Solve 3/8+3{4+frac{1/2}}

$$\frac{ 3 }{ 8+ \frac{ 3 }{ 4+ \frac{ 1 }{ 2 } } }$$

Evaluate

$$\frac{9}{26}\approx 0.346153846$$

Solution Steps

Convert 4 to fraction \frac{8}{2}.

$$\frac{3}{8+\frac{3}{\frac{8}{2}+\frac{1}{2}}}$$

Since \frac{8}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{3}{8+\frac{3}{\frac{8+1}{2}}}$$

Add 8 and 1 to get 9.

$$\frac{3}{8+\frac{3}{\frac{9}{2}}}$$

Divide 3 by \frac{9}{2} by multiplying 3 by the reciprocal of \frac{9}{2}.

$$\frac{3}{8+3\times \frac{2}{9}}$$

Express 3\times \frac{2}{9} as a single fraction.

$$\frac{3}{8+\frac{3\times 2}{9}}$$

Multiply 3 and 2 to get 6.

$$\frac{3}{8+\frac{6}{9}}$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$\frac{3}{8+\frac{2}{3}}$$

Convert 8 to fraction \frac{24}{3}.

$$\frac{3}{\frac{24}{3}+\frac{2}{3}}$$

Since \frac{24}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{3}{\frac{24+2}{3}}$$

Add 24 and 2 to get 26.

$$\frac{3}{\frac{26}{3}}$$

Divide 3 by \frac{26}{3} by multiplying 3 by the reciprocal of \frac{26}{3}.

$$3\times \frac{3}{26}$$

Express 3\times \frac{3}{26} as a single fraction.

$$\frac{3\times 3}{26}$$

Multiply 3 and 3 to get 9.

$$\frac{9}{26}$$

Factor

$$\frac{3 ^ {2}}{2 \cdot 13} = 0.34615384615384615$$