Solve 7:(5/2-2/5)+11/30:12/3+(-1)^2005

$$7 : ( \frac { 5 } { 2 } - \frac { 2 } { 5 } ) + \frac { 11 } { 30 } : 1 \frac { 2 } { 3 } + ( - 1 ) ^ { 2005 }$$

Evaluate

$$\frac{383}{150}\approx 2.553333333$$

Solution Steps

Least common multiple of 2 and 5 is 10. Convert \frac{5}{2} and \frac{2}{5} to fractions with denominator 10.

$$\frac{7}{\frac{25}{10}-\frac{4}{10}}+\frac{\frac{11}{30}}{\frac{1\times 3+2}{3}}+\left(-1\right)^{2005}$$

Since \frac{25}{10} and \frac{4}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{\frac{25-4}{10}}+\frac{\frac{11}{30}}{\frac{1\times 3+2}{3}}+\left(-1\right)^{2005}$$

Subtract 4 from 25 to get 21.

$$\frac{7}{\frac{21}{10}}+\frac{\frac{11}{30}}{\frac{1\times 3+2}{3}}+\left(-1\right)^{2005}$$

Divide 7 by \frac{21}{10} by multiplying 7 by the reciprocal of \frac{21}{10}.

$$7\times \frac{10}{21}+\frac{\frac{11}{30}}{\frac{1\times 3+2}{3}}+\left(-1\right)^{2005}$$

Express 7\times \frac{10}{21} as a single fraction.

$$\frac{7\times 10}{21}+\frac{\frac{11}{30}}{\frac{1\times 3+2}{3}}+\left(-1\right)^{2005}$$

Multiply 7 and 10 to get 70.

$$\frac{70}{21}+\frac{\frac{11}{30}}{\frac{1\times 3+2}{3}}+\left(-1\right)^{2005}$$

Reduce the fraction \frac{70}{21} to lowest terms by extracting and canceling out 7.

$$\frac{10}{3}+\frac{\frac{11}{30}}{\frac{1\times 3+2}{3}}+\left(-1\right)^{2005}$$

Divide \frac{11}{30} by \frac{1\times 3+2}{3} by multiplying \frac{11}{30} by the reciprocal of \frac{1\times 3+2}{3}.

$$\frac{10}{3}+\frac{11\times 3}{30\left(1\times 3+2\right)}+\left(-1\right)^{2005}$$

Cancel out 3 in both numerator and denominator.

$$\frac{10}{3}+\frac{11}{10\left(2+3\right)}+\left(-1\right)^{2005}$$

Add 2 and 3 to get 5.

$$\frac{10}{3}+\frac{11}{10\times 5}+\left(-1\right)^{2005}$$

Multiply 10 and 5 to get 50.

$$\frac{10}{3}+\frac{11}{50}+\left(-1\right)^{2005}$$

Least common multiple of 3 and 50 is 150. Convert \frac{10}{3} and \frac{11}{50} to fractions with denominator 150.

$$\frac{500}{150}+\frac{33}{150}+\left(-1\right)^{2005}$$

Since \frac{500}{150} and \frac{33}{150} have the same denominator, add them by adding their numerators.

$$\frac{500+33}{150}+\left(-1\right)^{2005}$$

Add 500 and 33 to get 533.

$$\frac{533}{150}+\left(-1\right)^{2005}$$

Calculate -1 to the power of 2005 and get -1.

$$\frac{533}{150}-1$$

Convert 1 to fraction \frac{150}{150}.

$$\frac{533}{150}-\frac{150}{150}$$

Since \frac{533}{150} and \frac{150}{150} have the same denominator, subtract them by subtracting their numerators.

$$\frac{533-150}{150}$$

Subtract 150 from 533 to get 383.

$$\frac{383}{150}$$

Factor

$$\frac{383}{2 \cdot 3 \cdot 5 ^ {2}} = 2\frac{83}{150} = 2.5533333333333332$$