Solve (-21/3+13/4)-{1/6-(-1/2)^2}

$$( - 2 \frac { 1 } { 3 } + 1 \frac { 3 } { 4 } ) - \{ \frac { 1 } { 6 } - ( - \frac { 1 } { 2 } ) ^ { 2 } \}$$

Evaluate

$$-\frac{1}{2}=-0.5$$

Solution Steps

Multiply 2 and 3 to get 6.

$$-\frac{6+1}{3}+\frac{1\times 4+3}{4}-\left(\frac{1}{6}-\left(-\frac{1}{2}\right)^{2}\right)$$

Add 6 and 1 to get 7.

$$-\frac{7}{3}+\frac{1\times 4+3}{4}-\left(\frac{1}{6}-\left(-\frac{1}{2}\right)^{2}\right)$$

Multiply 1 and 4 to get 4.

$$-\frac{7}{3}+\frac{4+3}{4}-\left(\frac{1}{6}-\left(-\frac{1}{2}\right)^{2}\right)$$

Add 4 and 3 to get 7.

$$-\frac{7}{3}+\frac{7}{4}-\left(\frac{1}{6}-\left(-\frac{1}{2}\right)^{2}\right)$$

Least common multiple of 3 and 4 is 12. Convert -\frac{7}{3} and \frac{7}{4} to fractions with denominator 12.

$$-\frac{28}{12}+\frac{21}{12}-\left(\frac{1}{6}-\left(-\frac{1}{2}\right)^{2}\right)$$

Since -\frac{28}{12} and \frac{21}{12} have the same denominator, add them by adding their numerators.

$$\frac{-28+21}{12}-\left(\frac{1}{6}-\left(-\frac{1}{2}\right)^{2}\right)$$

Add -28 and 21 to get -7.

$$-\frac{7}{12}-\left(\frac{1}{6}-\left(-\frac{1}{2}\right)^{2}\right)$$

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

$$-\frac{7}{12}-\left(\frac{1}{6}-\frac{1}{4}\right)$$

Least common multiple of 6 and 4 is 12. Convert \frac{1}{6} and \frac{1}{4} to fractions with denominator 12.

$$-\frac{7}{12}-\left(\frac{2}{12}-\frac{3}{12}\right)$$

Since \frac{2}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{7}{12}-\frac{2-3}{12}$$

Subtract 3 from 2 to get -1.

$$-\frac{7}{12}-\left(-\frac{1}{12}\right)$$

The opposite of -\frac{1}{12} is \frac{1}{12}.

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

Since -\frac{7}{12} and \frac{1}{12} have the same denominator, add them by adding their numerators.

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

Add -7 and 1 to get -6.

$$\frac{-6}{12}$$

Reduce the fraction \frac{-6}{12} to lowest terms by extracting and canceling out 6.

$$-\frac{1}{2}$$

Factor

$$-\frac{1}{2} = -0.5$$