Solve 5/2:{-1/2+1/2[1/2:(frac{11}{22})+frac{1}{2}(1+frac{1}{2})frac{1}{2}]-1}=

$$\frac { 5 } { 2 } : \{ - \frac { 1 } { 2 } + \frac { 1 } { 2 } [ \frac { 1 } { 2 } : ( \frac { 11 } { 22 } ) + \frac { 1 } { 2 } ( 1 + \frac { 1 } { 2 } ) \frac { 1 } { 2 } ] - 1 \} =$$

Evaluate

$$-\frac{40}{13}\approx -3.076923077$$

Solution Steps

Divide \frac{1}{2} by \frac{11}{22} by multiplying \frac{1}{2} by the reciprocal of \frac{11}{22}.

$$\frac{\frac{5}{2}}{-\frac{1}{2}+\frac{1}{2}\left(\frac{22}{2\times 11}+\frac{1}{2}\left(1+\frac{1}{2}\right)\times \frac{1}{2}\right)-1}$$

Multiply 2 and 11 to get 22.

$$\frac{\frac{5}{2}}{-\frac{1}{2}+\frac{1}{2}\left(\frac{22}{22}+\frac{1}{2}\left(1+\frac{1}{2}\right)\times \frac{1}{2}\right)-1}$$

Divide 22 by 22 to get 1.

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

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

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

Add 2 and 1 to get 3.

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

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

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

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

$$\frac{\frac{5}{2}}{-\frac{1}{2}+\frac{1}{2}\left(1+\frac{3}{4}\times \frac{1}{2}\right)-1}$$

Multiply \frac{3}{4} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{2}}{-\frac{1}{2}+\frac{1}{2}\left(1+\frac{3\times 1}{4\times 2}\right)-1}$$

Do the multiplications in the fraction \frac{3\times 1}{4\times 2}.

$$\frac{\frac{5}{2}}{-\frac{1}{2}+\frac{1}{2}\left(1+\frac{3}{8}\right)-1}$$

Convert 1 to fraction \frac{8}{8}.

$$\frac{\frac{5}{2}}{-\frac{1}{2}+\frac{1}{2}\left(\frac{8}{8}+\frac{3}{8}\right)-1}$$

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

$$\frac{\frac{5}{2}}{-\frac{1}{2}+\frac{1}{2}\times \frac{8+3}{8}-1}$$

Add 8 and 3 to get 11.

$$\frac{\frac{5}{2}}{-\frac{1}{2}+\frac{1}{2}\times \frac{11}{8}-1}$$

Multiply \frac{1}{2} times \frac{11}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{2}}{-\frac{1}{2}+\frac{1\times 11}{2\times 8}-1}$$

Do the multiplications in the fraction \frac{1\times 11}{2\times 8}.

$$\frac{\frac{5}{2}}{-\frac{1}{2}+\frac{11}{16}-1}$$

Least common multiple of 2 and 16 is 16. Convert -\frac{1}{2} and \frac{11}{16} to fractions with denominator 16.

$$\frac{\frac{5}{2}}{-\frac{8}{16}+\frac{11}{16}-1}$$

Since -\frac{8}{16} and \frac{11}{16} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5}{2}}{\frac{-8+11}{16}-1}$$

Add -8 and 11 to get 3.

$$\frac{\frac{5}{2}}{\frac{3}{16}-1}$$

Convert 1 to fraction \frac{16}{16}.

$$\frac{\frac{5}{2}}{\frac{3}{16}-\frac{16}{16}}$$

Since \frac{3}{16} and \frac{16}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{2}}{\frac{3-16}{16}}$$

Subtract 16 from 3 to get -13.

$$\frac{\frac{5}{2}}{-\frac{13}{16}}$$

Divide \frac{5}{2} by -\frac{13}{16} by multiplying \frac{5}{2} by the reciprocal of -\frac{13}{16}.

$$\frac{5}{2}\left(-\frac{16}{13}\right)$$

Multiply \frac{5}{2} times -\frac{16}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(-16\right)}{2\times 13}$$

Do the multiplications in the fraction \frac{5\left(-16\right)}{2\times 13}.

$$\frac{-80}{26}$$

Reduce the fraction \frac{-80}{26} to lowest terms by extracting and canceling out 2.

$$-\frac{40}{13}$$

Factor

$$-\frac{40}{13} = -3\frac{1}{13} = -3.076923076923077$$