Solve (2/5+3/5*2/5)*13/7

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

Evaluate

$$\frac{32}{35}\approx 0.914285714$$

Solution Steps

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

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

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

$$\left(\frac{2}{5}+\frac{6}{25}\right)\times \frac{1\times 7+3}{7}$$

Least common multiple of 5 and 25 is 25. Convert \frac{2}{5} and \frac{6}{25} to fractions with denominator 25.

$$\left(\frac{10}{25}+\frac{6}{25}\right)\times \frac{1\times 7+3}{7}$$

Since \frac{10}{25} and \frac{6}{25} have the same denominator, add them by adding their numerators.

$$\frac{10+6}{25}\times \frac{1\times 7+3}{7}$$

Add 10 and 6 to get 16.

$$\frac{16}{25}\times \frac{1\times 7+3}{7}$$

Multiply 1 and 7 to get 7.

$$\frac{16}{25}\times \frac{7+3}{7}$$

Add 7 and 3 to get 10.

$$\frac{16}{25}\times \frac{10}{7}$$

Multiply \frac{16}{25} times \frac{10}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16\times 10}{25\times 7}$$

Do the multiplications in the fraction \frac{16\times 10}{25\times 7}.

$$\frac{160}{175}$$

Reduce the fraction \frac{160}{175} to lowest terms by extracting and canceling out 5.

$$\frac{32}{35}$$

Factor

$$\frac{2 ^ {5}}{5 \cdot 7} = 0.9142857142857143$$