Solve 3+1/4/3+frac{frac{1{4}}{5/8}}

$$3+ \frac{ \frac{ 1 }{ 4 } }{ 3+ \frac{ \frac{ 1 }{ 4 } }{ \frac{ 5 }{ 8 } } }$$

Evaluate

$$\frac{209}{68}\approx 3.073529412$$

Solution Steps

Divide \frac{1}{4} by \frac{5}{8} by multiplying \frac{1}{4} by the reciprocal of \frac{5}{8}.

$$3+\frac{\frac{1}{4}}{3+\frac{1}{4}\times \frac{8}{5}}$$

Multiply \frac{1}{4} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$3+\frac{\frac{1}{4}}{3+\frac{1\times 8}{4\times 5}}$$

Do the multiplications in the fraction \frac{1\times 8}{4\times 5}.

$$3+\frac{\frac{1}{4}}{3+\frac{8}{20}}$$

Reduce the fraction \frac{8}{20} to lowest terms by extracting and canceling out 4.

$$3+\frac{\frac{1}{4}}{3+\frac{2}{5}}$$

Convert 3 to fraction \frac{15}{5}.

$$3+\frac{\frac{1}{4}}{\frac{15}{5}+\frac{2}{5}}$$

Since \frac{15}{5} and \frac{2}{5} have the same denominator, add them by adding their numerators.

$$3+\frac{\frac{1}{4}}{\frac{15+2}{5}}$$

Add 15 and 2 to get 17.

$$3+\frac{\frac{1}{4}}{\frac{17}{5}}$$

Divide \frac{1}{4} by \frac{17}{5} by multiplying \frac{1}{4} by the reciprocal of \frac{17}{5}.

$$3+\frac{1}{4}\times \frac{5}{17}$$

Multiply \frac{1}{4} times \frac{5}{17} by multiplying numerator times numerator and denominator times denominator.

$$3+\frac{1\times 5}{4\times 17}$$

Do the multiplications in the fraction \frac{1\times 5}{4\times 17}.

$$3+\frac{5}{68}$$

Convert 3 to fraction \frac{204}{68}.

$$\frac{204}{68}+\frac{5}{68}$$

Since \frac{204}{68} and \frac{5}{68} have the same denominator, add them by adding their numerators.

$$\frac{204+5}{68}$$

Add 204 and 5 to get 209.

$$\frac{209}{68}$$

Factor

$$\frac{11 \cdot 19}{2 ^ {2} \cdot 17} = 3\frac{5}{68} = 3.073529411764706$$