Solve (1-5/7)*[(3-6/7-5/14):(5/6-frac{1}{3}-frac{3}{7})-frac{5}{12}]

$$( 1 - \frac { 5 } { 7 } ) \cdot [ ( 3 - \frac { 6 } { 7 } - \frac { 5 } { 14 } ) : ( \frac { 5 } { 6 } - \frac { 1 } { 3 } - \frac { 3 } { 7 } ) - \frac { 5 } { 12 } ]$$

Evaluate

$$\frac{295}{42}\approx 7.023809524$$

Solution Steps

Convert 1 to fraction \frac{7}{7}.

$$\left(\frac{7}{7}-\frac{5}{7}\right)\left(\frac{3-\frac{6}{7}-\frac{5}{14}}{\frac{5}{6}-\frac{1}{3}-\frac{3}{7}}-\frac{5}{12}\right)$$

Since \frac{7}{7} and \frac{5}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-5}{7}\left(\frac{3-\frac{6}{7}-\frac{5}{14}}{\frac{5}{6}-\frac{1}{3}-\frac{3}{7}}-\frac{5}{12}\right)$$

Subtract 5 from 7 to get 2.

$$\frac{2}{7}\left(\frac{3-\frac{6}{7}-\frac{5}{14}}{\frac{5}{6}-\frac{1}{3}-\frac{3}{7}}-\frac{5}{12}\right)$$

Convert 3 to fraction \frac{21}{7}.

$$\frac{2}{7}\left(\frac{\frac{21}{7}-\frac{6}{7}-\frac{5}{14}}{\frac{5}{6}-\frac{1}{3}-\frac{3}{7}}-\frac{5}{12}\right)$$

Since \frac{21}{7} and \frac{6}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{7}\left(\frac{\frac{21-6}{7}-\frac{5}{14}}{\frac{5}{6}-\frac{1}{3}-\frac{3}{7}}-\frac{5}{12}\right)$$

Subtract 6 from 21 to get 15.

$$\frac{2}{7}\left(\frac{\frac{15}{7}-\frac{5}{14}}{\frac{5}{6}-\frac{1}{3}-\frac{3}{7}}-\frac{5}{12}\right)$$

Least common multiple of 7 and 14 is 14. Convert \frac{15}{7} and \frac{5}{14} to fractions with denominator 14.

$$\frac{2}{7}\left(\frac{\frac{30}{14}-\frac{5}{14}}{\frac{5}{6}-\frac{1}{3}-\frac{3}{7}}-\frac{5}{12}\right)$$

Since \frac{30}{14} and \frac{5}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{7}\left(\frac{\frac{30-5}{14}}{\frac{5}{6}-\frac{1}{3}-\frac{3}{7}}-\frac{5}{12}\right)$$

Subtract 5 from 30 to get 25.

$$\frac{2}{7}\left(\frac{\frac{25}{14}}{\frac{5}{6}-\frac{1}{3}-\frac{3}{7}}-\frac{5}{12}\right)$$

Least common multiple of 6 and 3 is 6. Convert \frac{5}{6} and \frac{1}{3} to fractions with denominator 6.

$$\frac{2}{7}\left(\frac{\frac{25}{14}}{\frac{5}{6}-\frac{2}{6}-\frac{3}{7}}-\frac{5}{12}\right)$$

Since \frac{5}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{7}\left(\frac{\frac{25}{14}}{\frac{5-2}{6}-\frac{3}{7}}-\frac{5}{12}\right)$$

Subtract 2 from 5 to get 3.

$$\frac{2}{7}\left(\frac{\frac{25}{14}}{\frac{3}{6}-\frac{3}{7}}-\frac{5}{12}\right)$$

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

$$\frac{2}{7}\left(\frac{\frac{25}{14}}{\frac{1}{2}-\frac{3}{7}}-\frac{5}{12}\right)$$

Least common multiple of 2 and 7 is 14. Convert \frac{1}{2} and \frac{3}{7} to fractions with denominator 14.

$$\frac{2}{7}\left(\frac{\frac{25}{14}}{\frac{7}{14}-\frac{6}{14}}-\frac{5}{12}\right)$$

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

$$\frac{2}{7}\left(\frac{\frac{25}{14}}{\frac{7-6}{14}}-\frac{5}{12}\right)$$

Subtract 6 from 7 to get 1.

$$\frac{2}{7}\left(\frac{\frac{25}{14}}{\frac{1}{14}}-\frac{5}{12}\right)$$

Divide \frac{25}{14} by \frac{1}{14} by multiplying \frac{25}{14} by the reciprocal of \frac{1}{14}.

$$\frac{2}{7}\left(\frac{25}{14}\times 14-\frac{5}{12}\right)$$

Cancel out 14 and 14.

$$\frac{2}{7}\left(25-\frac{5}{12}\right)$$

Convert 25 to fraction \frac{300}{12}.

$$\frac{2}{7}\left(\frac{300}{12}-\frac{5}{12}\right)$$

Since \frac{300}{12} and \frac{5}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{7}\times \frac{300-5}{12}$$

Subtract 5 from 300 to get 295.

$$\frac{2}{7}\times \frac{295}{12}$$

Multiply \frac{2}{7} times \frac{295}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 295}{7\times 12}$$

Do the multiplications in the fraction \frac{2\times 295}{7\times 12}.

$$\frac{590}{84}$$

Reduce the fraction \frac{590}{84} to lowest terms by extracting and canceling out 2.

$$\frac{295}{42}$$

Factor

$$\frac{5 \cdot 59}{2 \cdot 3 \cdot 7} = 7\frac{1}{42} = 7.023809523809524$$