Solve 8/3-4/9/(frac{5{3})^2}

$$\frac { \frac { 8 } { 3 } - \frac { 4 } { 9 } } { ( \frac { 5 } { 3 } ) ^ { 2 } }$$

Evaluate

$$\frac{4}{5}=0.8$$

Solution Steps

Least common multiple of 3 and 9 is 9. Convert \frac{8}{3} and \frac{4}{9} to fractions with denominator 9.

$$\frac{\frac{24}{9}-\frac{4}{9}}{\left(\frac{5}{3}\right)^{2}}$$

Since \frac{24}{9} and \frac{4}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{24-4}{9}}{\left(\frac{5}{3}\right)^{2}}$$

Subtract 4 from 24 to get 20.

$$\frac{\frac{20}{9}}{\left(\frac{5}{3}\right)^{2}}$$

Calculate \frac{5}{3} to the power of 2 and get \frac{25}{9}.

$$\frac{\frac{20}{9}}{\frac{25}{9}}$$

Divide \frac{20}{9} by \frac{25}{9} by multiplying \frac{20}{9} by the reciprocal of \frac{25}{9}.

$$\frac{20}{9}\times \frac{9}{25}$$

Multiply \frac{20}{9} times \frac{9}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{20\times 9}{9\times 25}$$

Cancel out 9 in both numerator and denominator.

$$\frac{20}{25}$$

Reduce the fraction \frac{20}{25} to lowest terms by extracting and canceling out 5.

$$\frac{4}{5}$$

Factor

$$\frac{2 ^ {2}}{5} = 0.8$$