Solve 4-2/5/frac{5{9}-2/6}=

$$\frac { 4 - \frac { 2 } { 5 } } { \frac { 5 } { 9 } - \frac { 2 } { 6 } } =$$

Evaluate

$$\frac{81}{5}=16.2$$

Solution Steps

Convert 4 to fraction \frac{20}{5}.

$$\frac{\frac{20}{5}-\frac{2}{5}}{\frac{5}{9}-\frac{2}{6}}$$

Since \frac{20}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{20-2}{5}}{\frac{5}{9}-\frac{2}{6}}$$

Subtract 2 from 20 to get 18.

$$\frac{\frac{18}{5}}{\frac{5}{9}-\frac{2}{6}}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{18}{5}}{\frac{5}{9}-\frac{1}{3}}$$

Least common multiple of 9 and 3 is 9. Convert \frac{5}{9} and \frac{1}{3} to fractions with denominator 9.

$$\frac{\frac{18}{5}}{\frac{5}{9}-\frac{3}{9}}$$

Since \frac{5}{9} and \frac{3}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{18}{5}}{\frac{5-3}{9}}$$

Subtract 3 from 5 to get 2.

$$\frac{\frac{18}{5}}{\frac{2}{9}}$$

Divide \frac{18}{5} by \frac{2}{9} by multiplying \frac{18}{5} by the reciprocal of \frac{2}{9}.

$$\frac{18}{5}\times \frac{9}{2}$$

Multiply \frac{18}{5} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{18\times 9}{5\times 2}$$

Do the multiplications in the fraction \frac{18\times 9}{5\times 2}.

$$\frac{162}{10}$$

Reduce the fraction \frac{162}{10} to lowest terms by extracting and canceling out 2.

$$\frac{81}{5}$$

Factor

$$\frac{3 ^ {4}}{5} = 16\frac{1}{5} = 16.2$$