Solve 135/6-(-3/4)div5/6-(-7/12)

$$13 \frac { 5 } { 6 } - ( - \frac { 3 } { 4 } ) \div \frac { 5 } { 6 } - ( - \frac { 7 } { 12 } )$$

Evaluate

$$\frac{919}{60}\approx 15.316666667$$

Solution Steps

Multiply 13 and 6 to get 78.

$$\frac{78+5}{6}-\frac{-\frac{3}{4}}{\frac{5}{6}}-\left(-\frac{7}{12}\right)$$

Add 78 and 5 to get 83.

$$\frac{83}{6}-\frac{-\frac{3}{4}}{\frac{5}{6}}-\left(-\frac{7}{12}\right)$$

Divide -\frac{3}{4} by \frac{5}{6} by multiplying -\frac{3}{4} by the reciprocal of \frac{5}{6}.

$$\frac{83}{6}-\left(-\frac{3}{4}\times \frac{6}{5}\right)-\left(-\frac{7}{12}\right)$$

Multiply -\frac{3}{4} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{83}{6}-\frac{-3\times 6}{4\times 5}-\left(-\frac{7}{12}\right)$$

Do the multiplications in the fraction \frac{-3\times 6}{4\times 5}.

$$\frac{83}{6}-\frac{-18}{20}-\left(-\frac{7}{12}\right)$$

Reduce the fraction \frac{-18}{20} to lowest terms by extracting and canceling out 2.

$$\frac{83}{6}-\left(-\frac{9}{10}\right)-\left(-\frac{7}{12}\right)$$

The opposite of -\frac{9}{10} is \frac{9}{10}.

$$\frac{83}{6}+\frac{9}{10}-\left(-\frac{7}{12}\right)$$

Least common multiple of 6 and 10 is 30. Convert \frac{83}{6} and \frac{9}{10} to fractions with denominator 30.

$$\frac{415}{30}+\frac{27}{30}-\left(-\frac{7}{12}\right)$$

Since \frac{415}{30} and \frac{27}{30} have the same denominator, add them by adding their numerators.

$$\frac{415+27}{30}-\left(-\frac{7}{12}\right)$$

Add 415 and 27 to get 442.

$$\frac{442}{30}-\left(-\frac{7}{12}\right)$$

Reduce the fraction \frac{442}{30} to lowest terms by extracting and canceling out 2.

$$\frac{221}{15}-\left(-\frac{7}{12}\right)$$

The opposite of -\frac{7}{12} is \frac{7}{12}.

$$\frac{221}{15}+\frac{7}{12}$$

Least common multiple of 15 and 12 is 60. Convert \frac{221}{15} and \frac{7}{12} to fractions with denominator 60.

$$\frac{884}{60}+\frac{35}{60}$$

Since \frac{884}{60} and \frac{35}{60} have the same denominator, add them by adding their numerators.

$$\frac{884+35}{60}$$

Add 884 and 35 to get 919.

$$\frac{919}{60}$$

Factor

$$\frac{919}{2 ^ {2} \cdot 3 \cdot 5} = 15\frac{19}{60} = 15.316666666666666$$