Solve -81/60-(2/5)^2div22/15*17/9

$$- 8 \frac { 1 } { 60 } - ( \frac { 2 } { 5 } ) ^ { 2 } \div 2 \frac { 2 } { 15 } \times 1 \frac { 7 } { 9 }$$

Evaluate

$$-\frac{163}{20}=-8.15$$

Solution Steps

Multiply 8 and 60 to get 480.

$$-\frac{480+1}{60}-\frac{\left(\frac{2}{5}\right)^{2}}{\frac{2\times 15+2}{15}}\times \frac{1\times 9+7}{9}$$

Add 480 and 1 to get 481.

$$-\frac{481}{60}-\frac{\left(\frac{2}{5}\right)^{2}}{\frac{2\times 15+2}{15}}\times \frac{1\times 9+7}{9}$$

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

$$-\frac{481}{60}-\frac{\frac{4}{25}}{\frac{2\times 15+2}{15}}\times \frac{1\times 9+7}{9}$$

Multiply 2 and 15 to get 30.

$$-\frac{481}{60}-\frac{\frac{4}{25}}{\frac{30+2}{15}}\times \frac{1\times 9+7}{9}$$

Add 30 and 2 to get 32.

$$-\frac{481}{60}-\frac{\frac{4}{25}}{\frac{32}{15}}\times \frac{1\times 9+7}{9}$$

Divide \frac{4}{25} by \frac{32}{15} by multiplying \frac{4}{25} by the reciprocal of \frac{32}{15}.

$$-\frac{481}{60}-\frac{4}{25}\times \frac{15}{32}\times \frac{1\times 9+7}{9}$$

Multiply \frac{4}{25} times \frac{15}{32} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{481}{60}-\frac{4\times 15}{25\times 32}\times \frac{1\times 9+7}{9}$$

Do the multiplications in the fraction \frac{4\times 15}{25\times 32}.

$$-\frac{481}{60}-\frac{60}{800}\times \frac{1\times 9+7}{9}$$

Reduce the fraction \frac{60}{800} to lowest terms by extracting and canceling out 20.

$$-\frac{481}{60}-\frac{3}{40}\times \frac{1\times 9+7}{9}$$

Multiply 1 and 9 to get 9.

$$-\frac{481}{60}-\frac{3}{40}\times \frac{9+7}{9}$$

Add 9 and 7 to get 16.

$$-\frac{481}{60}-\frac{3}{40}\times \frac{16}{9}$$

Multiply \frac{3}{40} times \frac{16}{9} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{481}{60}-\frac{3\times 16}{40\times 9}$$

Do the multiplications in the fraction \frac{3\times 16}{40\times 9}.

$$-\frac{481}{60}-\frac{48}{360}$$

Reduce the fraction \frac{48}{360} to lowest terms by extracting and canceling out 24.

$$-\frac{481}{60}-\frac{2}{15}$$

Least common multiple of 60 and 15 is 60. Convert -\frac{481}{60} and \frac{2}{15} to fractions with denominator 60.

$$-\frac{481}{60}-\frac{8}{60}$$

Since -\frac{481}{60} and \frac{8}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-481-8}{60}$$

Subtract 8 from -481 to get -489.

$$\frac{-489}{60}$$

Reduce the fraction \frac{-489}{60} to lowest terms by extracting and canceling out 3.

$$-\frac{163}{20}$$

Factor

$$-\frac{163}{20} = -8\frac{3}{20} = -8.15$$