Solve -51/2+82/3-125/6

$$- 5 \frac { 1 } { 2 } + 8 \frac { 2 } { 3 } - 12 \frac { 5 } { 6 }$$

Evaluate

$$-\frac{29}{3}\approx -9.666666667$$

Solution Steps

Multiply 5 and 2 to get 10.

$$-\frac{10+1}{2}+\frac{8\times 3+2}{3}-\frac{12\times 6+5}{6}$$

Add 10 and 1 to get 11.

$$-\frac{11}{2}+\frac{8\times 3+2}{3}-\frac{12\times 6+5}{6}$$

Multiply 8 and 3 to get 24.

$$-\frac{11}{2}+\frac{24+2}{3}-\frac{12\times 6+5}{6}$$

Add 24 and 2 to get 26.

$$-\frac{11}{2}+\frac{26}{3}-\frac{12\times 6+5}{6}$$

Least common multiple of 2 and 3 is 6. Convert -\frac{11}{2} and \frac{26}{3} to fractions with denominator 6.

$$-\frac{33}{6}+\frac{52}{6}-\frac{12\times 6+5}{6}$$

Since -\frac{33}{6} and \frac{52}{6} have the same denominator, add them by adding their numerators.

$$\frac{-33+52}{6}-\frac{12\times 6+5}{6}$$

Add -33 and 52 to get 19.

$$\frac{19}{6}-\frac{12\times 6+5}{6}$$

Multiply 12 and 6 to get 72.

$$\frac{19}{6}-\frac{72+5}{6}$$

Add 72 and 5 to get 77.

$$\frac{19}{6}-\frac{77}{6}$$

Since \frac{19}{6} and \frac{77}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19-77}{6}$$

Subtract 77 from 19 to get -58.

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

Reduce the fraction \frac{-58}{6} to lowest terms by extracting and canceling out 2.

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

Factor

$$-\frac{29}{3} = -9\frac{2}{3} = -9.666666666666666$$