Solve -2-5/6+2(-31/3)-3-4

$$-2- \frac{ 5 }{ 6 } +2(- \frac{ 31 }{ 3 } )-3-4$$

Evaluate

$$-\frac{61}{2}=-30.5$$

Solution Steps

Convert -2 to fraction -\frac{12}{6}.

$$-\frac{12}{6}-\frac{5}{6}+2\left(-\frac{31}{3}\right)-3-4$$

Since -\frac{12}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-12-5}{6}+2\left(-\frac{31}{3}\right)-3-4$$

Subtract 5 from -12 to get -17.

$$-\frac{17}{6}+2\left(-\frac{31}{3}\right)-3-4$$

Express 2\left(-\frac{31}{3}\right) as a single fraction.

$$-\frac{17}{6}+\frac{2\left(-31\right)}{3}-3-4$$

Multiply 2 and -31 to get -62.

$$-\frac{17}{6}+\frac{-62}{3}-3-4$$

Fraction \frac{-62}{3} can be rewritten as -\frac{62}{3} by extracting the negative sign.

$$-\frac{17}{6}-\frac{62}{3}-3-4$$

Least common multiple of 6 and 3 is 6. Convert -\frac{17}{6} and \frac{62}{3} to fractions with denominator 6.

$$-\frac{17}{6}-\frac{124}{6}-3-4$$

Since -\frac{17}{6} and \frac{124}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-17-124}{6}-3-4$$

Subtract 124 from -17 to get -141.

$$\frac{-141}{6}-3-4$$

Reduce the fraction \frac{-141}{6} to lowest terms by extracting and canceling out 3.

$$-\frac{47}{2}-3-4$$

Convert 3 to fraction \frac{6}{2}.

$$-\frac{47}{2}-\frac{6}{2}-4$$

Since -\frac{47}{2} and \frac{6}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-47-6}{2}-4$$

Subtract 6 from -47 to get -53.

$$-\frac{53}{2}-4$$

Convert 4 to fraction \frac{8}{2}.

$$-\frac{53}{2}-\frac{8}{2}$$

Since -\frac{53}{2} and \frac{8}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-53-8}{2}$$

Subtract 8 from -53 to get -61.

$$-\frac{61}{2}$$

Factor

$$-\frac{61}{2} = -30\frac{1}{2} = -30.5$$