Solve 5/(8+2)/1+(frac{1{8}*5/(8+2))}

$$\frac { \frac { 5 } { ( 8 + 2 ) } } { 1 + ( \frac { 1 } { 8 } \times \frac { 5 } { ( 8 + 2 ) } ) }$$

Evaluate

$$\frac{8}{17}\approx 0.470588235$$

Solution Steps

Add 8 and 2 to get 10.

$$\frac{\frac{5}{10}}{1+\frac{1}{8}\times \frac{5}{8+2}}$$

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

$$\frac{\frac{1}{2}}{1+\frac{1}{8}\times \frac{5}{8+2}}$$

Add 8 and 2 to get 10.

$$\frac{\frac{1}{2}}{1+\frac{1}{8}\times \frac{5}{10}}$$

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

$$\frac{\frac{1}{2}}{1+\frac{1}{8}\times \frac{1}{2}}$$

Multiply \frac{1}{8} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{2}}{1+\frac{1\times 1}{8\times 2}}$$

Do the multiplications in the fraction \frac{1\times 1}{8\times 2}.

$$\frac{\frac{1}{2}}{1+\frac{1}{16}}$$

Convert 1 to fraction \frac{16}{16}.

$$\frac{\frac{1}{2}}{\frac{16}{16}+\frac{1}{16}}$$

Since \frac{16}{16} and \frac{1}{16} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{2}}{\frac{16+1}{16}}$$

Add 16 and 1 to get 17.

$$\frac{\frac{1}{2}}{\frac{17}{16}}$$

Divide \frac{1}{2} by \frac{17}{16} by multiplying \frac{1}{2} by the reciprocal of \frac{17}{16}.

$$\frac{1}{2}\times \frac{16}{17}$$

Multiply \frac{1}{2} times \frac{16}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 16}{2\times 17}$$

Do the multiplications in the fraction \frac{1\times 16}{2\times 17}.

$$\frac{16}{34}$$

Reduce the fraction \frac{16}{34} to lowest terms by extracting and canceling out 2.

$$\frac{8}{17}$$

Factor

$$\frac{2 ^ {3}}{17} = 0.47058823529411764$$