Solve -55/6-92/3div173/4-31/2

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

Evaluate

$$-\frac{2104}{213}\approx -9.877934272$$

Solution Steps

Multiply 5 and 6 to get 30.

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

Add 30 and 5 to get 35.

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

Divide \frac{9\times 3+2}{3} by \frac{17\times 4+3}{4} by multiplying \frac{9\times 3+2}{3} by the reciprocal of \frac{17\times 4+3}{4}.

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

Multiply 9 and 3 to get 27.

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

Add 27 and 2 to get 29.

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

Multiply 29 and 4 to get 116.

$$-\frac{35}{6}-\frac{116}{3\left(17\times 4+3\right)}-\frac{3\times 2+1}{2}$$

Multiply 17 and 4 to get 68.

$$-\frac{35}{6}-\frac{116}{3\left(68+3\right)}-\frac{3\times 2+1}{2}$$

Add 68 and 3 to get 71.

$$-\frac{35}{6}-\frac{116}{3\times 71}-\frac{3\times 2+1}{2}$$

Multiply 3 and 71 to get 213.

$$-\frac{35}{6}-\frac{116}{213}-\frac{3\times 2+1}{2}$$

Least common multiple of 6 and 213 is 426. Convert -\frac{35}{6} and \frac{116}{213} to fractions with denominator 426.

$$-\frac{2485}{426}-\frac{232}{426}-\frac{3\times 2+1}{2}$$

Since -\frac{2485}{426} and \frac{232}{426} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2485-232}{426}-\frac{3\times 2+1}{2}$$

Subtract 232 from -2485 to get -2717.

$$-\frac{2717}{426}-\frac{3\times 2+1}{2}$$

Multiply 3 and 2 to get 6.

$$-\frac{2717}{426}-\frac{6+1}{2}$$

Add 6 and 1 to get 7.

$$-\frac{2717}{426}-\frac{7}{2}$$

Least common multiple of 426 and 2 is 426. Convert -\frac{2717}{426} and \frac{7}{2} to fractions with denominator 426.

$$-\frac{2717}{426}-\frac{1491}{426}$$

Since -\frac{2717}{426} and \frac{1491}{426} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2717-1491}{426}$$

Subtract 1491 from -2717 to get -4208.

$$\frac{-4208}{426}$$

Reduce the fraction \frac{-4208}{426} to lowest terms by extracting and canceling out 2.

$$-\frac{2104}{213}$$

Factor

$$-\frac{2104}{213} = -9\frac{187}{213} = -9.87793427230047$$