Solve 1-1+5/2/2/1+frac{1+frac{5{2}}{2}}=

$$\frac { 1 - \frac { 1 + \frac { 5 } { 2 } } { 2 } } { 1 + \frac { 1 + \frac { 5 } { 2 } } { 2 } } =$$

Evaluate

$$-\frac{3}{11}\approx -0.272727273$$

Solution Steps

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

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

Since \frac{2}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

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

Add 2 and 5 to get 7.

$$\frac{1-\frac{\frac{7}{2}}{2}}{1+\frac{1+\frac{5}{2}}{2}}$$

Express \frac{\frac{7}{2}}{2} as a single fraction.

$$\frac{1-\frac{7}{2\times 2}}{1+\frac{1+\frac{5}{2}}{2}}$$

Multiply 2 and 2 to get 4.

$$\frac{1-\frac{7}{4}}{1+\frac{1+\frac{5}{2}}{2}}$$

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

$$\frac{\frac{4}{4}-\frac{7}{4}}{1+\frac{1+\frac{5}{2}}{2}}$$

Since \frac{4}{4} and \frac{7}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4-7}{4}}{1+\frac{1+\frac{5}{2}}{2}}$$

Subtract 7 from 4 to get -3.

$$\frac{-\frac{3}{4}}{1+\frac{1+\frac{5}{2}}{2}}$$

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

$$\frac{-\frac{3}{4}}{1+\frac{\frac{2}{2}+\frac{5}{2}}{2}}$$

Since \frac{2}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{3}{4}}{1+\frac{\frac{2+5}{2}}{2}}$$

Add 2 and 5 to get 7.

$$\frac{-\frac{3}{4}}{1+\frac{\frac{7}{2}}{2}}$$

Express \frac{\frac{7}{2}}{2} as a single fraction.

$$\frac{-\frac{3}{4}}{1+\frac{7}{2\times 2}}$$

Multiply 2 and 2 to get 4.

$$\frac{-\frac{3}{4}}{1+\frac{7}{4}}$$

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

$$\frac{-\frac{3}{4}}{\frac{4}{4}+\frac{7}{4}}$$

Since \frac{4}{4} and \frac{7}{4} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{3}{4}}{\frac{4+7}{4}}$$

Add 4 and 7 to get 11.

$$\frac{-\frac{3}{4}}{\frac{11}{4}}$$

Divide -\frac{3}{4} by \frac{11}{4} by multiplying -\frac{3}{4} by the reciprocal of \frac{11}{4}.

$$-\frac{3}{4}\times \frac{4}{11}$$

Multiply -\frac{3}{4} times \frac{4}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\times 4}{4\times 11}$$

Cancel out 4 in both numerator and denominator.

$$\frac{-3}{11}$$

Fraction \frac{-3}{11} can be rewritten as -\frac{3}{11} by extracting the negative sign.

$$-\frac{3}{11}$$

Factor

$$-\frac{3}{11} = -0.2727272727272727$$