Solve (1/2)^2-4(1/2)^2-3(-1/2)+10^2

$$( \frac { 1 } { 2 } ) ^ { 2 } - 4 ( \frac { 1 } { 2 } ) ^ { 2 } - 3 ( - \frac { 1 } { 2 } ) + 10 ^ { 2 }$$

Evaluate

$$\frac{403}{4}=100.75$$

Solution Steps

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

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

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

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

Cancel out 4 and 4.

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

Convert 1 to fraction \frac{4}{4}.

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

Since \frac{1}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from 1 to get -3.

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

Express 3\left(-\frac{1}{2}\right) as a single fraction.

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

Multiply 3 and -1 to get -3.

$$-\frac{3}{4}-\frac{-3}{2}+10^{2}$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

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

The opposite of -\frac{3}{2} is \frac{3}{2}.

$$-\frac{3}{4}+\frac{3}{2}+10^{2}$$

Least common multiple of 4 and 2 is 4. Convert -\frac{3}{4} and \frac{3}{2} to fractions with denominator 4.

$$-\frac{3}{4}+\frac{6}{4}+10^{2}$$

Since -\frac{3}{4} and \frac{6}{4} have the same denominator, add them by adding their numerators.

$$\frac{-3+6}{4}+10^{2}$$

Add -3 and 6 to get 3.

$$\frac{3}{4}+10^{2}$$

Calculate 10 to the power of 2 and get 100.

$$\frac{3}{4}+100$$

Convert 100 to fraction \frac{400}{4}.

$$\frac{3}{4}+\frac{400}{4}$$

Since \frac{3}{4} and \frac{400}{4} have the same denominator, add them by adding their numerators.

$$\frac{3+400}{4}$$

Add 3 and 400 to get 403.

$$\frac{403}{4}$$

Factor

$$\frac{13 \cdot 31}{2 ^ {2}} = 100\frac{3}{4} = 100.75$$