Solve 8/10/frac{1{5}+1/81}

$$\frac { \frac { 8 } { 10 } } { \frac { 1 } { 5 } + \frac { 1 } { 81 } }$$

Evaluate

$$\frac{162}{43}\approx 3.76744186$$

Solution Steps

Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{4}{5}}{\frac{1}{5}+\frac{1}{81}}$$

Least common multiple of 5 and 81 is 405. Convert \frac{1}{5} and \frac{1}{81} to fractions with denominator 405.

$$\frac{\frac{4}{5}}{\frac{81}{405}+\frac{5}{405}}$$

Since \frac{81}{405} and \frac{5}{405} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4}{5}}{\frac{81+5}{405}}$$

Add 81 and 5 to get 86.

$$\frac{\frac{4}{5}}{\frac{86}{405}}$$

Divide \frac{4}{5} by \frac{86}{405} by multiplying \frac{4}{5} by the reciprocal of \frac{86}{405}.

$$\frac{4}{5}\times \frac{405}{86}$$

Multiply \frac{4}{5} times \frac{405}{86} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 405}{5\times 86}$$

Do the multiplications in the fraction \frac{4\times 405}{5\times 86}.

$$\frac{1620}{430}$$

Reduce the fraction \frac{1620}{430} to lowest terms by extracting and canceling out 10.

$$\frac{162}{43}$$

Factor

$$\frac{2 \cdot 3 ^ {4}}{43} = 3\frac{33}{43} = 3.7674418604651163$$