Solve (-27)+11/3+16+(-45/6)

$$( - 27 ) + 1 \frac { 1 } { 3 } + 16 + ( - 4 \frac { 5 } { 6 } )$$

Evaluate

$$-\frac{29}{2}=-14.5$$

Solution Steps

Multiply 1 and 3 to get 3.

$$-27+\frac{3+1}{3}+16-\frac{4\times 6+5}{6}$$

Add 3 and 1 to get 4.

$$-27+\frac{4}{3}+16-\frac{4\times 6+5}{6}$$

Convert -27 to fraction -\frac{81}{3}.

$$-\frac{81}{3}+\frac{4}{3}+16-\frac{4\times 6+5}{6}$$

Since -\frac{81}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

$$\frac{-81+4}{3}+16-\frac{4\times 6+5}{6}$$

Add -81 and 4 to get -77.

$$-\frac{77}{3}+16-\frac{4\times 6+5}{6}$$

Convert 16 to fraction \frac{48}{3}.

$$-\frac{77}{3}+\frac{48}{3}-\frac{4\times 6+5}{6}$$

Since -\frac{77}{3} and \frac{48}{3} have the same denominator, add them by adding their numerators.

$$\frac{-77+48}{3}-\frac{4\times 6+5}{6}$$

Add -77 and 48 to get -29.

$$-\frac{29}{3}-\frac{4\times 6+5}{6}$$

Multiply 4 and 6 to get 24.

$$-\frac{29}{3}-\frac{24+5}{6}$$

Add 24 and 5 to get 29.

$$-\frac{29}{3}-\frac{29}{6}$$

Least common multiple of 3 and 6 is 6. Convert -\frac{29}{3} and \frac{29}{6} to fractions with denominator 6.

$$-\frac{58}{6}-\frac{29}{6}$$

Since -\frac{58}{6} and \frac{29}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-58-29}{6}$$

Subtract 29 from -58 to get -87.

$$\frac{-87}{6}$$

Reduce the fraction \frac{-87}{6} to lowest terms by extracting and canceling out 3.

$$-\frac{29}{2}$$

Factor

$$-\frac{29}{2} = -14\frac{1}{2} = -14.5$$