Solve 4+5/6/5-frac{4{5}}

$$\frac { 4 + \frac { 5 } { 6 } } { 5 - \frac { 4 } { 5 } }$$

Evaluate

$$\frac{145}{126}\approx 1.150793651$$

Solution Steps

Convert 4 to fraction \frac{24}{6}.

$$\frac{\frac{24}{6}+\frac{5}{6}}{5-\frac{4}{5}}$$

Since \frac{24}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{24+5}{6}}{5-\frac{4}{5}}$$

Add 24 and 5 to get 29.

$$\frac{\frac{29}{6}}{5-\frac{4}{5}}$$

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

$$\frac{\frac{29}{6}}{\frac{25}{5}-\frac{4}{5}}$$

Since \frac{25}{5} and \frac{4}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{29}{6}}{\frac{25-4}{5}}$$

Subtract 4 from 25 to get 21.

$$\frac{\frac{29}{6}}{\frac{21}{5}}$$

Divide \frac{29}{6} by \frac{21}{5} by multiplying \frac{29}{6} by the reciprocal of \frac{21}{5}.

$$\frac{29}{6}\times \frac{5}{21}$$

Multiply \frac{29}{6} times \frac{5}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{29\times 5}{6\times 21}$$

Do the multiplications in the fraction \frac{29\times 5}{6\times 21}.

$$\frac{145}{126}$$

Factor

$$\frac{5 \cdot 29}{2 \cdot 3 ^ {2} \cdot 7} = 1\frac{19}{126} = 1.1507936507936507$$