Solve 8/9*(2/5+3/7*1/5+frac{3}{5})*4

$$\frac { 8 } { 9 } \times ( \frac { 2 } { 5 } + \frac { 3 } { 7 } \times \frac { 1 } { 5 } + \frac { 3 } { 5 } ) \times 4$$

Evaluate

$$\frac{1216}{315}\approx 3.86031746$$

Solution Steps

Multiply \frac{3}{7} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{9}\left(\frac{2}{5}+\frac{3\times 1}{7\times 5}+\frac{3}{5}\right)\times 4$$

Do the multiplications in the fraction \frac{3\times 1}{7\times 5}.

$$\frac{8}{9}\left(\frac{2}{5}+\frac{3}{35}+\frac{3}{5}\right)\times 4$$

Least common multiple of 5 and 35 is 35. Convert \frac{2}{5} and \frac{3}{35} to fractions with denominator 35.

$$\frac{8}{9}\left(\frac{14}{35}+\frac{3}{35}+\frac{3}{5}\right)\times 4$$

Since \frac{14}{35} and \frac{3}{35} have the same denominator, add them by adding their numerators.

$$\frac{8}{9}\left(\frac{14+3}{35}+\frac{3}{5}\right)\times 4$$

Add 14 and 3 to get 17.

$$\frac{8}{9}\left(\frac{17}{35}+\frac{3}{5}\right)\times 4$$

Least common multiple of 35 and 5 is 35. Convert \frac{17}{35} and \frac{3}{5} to fractions with denominator 35.

$$\frac{8}{9}\left(\frac{17}{35}+\frac{21}{35}\right)\times 4$$

Since \frac{17}{35} and \frac{21}{35} have the same denominator, add them by adding their numerators.

$$\frac{8}{9}\times \frac{17+21}{35}\times 4$$

Add 17 and 21 to get 38.

$$\frac{8}{9}\times \frac{38}{35}\times 4$$

Multiply \frac{8}{9} times \frac{38}{35} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 38}{9\times 35}\times 4$$

Do the multiplications in the fraction \frac{8\times 38}{9\times 35}.

$$\frac{304}{315}\times 4$$

Express \frac{304}{315}\times 4 as a single fraction.

$$\frac{304\times 4}{315}$$

Multiply 304 and 4 to get 1216.

$$\frac{1216}{315}$$

Factor

$$\frac{2 ^ {6} \cdot 19}{3 ^ {2} \cdot 5 \cdot 7} = 3\frac{271}{315} = 3.8603174603174604$$