Solve 1+4/3+4{5-frac{1/-5}}

$$1 + \frac { 4 } { 3 + \frac { 4 } { 5 - \frac { 1 } { - 5 } } }$$

Evaluate

$$\frac{101}{49}\approx 2.06122449$$

Solution Steps

Fraction \frac{1}{-5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

$$1+\frac{4}{3+\frac{4}{5-\left(-\frac{1}{5}\right)}}$$

The opposite of -\frac{1}{5} is \frac{1}{5}.

$$1+\frac{4}{3+\frac{4}{5+\frac{1}{5}}}$$

Convert 5 to fraction \frac{25}{5}.

$$1+\frac{4}{3+\frac{4}{\frac{25}{5}+\frac{1}{5}}}$$

Since \frac{25}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

$$1+\frac{4}{3+\frac{4}{\frac{25+1}{5}}}$$

Add 25 and 1 to get 26.

$$1+\frac{4}{3+\frac{4}{\frac{26}{5}}}$$

Divide 4 by \frac{26}{5} by multiplying 4 by the reciprocal of \frac{26}{5}.

$$1+\frac{4}{3+4\times \frac{5}{26}}$$

Express 4\times \frac{5}{26} as a single fraction.

$$1+\frac{4}{3+\frac{4\times 5}{26}}$$

Multiply 4 and 5 to get 20.

$$1+\frac{4}{3+\frac{20}{26}}$$

Reduce the fraction \frac{20}{26} to lowest terms by extracting and canceling out 2.

$$1+\frac{4}{3+\frac{10}{13}}$$

Convert 3 to fraction \frac{39}{13}.

$$1+\frac{4}{\frac{39}{13}+\frac{10}{13}}$$

Since \frac{39}{13} and \frac{10}{13} have the same denominator, add them by adding their numerators.

$$1+\frac{4}{\frac{39+10}{13}}$$

Add 39 and 10 to get 49.

$$1+\frac{4}{\frac{49}{13}}$$

Divide 4 by \frac{49}{13} by multiplying 4 by the reciprocal of \frac{49}{13}.

$$1+4\times \frac{13}{49}$$

Express 4\times \frac{13}{49} as a single fraction.

$$1+\frac{4\times 13}{49}$$

Multiply 4 and 13 to get 52.

$$1+\frac{52}{49}$$

Convert 1 to fraction \frac{49}{49}.

$$\frac{49}{49}+\frac{52}{49}$$

Since \frac{49}{49} and \frac{52}{49} have the same denominator, add them by adding their numerators.

$$\frac{49+52}{49}$$

Add 49 and 52 to get 101.

$$\frac{101}{49}$$

Factor

$$\frac{101}{7 ^ {2}} = 2\frac{3}{49} = 2.061224489795918$$