Solve 1div{2-3div(4+1/5)}

$$1 \div \{ 2 - 3 \div ( 4 + \frac { 1 } { 5 } ) \}$$

Evaluate

$$\frac{7}{9}\approx 0.777777778$$

Solution Steps

Convert 4 to fraction \frac{20}{5}.

$$\frac{1}{2-\frac{3}{\frac{20}{5}+\frac{1}{5}}}$$

Since \frac{20}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

$$\frac{1}{2-\frac{3}{\frac{20+1}{5}}}$$

Add 20 and 1 to get 21.

$$\frac{1}{2-\frac{3}{\frac{21}{5}}}$$

Divide 3 by \frac{21}{5} by multiplying 3 by the reciprocal of \frac{21}{5}.

$$\frac{1}{2-3\times \frac{5}{21}}$$

Express 3\times \frac{5}{21} as a single fraction.

$$\frac{1}{2-\frac{3\times 5}{21}}$$

Multiply 3 and 5 to get 15.

$$\frac{1}{2-\frac{15}{21}}$$

Reduce the fraction \frac{15}{21} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2-\frac{5}{7}}$$

Convert 2 to fraction \frac{14}{7}.

$$\frac{1}{\frac{14}{7}-\frac{5}{7}}$$

Since \frac{14}{7} and \frac{5}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{14-5}{7}}$$

Subtract 5 from 14 to get 9.

$$\frac{1}{\frac{9}{7}}$$

Divide 1 by \frac{9}{7} by multiplying 1 by the reciprocal of \frac{9}{7}.

$$1\times \frac{7}{9}$$

Multiply 1 and \frac{7}{9} to get \frac{7}{9}.

$$\frac{7}{9}$$

Factor

$$\frac{7}{3 ^ {2}} = 0.7777777777777778$$