Solve 8/5*[(7/5+1/2)*4]

$$\frac { 8 } { 5 } \times [ ( \frac { 7 } { 5 } + \frac { 1 } { 2 } ) \times 4 ]$$

Evaluate

$$\frac{304}{25}=12.16$$

Solution Steps

Least common multiple of 5 and 2 is 10. Convert \frac{7}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{8}{5}\left(\frac{14}{10}+\frac{5}{10}\right)\times 4$$

Since \frac{14}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{8}{5}\times \frac{14+5}{10}\times 4$$

Add 14 and 5 to get 19.

$$\frac{8}{5}\times \frac{19}{10}\times 4$$

Multiply \frac{8}{5} times \frac{19}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 19}{5\times 10}\times 4$$

Do the multiplications in the fraction \frac{8\times 19}{5\times 10}.

$$\frac{152}{50}\times 4$$

Reduce the fraction \frac{152}{50} to lowest terms by extracting and canceling out 2.

$$\frac{76}{25}\times 4$$

Express \frac{76}{25}\times 4 as a single fraction.

$$\frac{76\times 4}{25}$$

Multiply 76 and 4 to get 304.

$$\frac{304}{25}$$

Factor

$$\frac{2 ^ {4} \cdot 19}{5 ^ {2}} = 12\frac{4}{25} = 12.16$$