Solve -[1/2]^2+[2/3]^2

$$- [ \frac { 1 } { 2 } ] ^ { 2 } + [ \frac { 2 } { 3 } ] ^ { 2 }$$

Evaluate

$$\frac{7}{36}\approx 0.194444444$$

Solution Steps

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

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

Calculate \frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$-\frac{1}{4}+\frac{4}{9}$$

Least common multiple of 4 and 9 is 36. Convert -\frac{1}{4} and \frac{4}{9} to fractions with denominator 36.

$$-\frac{9}{36}+\frac{16}{36}$$

Since -\frac{9}{36} and \frac{16}{36} have the same denominator, add them by adding their numerators.

$$\frac{-9+16}{36}$$

Add -9 and 16 to get 7.

$$\frac{7}{36}$$

Factor

$$\frac{7}{2 ^ {2} \cdot 3 ^ {2}} = 0.19444444444444445$$