Solve -5/6+12/3div(-3/7)

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

Evaluate

$$-\frac{85}{18}\approx -4.722222222$$

Solution Steps

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

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

Multiply 1 and 3 to get 3.

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

Add 3 and 2 to get 5.

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

Multiply 5 and 7 to get 35.

$$-\frac{5}{6}+\frac{35}{3\left(-3\right)}$$

Multiply 3 and -3 to get -9.

$$-\frac{5}{6}+\frac{35}{-9}$$

Fraction \frac{35}{-9} can be rewritten as -\frac{35}{9} by extracting the negative sign.

$$-\frac{5}{6}-\frac{35}{9}$$

Least common multiple of 6 and 9 is 18. Convert -\frac{5}{6} and \frac{35}{9} to fractions with denominator 18.

$$-\frac{15}{18}-\frac{70}{18}$$

Since -\frac{15}{18} and \frac{70}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-15-70}{18}$$

Subtract 70 from -15 to get -85.

$$-\frac{85}{18}$$

Factor

$$-\frac{85}{18} = -4\frac{13}{18} = -4.722222222222222$$