Solve 2-1/5/1-1{3+frac{3/1}}

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

Evaluate

$$\frac{54}{25}=2.16$$

Solution Steps

Convert 2 to fraction \frac{10}{5}.

$$\frac{\frac{10}{5}-\frac{1}{5}}{1-\frac{1}{3+\frac{3}{1}}}$$

Since \frac{10}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{10-1}{5}}{1-\frac{1}{3+\frac{3}{1}}}$$

Subtract 1 from 10 to get 9.

$$\frac{\frac{9}{5}}{1-\frac{1}{3+\frac{3}{1}}}$$

Anything divided by one gives itself.

$$\frac{\frac{9}{5}}{1-\frac{1}{3+3}}$$

Add 3 and 3 to get 6.

$$\frac{\frac{9}{5}}{1-\frac{1}{6}}$$

Convert 1 to fraction \frac{6}{6}.

$$\frac{\frac{9}{5}}{\frac{6}{6}-\frac{1}{6}}$$

Since \frac{6}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9}{5}}{\frac{6-1}{6}}$$

Subtract 1 from 6 to get 5.

$$\frac{\frac{9}{5}}{\frac{5}{6}}$$

Divide \frac{9}{5} by \frac{5}{6} by multiplying \frac{9}{5} by the reciprocal of \frac{5}{6}.

$$\frac{9}{5}\times \frac{6}{5}$$

Multiply \frac{9}{5} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 6}{5\times 5}$$

Do the multiplications in the fraction \frac{9\times 6}{5\times 5}.

$$\frac{54}{25}$$

Factor

$$\frac{2 \cdot 3 ^ {3}}{5 ^ {2}} = 2\frac{4}{25} = 2.16$$