Solve 4/15*2/7+8/15div7/2+frac{2}{15}*frac{3}{7}

$$\frac{ 4 }{ 15 } \times \frac{ 2 }{ 7 } + \frac{ 8 }{ 15 } \div \frac{ 7 }{ 2 } + \frac{ 2 }{ 15 } \times \frac{ 3 }{ 7 }$$

Evaluate

$$\frac{2}{7}\approx 0.285714286$$

Solution Steps

Multiply \frac{4}{15} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 2}{15\times 7}+\frac{\frac{8}{15}}{\frac{7}{2}}+\frac{2}{15}\times \frac{3}{7}$$

Do the multiplications in the fraction \frac{4\times 2}{15\times 7}.

$$\frac{8}{105}+\frac{\frac{8}{15}}{\frac{7}{2}}+\frac{2}{15}\times \frac{3}{7}$$

Divide \frac{8}{15} by \frac{7}{2} by multiplying \frac{8}{15} by the reciprocal of \frac{7}{2}.

$$\frac{8}{105}+\frac{8}{15}\times \frac{2}{7}+\frac{2}{15}\times \frac{3}{7}$$

Multiply \frac{8}{15} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{105}+\frac{8\times 2}{15\times 7}+\frac{2}{15}\times \frac{3}{7}$$

Do the multiplications in the fraction \frac{8\times 2}{15\times 7}.

$$\frac{8}{105}+\frac{16}{105}+\frac{2}{15}\times \frac{3}{7}$$

Since \frac{8}{105} and \frac{16}{105} have the same denominator, add them by adding their numerators.

$$\frac{8+16}{105}+\frac{2}{15}\times \frac{3}{7}$$

Add 8 and 16 to get 24.

$$\frac{24}{105}+\frac{2}{15}\times \frac{3}{7}$$

Reduce the fraction \frac{24}{105} to lowest terms by extracting and canceling out 3.

$$\frac{8}{35}+\frac{2}{15}\times \frac{3}{7}$$

Multiply \frac{2}{15} times \frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{35}+\frac{2\times 3}{15\times 7}$$

Do the multiplications in the fraction \frac{2\times 3}{15\times 7}.

$$\frac{8}{35}+\frac{6}{105}$$

Reduce the fraction \frac{6}{105} to lowest terms by extracting and canceling out 3.

$$\frac{8}{35}+\frac{2}{35}$$

Since \frac{8}{35} and \frac{2}{35} have the same denominator, add them by adding their numerators.

$$\frac{8+2}{35}$$

Add 8 and 2 to get 10.

$$\frac{10}{35}$$

Reduce the fraction \frac{10}{35} to lowest terms by extracting and canceling out 5.

$$\frac{2}{7}$$

Factor

$$\frac{2}{7} = 0.2857142857142857$$