Solve -1/2*1/2+[1/4-(1/4+frac{1}{3})-(frac{1}{2})^2]

$$- \frac { 1 } { 2 } \cdot \frac { 1 } { 2 } + [ \frac { 1 } { 4 } - ( \frac { 1 } { 4 } + \frac { 1 } { 3 } ) - ( \frac { 1 } { 2 } ) ^ { 2 } ]$$

Evaluate

$$-\frac{5}{6}\approx -0.833333333$$

Solution Steps

Multiply -\frac{1}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-1}{2\times 2}.

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

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

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

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{1}{3} to fractions with denominator 12.

$$-\frac{1}{4}+\frac{1}{4}-\left(\frac{3}{12}+\frac{4}{12}\right)-\left(\frac{1}{2}\right)^{2}$$

Since \frac{3}{12} and \frac{4}{12} have the same denominator, add them by adding their numerators.

$$-\frac{1}{4}+\frac{1}{4}-\frac{3+4}{12}-\left(\frac{1}{2}\right)^{2}$$

Add 3 and 4 to get 7.

$$-\frac{1}{4}+\frac{1}{4}-\frac{7}{12}-\left(\frac{1}{2}\right)^{2}$$

Least common multiple of 4 and 12 is 12. Convert \frac{1}{4} and \frac{7}{12} to fractions with denominator 12.

$$-\frac{1}{4}+\frac{3}{12}-\frac{7}{12}-\left(\frac{1}{2}\right)^{2}$$

Since \frac{3}{12} and \frac{7}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{4}+\frac{3-7}{12}-\left(\frac{1}{2}\right)^{2}$$

Subtract 7 from 3 to get -4.

$$-\frac{1}{4}+\frac{-4}{12}-\left(\frac{1}{2}\right)^{2}$$

Reduce the fraction \frac{-4}{12} to lowest terms by extracting and canceling out 4.

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

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

$$-\frac{1}{4}-\frac{1}{3}-\frac{1}{4}$$

Least common multiple of 3 and 4 is 12. Convert -\frac{1}{3} and \frac{1}{4} to fractions with denominator 12.

$$-\frac{1}{4}-\frac{4}{12}-\frac{3}{12}$$

Since -\frac{4}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{4}+\frac{-4-3}{12}$$

Subtract 3 from -4 to get -7.

$$-\frac{1}{4}-\frac{7}{12}$$

Least common multiple of 4 and 12 is 12. Convert -\frac{1}{4} and \frac{7}{12} to fractions with denominator 12.

$$-\frac{3}{12}-\frac{7}{12}$$

Since -\frac{3}{12} and \frac{7}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-3-7}{12}$$

Subtract 7 from -3 to get -10.

$$\frac{-10}{12}$$

Reduce the fraction \frac{-10}{12} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{6}$$

Factor

$$-\frac{5}{6} = -0.8333333333333334$$