Solve 613/22+55/11:(-4)-5/132:(-1/6)+(-frac{5}{6})^2:1frac{7}{18}

$$6 \frac { 13 } { 22 } + 5 \frac { 5 } { 11 } : ( - 4 ) - \frac { 5 } { 132 } : ( - \frac { 1 } { 6 } ) + ( - \frac { 5 } { 6 } ) ^ { 2 } : 1 \frac { 7 } { 18 }$$

Evaluate

$$\frac{131}{22}\approx 5.954545455$$

Solution Steps

Multiply 6 and 22 to get 132.

$$\frac{132+13}{22}+\frac{\frac{5\times 11+5}{11}}{-4}-\frac{\frac{5}{132}}{-\frac{1}{6}}+\frac{\left(-\frac{5}{6}\right)^{2}}{\frac{1\times 18+7}{18}}$$

Add 132 and 13 to get 145.

$$\frac{145}{22}+\frac{\frac{5\times 11+5}{11}}{-4}-\frac{\frac{5}{132}}{-\frac{1}{6}}+\frac{\left(-\frac{5}{6}\right)^{2}}{\frac{1\times 18+7}{18}}$$

Express \frac{\frac{5\times 11+5}{11}}{-4} as a single fraction.

$$\frac{145}{22}+\frac{5\times 11+5}{11\left(-4\right)}-\frac{\frac{5}{132}}{-\frac{1}{6}}+\frac{\left(-\frac{5}{6}\right)^{2}}{\frac{1\times 18+7}{18}}$$

Multiply 5 and 11 to get 55.

$$\frac{145}{22}+\frac{55+5}{11\left(-4\right)}-\frac{\frac{5}{132}}{-\frac{1}{6}}+\frac{\left(-\frac{5}{6}\right)^{2}}{\frac{1\times 18+7}{18}}$$

Add 55 and 5 to get 60.

$$\frac{145}{22}+\frac{60}{11\left(-4\right)}-\frac{\frac{5}{132}}{-\frac{1}{6}}+\frac{\left(-\frac{5}{6}\right)^{2}}{\frac{1\times 18+7}{18}}$$

Multiply 11 and -4 to get -44.

$$\frac{145}{22}+\frac{60}{-44}-\frac{\frac{5}{132}}{-\frac{1}{6}}+\frac{\left(-\frac{5}{6}\right)^{2}}{\frac{1\times 18+7}{18}}$$

Reduce the fraction \frac{60}{-44} to lowest terms by extracting and canceling out 4.

$$\frac{145}{22}-\frac{15}{11}-\frac{\frac{5}{132}}{-\frac{1}{6}}+\frac{\left(-\frac{5}{6}\right)^{2}}{\frac{1\times 18+7}{18}}$$

Least common multiple of 22 and 11 is 22. Convert \frac{145}{22} and \frac{15}{11} to fractions with denominator 22.

$$\frac{145}{22}-\frac{30}{22}-\frac{\frac{5}{132}}{-\frac{1}{6}}+\frac{\left(-\frac{5}{6}\right)^{2}}{\frac{1\times 18+7}{18}}$$

Since \frac{145}{22} and \frac{30}{22} have the same denominator, subtract them by subtracting their numerators.

$$\frac{145-30}{22}-\frac{\frac{5}{132}}{-\frac{1}{6}}+\frac{\left(-\frac{5}{6}\right)^{2}}{\frac{1\times 18+7}{18}}$$

Subtract 30 from 145 to get 115.

$$\frac{115}{22}-\frac{\frac{5}{132}}{-\frac{1}{6}}+\frac{\left(-\frac{5}{6}\right)^{2}}{\frac{1\times 18+7}{18}}$$

Divide \frac{5}{132} by -\frac{1}{6} by multiplying \frac{5}{132} by the reciprocal of -\frac{1}{6}.

$$\frac{115}{22}-\frac{5}{132}\left(-6\right)+\frac{\left(-\frac{5}{6}\right)^{2}}{\frac{1\times 18+7}{18}}$$

Express \frac{5}{132}\left(-6\right) as a single fraction.

$$\frac{115}{22}-\frac{5\left(-6\right)}{132}+\frac{\left(-\frac{5}{6}\right)^{2}}{\frac{1\times 18+7}{18}}$$

Multiply 5 and -6 to get -30.

$$\frac{115}{22}-\frac{-30}{132}+\frac{\left(-\frac{5}{6}\right)^{2}}{\frac{1\times 18+7}{18}}$$

Reduce the fraction \frac{-30}{132} to lowest terms by extracting and canceling out 6.

$$\frac{115}{22}-\left(-\frac{5}{22}\right)+\frac{\left(-\frac{5}{6}\right)^{2}}{\frac{1\times 18+7}{18}}$$

The opposite of -\frac{5}{22} is \frac{5}{22}.

$$\frac{115}{22}+\frac{5}{22}+\frac{\left(-\frac{5}{6}\right)^{2}}{\frac{1\times 18+7}{18}}$$

Since \frac{115}{22} and \frac{5}{22} have the same denominator, add them by adding their numerators.

$$\frac{115+5}{22}+\frac{\left(-\frac{5}{6}\right)^{2}}{\frac{1\times 18+7}{18}}$$

Add 115 and 5 to get 120.

$$\frac{120}{22}+\frac{\left(-\frac{5}{6}\right)^{2}}{\frac{1\times 18+7}{18}}$$

Reduce the fraction \frac{120}{22} to lowest terms by extracting and canceling out 2.

$$\frac{60}{11}+\frac{\left(-\frac{5}{6}\right)^{2}}{\frac{1\times 18+7}{18}}$$

Calculate -\frac{5}{6} to the power of 2 and get \frac{25}{36}.

$$\frac{60}{11}+\frac{\frac{25}{36}}{\frac{1\times 18+7}{18}}$$

Multiply 1 and 18 to get 18.

$$\frac{60}{11}+\frac{\frac{25}{36}}{\frac{18+7}{18}}$$

Add 18 and 7 to get 25.

$$\frac{60}{11}+\frac{\frac{25}{36}}{\frac{25}{18}}$$

Divide \frac{25}{36} by \frac{25}{18} by multiplying \frac{25}{36} by the reciprocal of \frac{25}{18}.

$$\frac{60}{11}+\frac{25}{36}\times \frac{18}{25}$$

Multiply \frac{25}{36} times \frac{18}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{60}{11}+\frac{25\times 18}{36\times 25}$$

Cancel out 25 in both numerator and denominator.

$$\frac{60}{11}+\frac{18}{36}$$

Reduce the fraction \frac{18}{36} to lowest terms by extracting and canceling out 18.

$$\frac{60}{11}+\frac{1}{2}$$

Least common multiple of 11 and 2 is 22. Convert \frac{60}{11} and \frac{1}{2} to fractions with denominator 22.

$$\frac{120}{22}+\frac{11}{22}$$

Since \frac{120}{22} and \frac{11}{22} have the same denominator, add them by adding their numerators.

$$\frac{120+11}{22}$$

Add 120 and 11 to get 131.

$$\frac{131}{22}$$

Factor

$$\frac{131}{2 \cdot 11} = 5\frac{21}{22} = 5.954545454545454$$