Solve (-31/3)div(-10)*(-21/2)+(-31/9)^2

$$( - 3 \frac { 1 } { 3 } ) \div ( - 10 ) \times ( - 2 \frac { 1 } { 2 } ) + ( - 3 \frac { 1 } { 9 } ) ^ { 2 }$$

Evaluate

$$\frac{1433}{162}\approx 8.845679012$$

Solution Steps

Multiply 3 and 3 to get 9.

$$\frac{-\frac{9+1}{3}}{-10}\left(-\frac{2\times 2+1}{2}\right)+\left(-\frac{3\times 9+1}{9}\right)^{2}$$

Add 9 and 1 to get 10.

$$\frac{-\frac{10}{3}}{-10}\left(-\frac{2\times 2+1}{2}\right)+\left(-\frac{3\times 9+1}{9}\right)^{2}$$

Express \frac{-\frac{10}{3}}{-10} as a single fraction.

$$\frac{-10}{3\left(-10\right)}\left(-\frac{2\times 2+1}{2}\right)+\left(-\frac{3\times 9+1}{9}\right)^{2}$$

Cancel out -10 in both numerator and denominator.

$$\frac{1}{3}\left(-\frac{2\times 2+1}{2}\right)+\left(-\frac{3\times 9+1}{9}\right)^{2}$$

Multiply 2 and 2 to get 4.

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

Add 4 and 1 to get 5.

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

Multiply \frac{1}{3} and -\frac{5}{2} to get -\frac{5}{6}.

$$-\frac{5}{6}+\left(-\frac{3\times 9+1}{9}\right)^{2}$$

Multiply 3 and 9 to get 27.

$$-\frac{5}{6}+\left(-\frac{27+1}{9}\right)^{2}$$

Add 27 and 1 to get 28.

$$-\frac{5}{6}+\left(-\frac{28}{9}\right)^{2}$$

Calculate -\frac{28}{9} to the power of 2 and get \frac{784}{81}.

$$-\frac{5}{6}+\frac{784}{81}$$

Add -\frac{5}{6} and \frac{784}{81} to get \frac{1433}{162}.

$$\frac{1433}{162}$$

Factor

$$\frac{1433}{2 \cdot 3 ^ {4}} = 8\frac{137}{162} = 8.845679012345679$$