Solve 1+1/21/3-frac{1{4-1/3}}

$$1 + \frac { 1 } { 21 / 3 - \frac { 1 } { 4 - 1 / 3 } }$$

Evaluate

$$\frac{85}{74}\approx 1.148648649$$

Solution Steps

Divide 21 by 3 to get 7.

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

Convert 4 to fraction \frac{12}{3}.

$$1+\frac{1}{7-\frac{1}{\frac{12}{3}-\frac{1}{3}}}$$

Since \frac{12}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$1+\frac{1}{7-\frac{1}{\frac{12-1}{3}}}$$

Subtract 1 from 12 to get 11.

$$1+\frac{1}{7-\frac{1}{\frac{11}{3}}}$$

Divide 1 by \frac{11}{3} by multiplying 1 by the reciprocal of \frac{11}{3}.

$$1+\frac{1}{7-1\times \frac{3}{11}}$$

Multiply 1 and \frac{3}{11} to get \frac{3}{11}.

$$1+\frac{1}{7-\frac{3}{11}}$$

Convert 7 to fraction \frac{77}{11}.

$$1+\frac{1}{\frac{77}{11}-\frac{3}{11}}$$

Since \frac{77}{11} and \frac{3}{11} have the same denominator, subtract them by subtracting their numerators.

$$1+\frac{1}{\frac{77-3}{11}}$$

Subtract 3 from 77 to get 74.

$$1+\frac{1}{\frac{74}{11}}$$

Divide 1 by \frac{74}{11} by multiplying 1 by the reciprocal of \frac{74}{11}.

$$1+1\times \frac{11}{74}$$

Multiply 1 and \frac{11}{74} to get \frac{11}{74}.

$$1+\frac{11}{74}$$

Convert 1 to fraction \frac{74}{74}.

$$\frac{74}{74}+\frac{11}{74}$$

Since \frac{74}{74} and \frac{11}{74} have the same denominator, add them by adding their numerators.

$$\frac{74+11}{74}$$

Add 74 and 11 to get 85.

$$\frac{85}{74}$$

Factor

$$\frac{5 \cdot 17}{2 \cdot 37} = 1\frac{11}{74} = 1.1486486486486487$$