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

$$\frac{125}{12}\approx 10.416666667$$

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 -23.

$$-\frac{23}{6}+\frac{17\times 4+3}{4}-\frac{3\times 2+1}{2}$$

Multiply 17 and 4 to get 68.

$$-\frac{23}{6}+\frac{68+3}{4}-\frac{3\times 2+1}{2}$$

Add 68 and 3 to get 71.

$$-\frac{23}{6}+\frac{71}{4}-\frac{3\times 2+1}{2}$$

Least common multiple of 6 and 4 is 12. Convert -\frac{23}{6} and \frac{71}{4} to fractions with denominator 12.

$$-\frac{46}{12}+\frac{213}{12}-\frac{3\times 2+1}{2}$$

Since -\frac{46}{12} and \frac{213}{12} have the same denominator, add them by adding their numerators.

$$\frac{-46+213}{12}-\frac{3\times 2+1}{2}$$

Add -46 and 213 to get 167.

$$\frac{167}{12}-\frac{3\times 2+1}{2}$$

Multiply 3 and 2 to get 6.

$$\frac{167}{12}-\frac{6+1}{2}$$

Add 6 and 1 to get 7.

$$\frac{167}{12}-\frac{7}{2}$$

Least common multiple of 12 and 2 is 12. Convert \frac{167}{12} and \frac{7}{2} to fractions with denominator 12.

$$\frac{167}{12}-\frac{42}{12}$$

Since \frac{167}{12} and \frac{42}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{167-42}{12}$$

Subtract 42 from 167 to get 125.

$$\frac{125}{12}$$

Factor

$$\frac{5 ^ {3}}{2 ^ {2} \cdot 3} = 10\frac{5}{12} = 10.416666666666666$$