Solve [1/2+1/2*(1+2*5/6)]:(2-1/6)+(frac{1}{2})^2}^2:[(1-frac{1}{2})^2*frac{3}{4}]

$$[ \frac { 1 } { 2 } + \frac { 1 } { 2 } \times ( 1 + 2 \times \frac { 5 } { 6 } ) ] : ( 2 - \frac { 1 } { 6 } ) + ( \frac { 1 } { 2 } ) ^ { 2 } \} ^ { 2 } : [ ( 1 - \frac { 1 } { 2 } ) ^ { 2 } \times \frac { 3 } { 4 } ]$$

Evaluate

$$\frac{5}{4}=1.25$$

Solution Steps

Express 2\times \frac{5}{6} as a single fraction.

$$\frac{\frac{1}{2}+\frac{1}{2}\left(1+\frac{2\times 5}{6}\right)}{2-\frac{1}{6}}+\left(\frac{1}{2}\right)^{2}$$

Multiply 2 and 5 to get 10.

$$\frac{\frac{1}{2}+\frac{1}{2}\left(1+\frac{10}{6}\right)}{2-\frac{1}{6}}+\left(\frac{1}{2}\right)^{2}$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{2}+\frac{1}{2}\left(1+\frac{5}{3}\right)}{2-\frac{1}{6}}+\left(\frac{1}{2}\right)^{2}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{\frac{1}{2}+\frac{1}{2}\left(\frac{3}{3}+\frac{5}{3}\right)}{2-\frac{1}{6}}+\left(\frac{1}{2}\right)^{2}$$

Since \frac{3}{3} and \frac{5}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{2}+\frac{1}{2}\times \frac{3+5}{3}}{2-\frac{1}{6}}+\left(\frac{1}{2}\right)^{2}$$

Add 3 and 5 to get 8.

$$\frac{\frac{1}{2}+\frac{1}{2}\times \frac{8}{3}}{2-\frac{1}{6}}+\left(\frac{1}{2}\right)^{2}$$

Multiply \frac{1}{2} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{2}+\frac{1\times 8}{2\times 3}}{2-\frac{1}{6}}+\left(\frac{1}{2}\right)^{2}$$

Do the multiplications in the fraction \frac{1\times 8}{2\times 3}.

$$\frac{\frac{1}{2}+\frac{8}{6}}{2-\frac{1}{6}}+\left(\frac{1}{2}\right)^{2}$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

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

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{4}{3} to fractions with denominator 6.

$$\frac{\frac{3}{6}+\frac{8}{6}}{2-\frac{1}{6}}+\left(\frac{1}{2}\right)^{2}$$

Since \frac{3}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+8}{6}}{2-\frac{1}{6}}+\left(\frac{1}{2}\right)^{2}$$

Add 3 and 8 to get 11.

$$\frac{\frac{11}{6}}{2-\frac{1}{6}}+\left(\frac{1}{2}\right)^{2}$$

Convert 2 to fraction \frac{12}{6}.

$$\frac{\frac{11}{6}}{\frac{12}{6}-\frac{1}{6}}+\left(\frac{1}{2}\right)^{2}$$

Since \frac{12}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{11}{6}}{\frac{12-1}{6}}+\left(\frac{1}{2}\right)^{2}$$

Subtract 1 from 12 to get 11.

$$\frac{\frac{11}{6}}{\frac{11}{6}}+\left(\frac{1}{2}\right)^{2}$$

Divide \frac{11}{6} by \frac{11}{6} to get 1.

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

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

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

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

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

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

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

Add 4 and 1 to get 5.

$$\frac{5}{4}$$

Factor

$$\frac{5}{2 ^ {2}} = 1\frac{1}{4} = 1.25$$