Solve -35/6-24/9+813/24-211/12-3frac{2}{9}-4frac{5}{24}

$$-3 \frac{ 5 }{ 6 } -2 \frac{ 4 }{ 9 } +8 \frac{ 13 }{ 24 } -2 \frac{ 11 }{ 12 } -3 \frac{ 2 }{ 9 } -4 \frac{ 5 }{ 24 }$$

Evaluate

$$-\frac{97}{12}\approx -8.083333333$$

Solution Steps

Multiply 3 and 6 to get 18.

$$-\frac{18+5}{6}-\frac{2\times 9+4}{9}+\frac{8\times 24+13}{24}-\frac{2\times 12+11}{12}-\frac{3\times 9+2}{9}-\frac{4\times 24+5}{24}$$

Add 18 and 5 to get 23.

$$-\frac{23}{6}-\frac{2\times 9+4}{9}+\frac{8\times 24+13}{24}-\frac{2\times 12+11}{12}-\frac{3\times 9+2}{9}-\frac{4\times 24+5}{24}$$

Multiply 2 and 9 to get 18.

$$-\frac{23}{6}-\frac{18+4}{9}+\frac{8\times 24+13}{24}-\frac{2\times 12+11}{12}-\frac{3\times 9+2}{9}-\frac{4\times 24+5}{24}$$

Add 18 and 4 to get 22.

$$-\frac{23}{6}-\frac{22}{9}+\frac{8\times 24+13}{24}-\frac{2\times 12+11}{12}-\frac{3\times 9+2}{9}-\frac{4\times 24+5}{24}$$

Least common multiple of 6 and 9 is 18. Convert -\frac{23}{6} and \frac{22}{9} to fractions with denominator 18.

$$-\frac{69}{18}-\frac{44}{18}+\frac{8\times 24+13}{24}-\frac{2\times 12+11}{12}-\frac{3\times 9+2}{9}-\frac{4\times 24+5}{24}$$

Since -\frac{69}{18} and \frac{44}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-69-44}{18}+\frac{8\times 24+13}{24}-\frac{2\times 12+11}{12}-\frac{3\times 9+2}{9}-\frac{4\times 24+5}{24}$$

Subtract 44 from -69 to get -113.

$$-\frac{113}{18}+\frac{8\times 24+13}{24}-\frac{2\times 12+11}{12}-\frac{3\times 9+2}{9}-\frac{4\times 24+5}{24}$$

Multiply 8 and 24 to get 192.

$$-\frac{113}{18}+\frac{192+13}{24}-\frac{2\times 12+11}{12}-\frac{3\times 9+2}{9}-\frac{4\times 24+5}{24}$$

Add 192 and 13 to get 205.

$$-\frac{113}{18}+\frac{205}{24}-\frac{2\times 12+11}{12}-\frac{3\times 9+2}{9}-\frac{4\times 24+5}{24}$$

Least common multiple of 18 and 24 is 72. Convert -\frac{113}{18} and \frac{205}{24} to fractions with denominator 72.

$$-\frac{452}{72}+\frac{615}{72}-\frac{2\times 12+11}{12}-\frac{3\times 9+2}{9}-\frac{4\times 24+5}{24}$$

Since -\frac{452}{72} and \frac{615}{72} have the same denominator, add them by adding their numerators.

$$\frac{-452+615}{72}-\frac{2\times 12+11}{12}-\frac{3\times 9+2}{9}-\frac{4\times 24+5}{24}$$

Add -452 and 615 to get 163.

$$\frac{163}{72}-\frac{2\times 12+11}{12}-\frac{3\times 9+2}{9}-\frac{4\times 24+5}{24}$$

Multiply 2 and 12 to get 24.

$$\frac{163}{72}-\frac{24+11}{12}-\frac{3\times 9+2}{9}-\frac{4\times 24+5}{24}$$

Add 24 and 11 to get 35.

$$\frac{163}{72}-\frac{35}{12}-\frac{3\times 9+2}{9}-\frac{4\times 24+5}{24}$$

Least common multiple of 72 and 12 is 72. Convert \frac{163}{72} and \frac{35}{12} to fractions with denominator 72.

$$\frac{163}{72}-\frac{210}{72}-\frac{3\times 9+2}{9}-\frac{4\times 24+5}{24}$$

Since \frac{163}{72} and \frac{210}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{163-210}{72}-\frac{3\times 9+2}{9}-\frac{4\times 24+5}{24}$$

Subtract 210 from 163 to get -47.

$$-\frac{47}{72}-\frac{3\times 9+2}{9}-\frac{4\times 24+5}{24}$$

Multiply 3 and 9 to get 27.

$$-\frac{47}{72}-\frac{27+2}{9}-\frac{4\times 24+5}{24}$$

Add 27 and 2 to get 29.

$$-\frac{47}{72}-\frac{29}{9}-\frac{4\times 24+5}{24}$$

Least common multiple of 72 and 9 is 72. Convert -\frac{47}{72} and \frac{29}{9} to fractions with denominator 72.

$$-\frac{47}{72}-\frac{232}{72}-\frac{4\times 24+5}{24}$$

Since -\frac{47}{72} and \frac{232}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-47-232}{72}-\frac{4\times 24+5}{24}$$

Subtract 232 from -47 to get -279.

$$\frac{-279}{72}-\frac{4\times 24+5}{24}$$

Reduce the fraction \frac{-279}{72} to lowest terms by extracting and canceling out 9.

$$-\frac{31}{8}-\frac{4\times 24+5}{24}$$

Multiply 4 and 24 to get 96.

$$-\frac{31}{8}-\frac{96+5}{24}$$

Add 96 and 5 to get 101.

$$-\frac{31}{8}-\frac{101}{24}$$

Least common multiple of 8 and 24 is 24. Convert -\frac{31}{8} and \frac{101}{24} to fractions with denominator 24.

$$-\frac{93}{24}-\frac{101}{24}$$

Since -\frac{93}{24} and \frac{101}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-93-101}{24}$$

Subtract 101 from -93 to get -194.

$$\frac{-194}{24}$$

Reduce the fraction \frac{-194}{24} to lowest terms by extracting and canceling out 2.

$$-\frac{97}{12}$$

Factor

$$-\frac{97}{12} = -8\frac{1}{12} = -8.083333333333334$$