Solve -55/6-92/3+173/4-31/2

$$- 5 \frac { 5 } { 6 } - 9 \frac { 2 } { 3 } + 17 \frac { 3 } { 4 } - 3 \frac { 1 } { 2 }$$

Evaluate

$$-\frac{5}{4}=-1.25$$

Solution Steps

Multiply 5 and 6 to get 30.

$$-\frac{30+5}{6}-\frac{9\times 3+2}{3}+\frac{17\times 4+3}{4}-\frac{3\times 2+1}{2}$$

Add 30 and 5 to get 35.

$$-\frac{35}{6}-\frac{9\times 3+2}{3}+\frac{17\times 4+3}{4}-\frac{3\times 2+1}{2}$$

Multiply 9 and 3 to get 27.

$$-\frac{35}{6}-\frac{27+2}{3}+\frac{17\times 4+3}{4}-\frac{3\times 2+1}{2}$$

Add 27 and 2 to get 29.

$$-\frac{35}{6}-\frac{29}{3}+\frac{17\times 4+3}{4}-\frac{3\times 2+1}{2}$$

Least common multiple of 6 and 3 is 6. Convert -\frac{35}{6} and \frac{29}{3} to fractions with denominator 6.

$$-\frac{35}{6}-\frac{58}{6}+\frac{17\times 4+3}{4}-\frac{3\times 2+1}{2}$$

Since -\frac{35}{6} and \frac{58}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-35-58}{6}+\frac{17\times 4+3}{4}-\frac{3\times 2+1}{2}$$

Subtract 58 from -35 to get -93.

$$\frac{-93}{6}+\frac{17\times 4+3}{4}-\frac{3\times 2+1}{2}$$

Reduce the fraction \frac{-93}{6} to lowest terms by extracting and canceling out 3.

$$-\frac{31}{2}+\frac{17\times 4+3}{4}-\frac{3\times 2+1}{2}$$

Multiply 17 and 4 to get 68.

$$-\frac{31}{2}+\frac{68+3}{4}-\frac{3\times 2+1}{2}$$

Add 68 and 3 to get 71.

$$-\frac{31}{2}+\frac{71}{4}-\frac{3\times 2+1}{2}$$

Least common multiple of 2 and 4 is 4. Convert -\frac{31}{2} and \frac{71}{4} to fractions with denominator 4.

$$-\frac{62}{4}+\frac{71}{4}-\frac{3\times 2+1}{2}$$

Since -\frac{62}{4} and \frac{71}{4} have the same denominator, add them by adding their numerators.

$$\frac{-62+71}{4}-\frac{3\times 2+1}{2}$$

Add -62 and 71 to get 9.

$$\frac{9}{4}-\frac{3\times 2+1}{2}$$

Multiply 3 and 2 to get 6.

$$\frac{9}{4}-\frac{6+1}{2}$$

Add 6 and 1 to get 7.

$$\frac{9}{4}-\frac{7}{2}$$

Least common multiple of 4 and 2 is 4. Convert \frac{9}{4} and \frac{7}{2} to fractions with denominator 4.

$$\frac{9}{4}-\frac{14}{4}$$

Since \frac{9}{4} and \frac{14}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-14}{4}$$

Subtract 14 from 9 to get -5.

$$-\frac{5}{4}$$

Factor

$$-\frac{5}{4} = -1\frac{1}{4} = -1.25$$