Solve 35/36*(1/2+5/14)-5/6:frac{10}{27}

$$\frac { 35 } { 36 } \cdot ( \frac { 1 } { 2 } + \frac { 5 } { 14 } ) - \frac { 5 } { 6 } : \frac { 10 } { 27 }$$

Evaluate

$$-\frac{17}{12}\approx -1.416666667$$

Solution Steps

Least common multiple of 2 and 14 is 14. Convert \frac{1}{2} and \frac{5}{14} to fractions with denominator 14.

$$\frac{35}{36}\left(\frac{7}{14}+\frac{5}{14}\right)-\frac{\frac{5}{6}}{\frac{10}{27}}$$

Since \frac{7}{14} and \frac{5}{14} have the same denominator, add them by adding their numerators.

$$\frac{35}{36}\times \frac{7+5}{14}-\frac{\frac{5}{6}}{\frac{10}{27}}$$

Add 7 and 5 to get 12.

$$\frac{35}{36}\times \frac{12}{14}-\frac{\frac{5}{6}}{\frac{10}{27}}$$

Reduce the fraction \frac{12}{14} to lowest terms by extracting and canceling out 2.

$$\frac{35}{36}\times \frac{6}{7}-\frac{\frac{5}{6}}{\frac{10}{27}}$$

Multiply \frac{35}{36} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35\times 6}{36\times 7}-\frac{\frac{5}{6}}{\frac{10}{27}}$$

Do the multiplications in the fraction \frac{35\times 6}{36\times 7}.

$$\frac{210}{252}-\frac{\frac{5}{6}}{\frac{10}{27}}$$

Reduce the fraction \frac{210}{252} to lowest terms by extracting and canceling out 42.

$$\frac{5}{6}-\frac{\frac{5}{6}}{\frac{10}{27}}$$

Divide \frac{5}{6} by \frac{10}{27} by multiplying \frac{5}{6} by the reciprocal of \frac{10}{27}.

$$\frac{5}{6}-\frac{5}{6}\times \frac{27}{10}$$

Multiply \frac{5}{6} times \frac{27}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{6}-\frac{5\times 27}{6\times 10}$$

Do the multiplications in the fraction \frac{5\times 27}{6\times 10}.

$$\frac{5}{6}-\frac{135}{60}$$

Reduce the fraction \frac{135}{60} to lowest terms by extracting and canceling out 15.

$$\frac{5}{6}-\frac{9}{4}$$

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{9}{4} to fractions with denominator 12.

$$\frac{10}{12}-\frac{27}{12}$$

Since \frac{10}{12} and \frac{27}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-27}{12}$$

Subtract 27 from 10 to get -17.

$$-\frac{17}{12}$$

Factor

$$-\frac{17}{12} = -1\frac{5}{12} = -1.4166666666666667$$