Solve (5:10/12)+(6/9:2/5)-(12/18+frac{14}{8}-frac{2}{6})=

$$( 5 : \frac { 10 } { 12 } ) + ( \frac { 6 } { 9 } : \frac { 2 } { 5 } ) - ( \frac { 12 } { 18 } + \frac { 14 } { 8 } - \frac { 2 } { 6 } ) =$$

Evaluate

$$\frac{67}{12}\approx 5.583333333$$

Solution Steps

Divide 5 by \frac{10}{12} by multiplying 5 by the reciprocal of \frac{10}{12}.

$$\frac{5\times 12}{10}+\frac{\frac{6}{9}}{\frac{2}{5}}-\left(\frac{12}{18}+\frac{14}{8}-\frac{2}{6}\right)$$

Multiply 5 and 12 to get 60.

$$\frac{60}{10}+\frac{\frac{6}{9}}{\frac{2}{5}}-\left(\frac{12}{18}+\frac{14}{8}-\frac{2}{6}\right)$$

Divide 60 by 10 to get 6.

$$6+\frac{\frac{6}{9}}{\frac{2}{5}}-\left(\frac{12}{18}+\frac{14}{8}-\frac{2}{6}\right)$$

Divide \frac{6}{9} by \frac{2}{5} by multiplying \frac{6}{9} by the reciprocal of \frac{2}{5}.

$$6+\frac{6\times 5}{9\times 2}-\left(\frac{12}{18}+\frac{14}{8}-\frac{2}{6}\right)$$

Cancel out 2\times 3 in both numerator and denominator.

$$6+\frac{5}{3}-\left(\frac{12}{18}+\frac{14}{8}-\frac{2}{6}\right)$$

Convert 6 to fraction \frac{18}{3}.

$$\frac{18}{3}+\frac{5}{3}-\left(\frac{12}{18}+\frac{14}{8}-\frac{2}{6}\right)$$

Since \frac{18}{3} and \frac{5}{3} have the same denominator, add them by adding their numerators.

$$\frac{18+5}{3}-\left(\frac{12}{18}+\frac{14}{8}-\frac{2}{6}\right)$$

Add 18 and 5 to get 23.

$$\frac{23}{3}-\left(\frac{12}{18}+\frac{14}{8}-\frac{2}{6}\right)$$

Reduce the fraction \frac{12}{18} to lowest terms by extracting and canceling out 6.

$$\frac{23}{3}-\left(\frac{2}{3}+\frac{14}{8}-\frac{2}{6}\right)$$

Reduce the fraction \frac{14}{8} to lowest terms by extracting and canceling out 2.

$$\frac{23}{3}-\left(\frac{2}{3}+\frac{7}{4}-\frac{2}{6}\right)$$

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{7}{4} to fractions with denominator 12.

$$\frac{23}{3}-\left(\frac{8}{12}+\frac{21}{12}-\frac{2}{6}\right)$$

Since \frac{8}{12} and \frac{21}{12} have the same denominator, add them by adding their numerators.

$$\frac{23}{3}-\left(\frac{8+21}{12}-\frac{2}{6}\right)$$

Add 8 and 21 to get 29.

$$\frac{23}{3}-\left(\frac{29}{12}-\frac{2}{6}\right)$$

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

$$\frac{23}{3}-\left(\frac{29}{12}-\frac{1}{3}\right)$$

Least common multiple of 12 and 3 is 12. Convert \frac{29}{12} and \frac{1}{3} to fractions with denominator 12.

$$\frac{23}{3}-\left(\frac{29}{12}-\frac{4}{12}\right)$$

Since \frac{29}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{23}{3}-\frac{29-4}{12}$$

Subtract 4 from 29 to get 25.

$$\frac{23}{3}-\frac{25}{12}$$

Least common multiple of 3 and 12 is 12. Convert \frac{23}{3} and \frac{25}{12} to fractions with denominator 12.

$$\frac{92}{12}-\frac{25}{12}$$

Since \frac{92}{12} and \frac{25}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{92-25}{12}$$

Subtract 25 from 92 to get 67.

$$\frac{67}{12}$$

Factor

$$\frac{67}{2 ^ {2} \cdot 3} = 5\frac{7}{12} = 5.583333333333333$$