Solve (-1/2--51/2div4)^2+-31/8

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

Evaluate

$$-\frac{151}{64}=-2.359375$$

Solution Steps

Multiply 5 and 2 to get 10.

$$\left(-\frac{1}{2}-\frac{-\frac{10+1}{2}}{4}\right)^{2}-\frac{3\times 8+1}{8}$$

Add 10 and 1 to get 11.

$$\left(-\frac{1}{2}-\frac{-\frac{11}{2}}{4}\right)^{2}-\frac{3\times 8+1}{8}$$

Express \frac{-\frac{11}{2}}{4} as a single fraction.

$$\left(-\frac{1}{2}-\frac{-11}{2\times 4}\right)^{2}-\frac{3\times 8+1}{8}$$

Multiply 2 and 4 to get 8.

$$\left(-\frac{1}{2}-\frac{-11}{8}\right)^{2}-\frac{3\times 8+1}{8}$$

Fraction \frac{-11}{8} can be rewritten as -\frac{11}{8} by extracting the negative sign.

$$\left(-\frac{1}{2}-\left(-\frac{11}{8}\right)\right)^{2}-\frac{3\times 8+1}{8}$$

The opposite of -\frac{11}{8} is \frac{11}{8}.

$$\left(-\frac{1}{2}+\frac{11}{8}\right)^{2}-\frac{3\times 8+1}{8}$$

Add -\frac{1}{2} and \frac{11}{8} to get \frac{7}{8}.

$$\left(\frac{7}{8}\right)^{2}-\frac{3\times 8+1}{8}$$

Calculate \frac{7}{8} to the power of 2 and get \frac{49}{64}.

$$\frac{49}{64}-\frac{3\times 8+1}{8}$$

Multiply 3 and 8 to get 24.

$$\frac{49}{64}-\frac{24+1}{8}$$

Add 24 and 1 to get 25.

$$\frac{49}{64}-\frac{25}{8}$$

Subtract \frac{25}{8} from \frac{49}{64} to get -\frac{151}{64}.

$$-\frac{151}{64}$$

Factor

$$-\frac{151}{64} = -2\frac{23}{64} = -2.359375$$