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

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

Evaluate

$$\frac{17}{12}\approx 1.416666667$$

Solution Steps

Divide 5 by 5 to get 1.

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

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{4}{5} to fractions with denominator 15.

$$\frac{\frac{5}{15}+\frac{12}{15}}{1-\frac{1}{5}}$$

Since \frac{5}{15} and \frac{12}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+12}{15}}{1-\frac{1}{5}}$$

Add 5 and 12 to get 17.

$$\frac{\frac{17}{15}}{1-\frac{1}{5}}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{\frac{17}{15}}{\frac{5}{5}-\frac{1}{5}}$$

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

$$\frac{\frac{17}{15}}{\frac{5-1}{5}}$$

Subtract 1 from 5 to get 4.

$$\frac{\frac{17}{15}}{\frac{4}{5}}$$

Divide \frac{17}{15} by \frac{4}{5} by multiplying \frac{17}{15} by the reciprocal of \frac{4}{5}.

$$\frac{17}{15}\times \frac{5}{4}$$

Multiply \frac{17}{15} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17\times 5}{15\times 4}$$

Do the multiplications in the fraction \frac{17\times 5}{15\times 4}.

$$\frac{85}{60}$$

Reduce the fraction \frac{85}{60} to lowest terms by extracting and canceling out 5.

$$\frac{17}{12}$$

Factor

$$\frac{17}{2 ^ {2} \cdot 3} = 1\frac{5}{12} = 1.4166666666666667$$