Solve {(-1/3)^2-5/9}div8/9-(-4/5)^2*frac{15}{8}

$$\{ ( - \frac { 1 } { 3 } ) ^ { 2 } - \frac { 5 } { 9 } \} \div \frac { 8 } { 9 } - ( - \frac { 4 } { 5 } ) ^ { 2 } \times \frac { 15 } { 8 }$$

Evaluate

$$-\frac{17}{10}=-1.7$$

Solution Steps

Calculate -\frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}-\frac{5}{9}}{\frac{8}{9}}-\left(-\frac{4}{5}\right)^{2}\times \frac{15}{8}$$

Since \frac{1}{9} and \frac{5}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-5}{9}}{\frac{8}{9}}-\left(-\frac{4}{5}\right)^{2}\times \frac{15}{8}$$

Subtract 5 from 1 to get -4.

$$\frac{-\frac{4}{9}}{\frac{8}{9}}-\left(-\frac{4}{5}\right)^{2}\times \frac{15}{8}$$

Divide -\frac{4}{9} by \frac{8}{9} by multiplying -\frac{4}{9} by the reciprocal of \frac{8}{9}.

$$-\frac{4}{9}\times \frac{9}{8}-\left(-\frac{4}{5}\right)^{2}\times \frac{15}{8}$$

Multiply -\frac{4}{9} times \frac{9}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-4\times 9}{9\times 8}-\left(-\frac{4}{5}\right)^{2}\times \frac{15}{8}$$

Cancel out 9 in both numerator and denominator.

$$\frac{-4}{8}-\left(-\frac{4}{5}\right)^{2}\times \frac{15}{8}$$

Reduce the fraction \frac{-4}{8} to lowest terms by extracting and canceling out 4.

$$-\frac{1}{2}-\left(-\frac{4}{5}\right)^{2}\times \frac{15}{8}$$

Calculate -\frac{4}{5} to the power of 2 and get \frac{16}{25}.

$$-\frac{1}{2}-\frac{16}{25}\times \frac{15}{8}$$

Multiply \frac{16}{25} times \frac{15}{8} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1}{2}-\frac{16\times 15}{25\times 8}$$

Do the multiplications in the fraction \frac{16\times 15}{25\times 8}.

$$-\frac{1}{2}-\frac{240}{200}$$

Reduce the fraction \frac{240}{200} to lowest terms by extracting and canceling out 40.

$$-\frac{1}{2}-\frac{6}{5}$$

Least common multiple of 2 and 5 is 10. Convert -\frac{1}{2} and \frac{6}{5} to fractions with denominator 10.

$$-\frac{5}{10}-\frac{12}{10}$$

Since -\frac{5}{10} and \frac{12}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-12}{10}$$

Subtract 12 from -5 to get -17.

$$-\frac{17}{10}$$

Factor

$$-\frac{17}{10} = -1\frac{7}{10} = -1.7$$