Solve 11/18+(-1)^3*45/271+365/271-(-1)^5*27/18=

$$\frac { 11 } { 18 } + ( - 1 ) ^ { 3 } \times 4 \frac { 5 } { 271 } + 36 \frac { 5 } { 271 } - ( - 1 ) ^ { 5 } \times 2 \frac { 7 } { 18 } =$$

Evaluate

$$35$$

Solution Steps

Calculate -1 to the power of 3 and get -1.

$$\frac{11}{18}-\frac{4\times 271+5}{271}+\frac{36\times 271+5}{271}-\left(-1\right)^{5}\times \frac{2\times 18+7}{18}$$

Multiply 4 and 271 to get 1084.

$$\frac{11}{18}-\frac{1084+5}{271}+\frac{36\times 271+5}{271}-\left(-1\right)^{5}\times \frac{2\times 18+7}{18}$$

Add 1084 and 5 to get 1089.

$$\frac{11}{18}-\frac{1089}{271}+\frac{36\times 271+5}{271}-\left(-1\right)^{5}\times \frac{2\times 18+7}{18}$$

Least common multiple of 18 and 271 is 4878. Convert \frac{11}{18} and \frac{1089}{271} to fractions with denominator 4878.

$$\frac{2981}{4878}-\frac{19602}{4878}+\frac{36\times 271+5}{271}-\left(-1\right)^{5}\times \frac{2\times 18+7}{18}$$

Since \frac{2981}{4878} and \frac{19602}{4878} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2981-19602}{4878}+\frac{36\times 271+5}{271}-\left(-1\right)^{5}\times \frac{2\times 18+7}{18}$$

Subtract 19602 from 2981 to get -16621.

$$-\frac{16621}{4878}+\frac{36\times 271+5}{271}-\left(-1\right)^{5}\times \frac{2\times 18+7}{18}$$

Multiply 36 and 271 to get 9756.

$$-\frac{16621}{4878}+\frac{9756+5}{271}-\left(-1\right)^{5}\times \frac{2\times 18+7}{18}$$

Add 9756 and 5 to get 9761.

$$-\frac{16621}{4878}+\frac{9761}{271}-\left(-1\right)^{5}\times \frac{2\times 18+7}{18}$$

Least common multiple of 4878 and 271 is 4878. Convert -\frac{16621}{4878} and \frac{9761}{271} to fractions with denominator 4878.

$$-\frac{16621}{4878}+\frac{175698}{4878}-\left(-1\right)^{5}\times \frac{2\times 18+7}{18}$$

Since -\frac{16621}{4878} and \frac{175698}{4878} have the same denominator, add them by adding their numerators.

$$\frac{-16621+175698}{4878}-\left(-1\right)^{5}\times \frac{2\times 18+7}{18}$$

Add -16621 and 175698 to get 159077.

$$\frac{159077}{4878}-\left(-1\right)^{5}\times \frac{2\times 18+7}{18}$$

Reduce the fraction \frac{159077}{4878} to lowest terms by extracting and canceling out 271.

$$\frac{587}{18}-\left(-1\right)^{5}\times \frac{2\times 18+7}{18}$$

Calculate -1 to the power of 5 and get -1.

$$\frac{587}{18}-\left(-\frac{2\times 18+7}{18}\right)$$

Multiply 2 and 18 to get 36.

$$\frac{587}{18}-\left(-\frac{36+7}{18}\right)$$

Add 36 and 7 to get 43.

$$\frac{587}{18}-\left(-\frac{43}{18}\right)$$

The opposite of -\frac{43}{18} is \frac{43}{18}.

$$\frac{587}{18}+\frac{43}{18}$$

Since \frac{587}{18} and \frac{43}{18} have the same denominator, add them by adding their numerators.

$$\frac{587+43}{18}$$

Add 587 and 43 to get 630.

$$\frac{630}{18}$$

Divide 630 by 18 to get 35.

$$35$$

Factor

$$5\times 7$$