Solve (-3^2)div(41/2)^2+51/4*(-4/9)-(-1)^2

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

Evaluate

$$-\frac{34}{9}\approx -3.777777778$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

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

Multiply 4 and 2 to get 8.

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

Add 8 and 1 to get 9.

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

Calculate \frac{9}{2} to the power of 2 and get \frac{81}{4}.

$$\frac{-9}{\frac{81}{4}}+\frac{5\times 4+1}{4}\left(-\frac{4}{9}\right)-\left(-1\right)^{2}$$

Divide -9 by \frac{81}{4} by multiplying -9 by the reciprocal of \frac{81}{4}.

$$-9\times \frac{4}{81}+\frac{5\times 4+1}{4}\left(-\frac{4}{9}\right)-\left(-1\right)^{2}$$

Multiply -9 and \frac{4}{81} to get -\frac{4}{9}.

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

Multiply 5 and 4 to get 20.

$$-\frac{4}{9}+\frac{20+1}{4}\left(-\frac{4}{9}\right)-\left(-1\right)^{2}$$

Add 20 and 1 to get 21.

$$-\frac{4}{9}+\frac{21}{4}\left(-\frac{4}{9}\right)-\left(-1\right)^{2}$$

Multiply \frac{21}{4} and -\frac{4}{9} to get -\frac{7}{3}.

$$-\frac{4}{9}-\frac{7}{3}-\left(-1\right)^{2}$$

Subtract \frac{7}{3} from -\frac{4}{9} to get -\frac{25}{9}.

$$-\frac{25}{9}-\left(-1\right)^{2}$$

Calculate -1 to the power of 2 and get 1.

$$-\frac{25}{9}-1$$

Subtract 1 from -\frac{25}{9} to get -\frac{34}{9}.

$$-\frac{34}{9}$$

Factor

$$-\frac{34}{9} = -3\frac{7}{9} = -3.7777777777777777$$