)\times 3}{\frac{1}{3}-1}$$

Divide \frac{3}{10} by -\frac{1}{2} by multiplying \frac{3}{10} by the reciprocal of -\frac{1}{2}.

$$\frac{3}{10}\left(-2\right)\times \frac{\left(2-\frac{1}{3}\right)\times 3}{\frac{1}{3}-1}$$

Express \frac{3}{10}\left(-2\right) as a single fraction.

$$\frac{3\left(-2\right)}{10}\times \frac{\left(2-\frac{1}{3}\right)\times 3}{\frac{1}{3}-1}$$

Multiply 3 and -2 to get -6.

$$\frac{-6}{10}\times \frac{\left(2-\frac{1}{3}\right)\times 3}{\frac{1}{3}-1}$$

Reduce the fraction \frac{-6}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{3}{5}\times \frac{\left(2-\frac{1}{3}\right)\times 3}{\frac{1}{3}-1}$$

Convert 2 to fraction \frac{6}{3}.

$$-\frac{3}{5}\times \frac{\left(\frac{6}{3}-\frac{1}{3}\right)\times 3}{\frac{1}{3}-1}$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{5}\times \frac{\frac{6-1}{3}\times 3}{\frac{1}{3}-1}$$

Subtract 1 from 6 to get 5.

$$-\frac{3}{5}\times \frac{\frac{5}{3}\times 3}{\frac{1}{3}-1}$$

Cancel out 3 and 3.

$$-\frac{3}{5}\times \frac{5}{\frac{1}{3}-1}$$

Convert 1 to fraction \frac{3}{3}.

$$-\frac{3}{5}\times \frac{5}{\frac{1}{3}-\frac{3}{3}}$$

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

$$-\frac{3}{5}\times \frac{5}{\frac{1-3}{3}}$$

Subtract 3 from 1 to get -2.

$$-\frac{3}{5}\times \frac{5}{-\frac{2}{3}}$$

Divide 5 by -\frac{2}{3} by multiplying 5 by the reciprocal of -\frac{2}{3}.

$$-\frac{3}{5}\times 5\left(-\frac{3}{2}\right)$$

Express 5\left(-\frac{3}{2}\right) as a single fraction.

$$-\frac{3}{5}\times \frac{5\left(-3\right)}{2}$$

Multiply 5 and -3 to get -15.

$$-\frac{3}{5}\times \frac{-15}{2}$$

Fraction \frac{-15}{2} can be rewritten as -\frac{15}{2} by extracting the negative sign.

$$-\frac{3}{5}\left(-\frac{15}{2}\right)$$

Multiply -\frac{3}{5} times -\frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\left(-15\right)}{5\times 2}$$

Do the multiplications in the fraction \frac{-3\left(-15\right)}{5\times 2}.

$$\frac{45}{10}$$

Reduce the fraction \frac{45}{10} to lowest terms by extracting and canceling out 5.

$$\frac{9}{2}$$

Factor

$$\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5$$