Solve -7+1/2/-3+8div(-5/6)

$$\frac { - 7 + \frac { 1 } { 2 } } { - 3 + 8 } \div ( - \frac { 5 } { 6 } )$$

Evaluate

$$\frac{39}{25}=1.56$$

Solution Steps

Divide \frac{-7+\frac{1}{2}}{-3+8} by -\frac{5}{6} by multiplying \frac{-7+\frac{1}{2}}{-3+8} by the reciprocal of -\frac{5}{6}.

$$\frac{\left(-7+\frac{1}{2}\right)\times 6}{\left(-3+8\right)\left(-5\right)}$$

Convert -7 to fraction -\frac{14}{2}.

$$\frac{\left(-\frac{14}{2}+\frac{1}{2}\right)\times 6}{\left(-3+8\right)\left(-5\right)}$$

Since -\frac{14}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-14+1}{2}\times 6}{\left(-3+8\right)\left(-5\right)}$$

Add -14 and 1 to get -13.

$$\frac{-\frac{13}{2}\times 6}{\left(-3+8\right)\left(-5\right)}$$

Express -\frac{13}{2}\times 6 as a single fraction.

$$\frac{\frac{-13\times 6}{2}}{\left(-3+8\right)\left(-5\right)}$$

Multiply -13 and 6 to get -78.

$$\frac{\frac{-78}{2}}{\left(-3+8\right)\left(-5\right)}$$

Divide -78 by 2 to get -39.

$$\frac{-39}{\left(-3+8\right)\left(-5\right)}$$

Add -3 and 8 to get 5.

$$\frac{-39}{5\left(-5\right)}$$

Multiply 5 and -5 to get -25.

$$\frac{-39}{-25}$$

Fraction \frac{-39}{-25} can be simplified to \frac{39}{25} by removing the negative sign from both the numerator and the denominator.

$$\frac{39}{25}$$

Factor

$$\frac{3 \cdot 13}{5 ^ {2}} = 1\frac{14}{25} = 1.56$$