Solve 3+1/7+frac{1{16}}

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

Evaluate

$$\frac{355}{113}\approx 3.14159292$$

Solution Steps

Convert 7 to fraction \frac{112}{16}.

$$3+\frac{1}{\frac{112}{16}+\frac{1}{16}}$$

Since \frac{112}{16} and \frac{1}{16} have the same denominator, add them by adding their numerators.

$$3+\frac{1}{\frac{112+1}{16}}$$

Add 112 and 1 to get 113.

$$3+\frac{1}{\frac{113}{16}}$$

Divide 1 by \frac{113}{16} by multiplying 1 by the reciprocal of \frac{113}{16}.

$$3+1\times \frac{16}{113}$$

Multiply 1 and \frac{16}{113} to get \frac{16}{113}.

$$3+\frac{16}{113}$$

Convert 3 to fraction \frac{339}{113}.

$$\frac{339}{113}+\frac{16}{113}$$

Since \frac{339}{113} and \frac{16}{113} have the same denominator, add them by adding their numerators.

$$\frac{339+16}{113}$$

Add 339 and 16 to get 355.

$$\frac{355}{113}$$

Factor

$$\frac{5 \cdot 71}{113} = 3\frac{16}{113} = 3.1415929203539825$$