Solve (-1/2)^2div1/8-3/4*8/27-frac{1}{2^2}

$$( - \frac { 1 } { 2 } ) ^ { 2 } \div \frac { 1 } { 8 } - \frac { 3 } { 4 } \times \frac { 8 } { 27 } - \frac { 1 } { 2 ^ { 2 } }$$

Evaluate

$$\frac{55}{36}\approx 1.527777778$$

Solution Steps

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

$$\frac{\frac{1}{4}}{\frac{1}{8}}-\frac{3}{4}\times \frac{8}{27}-\frac{1}{2^{2}}$$

Divide \frac{1}{4} by \frac{1}{8} by multiplying \frac{1}{4} by the reciprocal of \frac{1}{8}.

$$\frac{1}{4}\times 8-\frac{3}{4}\times \frac{8}{27}-\frac{1}{2^{2}}$$

Multiply \frac{1}{4} and 8 to get \frac{8}{4}.

$$\frac{8}{4}-\frac{3}{4}\times \frac{8}{27}-\frac{1}{2^{2}}$$

Divide 8 by 4 to get 2.

$$2-\frac{3}{4}\times \frac{8}{27}-\frac{1}{2^{2}}$$

Multiply \frac{3}{4} times \frac{8}{27} by multiplying numerator times numerator and denominator times denominator.

$$2-\frac{3\times 8}{4\times 27}-\frac{1}{2^{2}}$$

Do the multiplications in the fraction \frac{3\times 8}{4\times 27}.

$$2-\frac{24}{108}-\frac{1}{2^{2}}$$

Reduce the fraction \frac{24}{108} to lowest terms by extracting and canceling out 12.

$$2-\frac{2}{9}-\frac{1}{2^{2}}$$

Convert 2 to fraction \frac{18}{9}.

$$\frac{18}{9}-\frac{2}{9}-\frac{1}{2^{2}}$$

Since \frac{18}{9} and \frac{2}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18-2}{9}-\frac{1}{2^{2}}$$

Subtract 2 from 18 to get 16.

$$\frac{16}{9}-\frac{1}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{16}{9}-\frac{1}{4}$$

Least common multiple of 9 and 4 is 36. Convert \frac{16}{9} and \frac{1}{4} to fractions with denominator 36.

$$\frac{64}{36}-\frac{9}{36}$$

Since \frac{64}{36} and \frac{9}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{64-9}{36}$$

Subtract 9 from 64 to get 55.

$$\frac{55}{36}$$

Factor

$$\frac{5 \cdot 11}{2 ^ {2} \cdot 3 ^ {2}} = 1\frac{19}{36} = 1.5277777777777777$$