Solve {l}{1/3*2/5*2/5+2/3*frac{3}{5}*frac{2}{5}}{+frac{2}{3}*frac{2}{5}*frac{3}{5}}

$$\left. \begin{array} { l } { \frac { 1 } { 3 } \times \frac { 2 } { 5 } \times \frac { 2 } { 5 } + \frac { 2 } { 3 } \times \frac { 3 } { 5 } \times \frac { 2 } { 5 } } \\ { + \frac { 2 } { 3 } \times \frac { 2 } { 5 } \times \frac { 3 } { 5 } } \end{array} \right.$$

Evaluate

$$\frac{28}{75}\approx 0.373333333$$

Solution Steps

Multiply \frac{1}{3} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 2}{3\times 5}\times \frac{2}{5}+\frac{2}{3}\times \frac{3}{5}\times \frac{2}{5}+\frac{2}{3}\times \frac{2}{5}\times \frac{3}{5}$$

Do the multiplications in the fraction \frac{1\times 2}{3\times 5}.

$$\frac{2}{15}\times \frac{2}{5}+\frac{2}{3}\times \frac{3}{5}\times \frac{2}{5}+\frac{2}{3}\times \frac{2}{5}\times \frac{3}{5}$$

Multiply \frac{2}{15} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 2}{15\times 5}+\frac{2}{3}\times \frac{3}{5}\times \frac{2}{5}+\frac{2}{3}\times \frac{2}{5}\times \frac{3}{5}$$

Do the multiplications in the fraction \frac{2\times 2}{15\times 5}.

$$\frac{4}{75}+\frac{2}{3}\times \frac{3}{5}\times \frac{2}{5}+\frac{2}{3}\times \frac{2}{5}\times \frac{3}{5}$$

Multiply \frac{2}{3} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{75}+\frac{2\times 3}{3\times 5}\times \frac{2}{5}+\frac{2}{3}\times \frac{2}{5}\times \frac{3}{5}$$

Cancel out 3 in both numerator and denominator.

$$\frac{4}{75}+\frac{2}{5}\times \frac{2}{5}+\frac{2}{3}\times \frac{2}{5}\times \frac{3}{5}$$

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

$$\frac{4}{75}+\frac{2\times 2}{5\times 5}+\frac{2}{3}\times \frac{2}{5}\times \frac{3}{5}$$

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

$$\frac{4}{75}+\frac{4}{25}+\frac{2}{3}\times \frac{2}{5}\times \frac{3}{5}$$

Least common multiple of 75 and 25 is 75. Convert \frac{4}{75} and \frac{4}{25} to fractions with denominator 75.

$$\frac{4}{75}+\frac{12}{75}+\frac{2}{3}\times \frac{2}{5}\times \frac{3}{5}$$

Since \frac{4}{75} and \frac{12}{75} have the same denominator, add them by adding their numerators.

$$\frac{4+12}{75}+\frac{2}{3}\times \frac{2}{5}\times \frac{3}{5}$$

Add 4 and 12 to get 16.

$$\frac{16}{75}+\frac{2}{3}\times \frac{2}{5}\times \frac{3}{5}$$

Multiply \frac{2}{3} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16}{75}+\frac{2\times 2}{3\times 5}\times \frac{3}{5}$$

Do the multiplications in the fraction \frac{2\times 2}{3\times 5}.

$$\frac{16}{75}+\frac{4}{15}\times \frac{3}{5}$$

Multiply \frac{4}{15} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16}{75}+\frac{4\times 3}{15\times 5}$$

Do the multiplications in the fraction \frac{4\times 3}{15\times 5}.

$$\frac{16}{75}+\frac{12}{75}$$

Since \frac{16}{75} and \frac{12}{75} have the same denominator, add them by adding their numerators.

$$\frac{16+12}{75}$$

Add 16 and 12 to get 28.

$$\frac{28}{75}$$

Factor

$$\frac{2 ^ {2} \cdot 7}{3 \cdot 5 ^ {2}} = 0.37333333333333335$$