Solve 150+1/4+1{frac{3/7-3}}

$$150 + \frac { 1 } { 4 + \frac { 1 } { \frac { 3 } { 7 } - 3 } }$$

Evaluate

$$\frac{9768}{65}\approx 150.276923077$$

Solution Steps

Convert 3 to fraction \frac{21}{7}.

$$150+\frac{1}{4+\frac{1}{\frac{3}{7}-\frac{21}{7}}}$$

Since \frac{3}{7} and \frac{21}{7} have the same denominator, subtract them by subtracting their numerators.

$$150+\frac{1}{4+\frac{1}{\frac{3-21}{7}}}$$

Subtract 21 from 3 to get -18.

$$150+\frac{1}{4+\frac{1}{-\frac{18}{7}}}$$

Divide 1 by -\frac{18}{7} by multiplying 1 by the reciprocal of -\frac{18}{7}.

$$150+\frac{1}{4+1\left(-\frac{7}{18}\right)}$$

Multiply 1 and -\frac{7}{18} to get -\frac{7}{18}.

$$150+\frac{1}{4-\frac{7}{18}}$$

Convert 4 to fraction \frac{72}{18}.

$$150+\frac{1}{\frac{72}{18}-\frac{7}{18}}$$

Since \frac{72}{18} and \frac{7}{18} have the same denominator, subtract them by subtracting their numerators.

$$150+\frac{1}{\frac{72-7}{18}}$$

Subtract 7 from 72 to get 65.

$$150+\frac{1}{\frac{65}{18}}$$

Divide 1 by \frac{65}{18} by multiplying 1 by the reciprocal of \frac{65}{18}.

$$150+1\times \frac{18}{65}$$

Multiply 1 and \frac{18}{65} to get \frac{18}{65}.

$$150+\frac{18}{65}$$

Convert 150 to fraction \frac{9750}{65}.

$$\frac{9750}{65}+\frac{18}{65}$$

Since \frac{9750}{65} and \frac{18}{65} have the same denominator, add them by adding their numerators.

$$\frac{9750+18}{65}$$

Add 9750 and 18 to get 9768.

$$\frac{9768}{65}$$

Factor

$$\frac{2 ^ {3} \cdot 3 \cdot 11 \cdot 37}{5 \cdot 13} = 150\frac{18}{65} = 150.27692307692308$$