Solve (-55/6+76/7):(-17/42)=

$$( - 5 \frac { 5 } { 6 } + 7 \frac { 6 } { 7 } ) : ( - \frac { 17 } { 42 } ) =$$

Evaluate

$$-5$$

Solution Steps

Multiply 5 and 6 to get 30.

$$\frac{-\frac{30+5}{6}+\frac{7\times 7+6}{7}}{-\frac{17}{42}}$$

Add 30 and 5 to get 35.

$$\frac{-\frac{35}{6}+\frac{7\times 7+6}{7}}{-\frac{17}{42}}$$

Multiply 7 and 7 to get 49.

$$\frac{-\frac{35}{6}+\frac{49+6}{7}}{-\frac{17}{42}}$$

Add 49 and 6 to get 55.

$$\frac{-\frac{35}{6}+\frac{55}{7}}{-\frac{17}{42}}$$

Least common multiple of 6 and 7 is 42. Convert -\frac{35}{6} and \frac{55}{7} to fractions with denominator 42.

$$\frac{-\frac{245}{42}+\frac{330}{42}}{-\frac{17}{42}}$$

Since -\frac{245}{42} and \frac{330}{42} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-245+330}{42}}{-\frac{17}{42}}$$

Add -245 and 330 to get 85.

$$\frac{\frac{85}{42}}{-\frac{17}{42}}$$

Divide \frac{85}{42} by -\frac{17}{42} by multiplying \frac{85}{42} by the reciprocal of -\frac{17}{42}.

$$\frac{85}{42}\left(-\frac{42}{17}\right)$$

Multiply \frac{85}{42} times -\frac{42}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{85\left(-42\right)}{42\times 17}$$

Do the multiplications in the fraction \frac{85\left(-42\right)}{42\times 17}.

$$\frac{-3570}{714}$$

Divide -3570 by 714 to get -5.

$$-5$$

Factor

$$-5$$