Solve 3+1/7+frac{1{15}}

$$3+ \frac{ 1 }{ 7+ \frac{ 1 }{ 15 } }$$

Evaluate

$$\frac{333}{106}\approx 3.141509434$$

Solution Steps

Convert 7 to fraction \frac{105}{15}.

$$3+\frac{1}{\frac{105}{15}+\frac{1}{15}}$$

Since \frac{105}{15} and \frac{1}{15} have the same denominator, add them by adding their numerators.

$$3+\frac{1}{\frac{105+1}{15}}$$

Add 105 and 1 to get 106.

$$3+\frac{1}{\frac{106}{15}}$$

Divide 1 by \frac{106}{15} by multiplying 1 by the reciprocal of \frac{106}{15}.

$$3+1\times \frac{15}{106}$$

Multiply 1 and \frac{15}{106} to get \frac{15}{106}.

$$3+\frac{15}{106}$$

Convert 3 to fraction \frac{318}{106}.

$$\frac{318}{106}+\frac{15}{106}$$

Since \frac{318}{106} and \frac{15}{106} have the same denominator, add them by adding their numerators.

$$\frac{318+15}{106}$$

Add 318 and 15 to get 333.

$$\frac{333}{106}$$

Factor

$$\frac{3 ^ {2} \cdot 37}{2 \cdot 53} = 3\frac{15}{106} = 3.141509433962264$$