Solve 2/5[(2/4+21/8)1/3+frac{2+frac{1}{5}}{frac{30}{17}}]

$$\frac { 2 } { 5 } [ ( \frac { 2 } { 4 } + \frac { 21 } { 8 } ) \frac { 1 } { 3 } + \frac { 2 + \frac { 1 } { 5 } } { \frac { 30 } { 17 } } ]$$

Evaluate

$$\frac{1373}{1500}\approx 0.915333333$$

Solution Steps

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{2}{5}\left(\left(\frac{1}{2}+\frac{21}{8}\right)\times \frac{1}{3}+\frac{2+\frac{1}{5}}{\frac{30}{17}}\right)$$

Least common multiple of 2 and 8 is 8. Convert \frac{1}{2} and \frac{21}{8} to fractions with denominator 8.

$$\frac{2}{5}\left(\left(\frac{4}{8}+\frac{21}{8}\right)\times \frac{1}{3}+\frac{2+\frac{1}{5}}{\frac{30}{17}}\right)$$

Since \frac{4}{8} and \frac{21}{8} have the same denominator, add them by adding their numerators.

$$\frac{2}{5}\left(\frac{4+21}{8}\times \frac{1}{3}+\frac{2+\frac{1}{5}}{\frac{30}{17}}\right)$$

Add 4 and 21 to get 25.

$$\frac{2}{5}\left(\frac{25}{8}\times \frac{1}{3}+\frac{2+\frac{1}{5}}{\frac{30}{17}}\right)$$

Multiply \frac{25}{8} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{5}\left(\frac{25\times 1}{8\times 3}+\frac{2+\frac{1}{5}}{\frac{30}{17}}\right)$$

Do the multiplications in the fraction \frac{25\times 1}{8\times 3}.

$$\frac{2}{5}\left(\frac{25}{24}+\frac{2+\frac{1}{5}}{\frac{30}{17}}\right)$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{2}{5}\left(\frac{25}{24}+\frac{\frac{10}{5}+\frac{1}{5}}{\frac{30}{17}}\right)$$

Since \frac{10}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

$$\frac{2}{5}\left(\frac{25}{24}+\frac{\frac{10+1}{5}}{\frac{30}{17}}\right)$$

Add 10 and 1 to get 11.

$$\frac{2}{5}\left(\frac{25}{24}+\frac{\frac{11}{5}}{\frac{30}{17}}\right)$$

Divide \frac{11}{5} by \frac{30}{17} by multiplying \frac{11}{5} by the reciprocal of \frac{30}{17}.

$$\frac{2}{5}\left(\frac{25}{24}+\frac{11}{5}\times \frac{17}{30}\right)$$

Multiply \frac{11}{5} times \frac{17}{30} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{5}\left(\frac{25}{24}+\frac{11\times 17}{5\times 30}\right)$$

Do the multiplications in the fraction \frac{11\times 17}{5\times 30}.

$$\frac{2}{5}\left(\frac{25}{24}+\frac{187}{150}\right)$$

Least common multiple of 24 and 150 is 600. Convert \frac{25}{24} and \frac{187}{150} to fractions with denominator 600.

$$\frac{2}{5}\left(\frac{625}{600}+\frac{748}{600}\right)$$

Since \frac{625}{600} and \frac{748}{600} have the same denominator, add them by adding their numerators.

$$\frac{2}{5}\times \frac{625+748}{600}$$

Add 625 and 748 to get 1373.

$$\frac{2}{5}\times \frac{1373}{600}$$

Multiply \frac{2}{5} times \frac{1373}{600} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 1373}{5\times 600}$$

Do the multiplications in the fraction \frac{2\times 1373}{5\times 600}.

$$\frac{2746}{3000}$$

Reduce the fraction \frac{2746}{3000} to lowest terms by extracting and canceling out 2.

$$\frac{1373}{1500}$$

Factor

$$\frac{1373}{2 ^ {2} \cdot 3 \cdot 5 ^ {3}} = 0.9153333333333333$$