Solve -5/4/1+1{1-frac{1/2/1+frac{1{2}}}}=?

$$- \frac { \frac { 5 } { 4 } } { 1 + \frac { 1 } { 1 - \frac { \frac { 1 } { 2 } } { 1 + \frac { 1 } { 2 } } } } = ?$$

Evaluate

$$-\frac{1}{2}=-0.5$$

Solution Steps

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

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

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

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

Add 2 and 1 to get 3.

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

Divide \frac{1}{2} by \frac{3}{2} by multiplying \frac{1}{2} by the reciprocal of \frac{3}{2}.

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

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

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

Cancel out 2 in both numerator and denominator.

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

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

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

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 3 to get 2.

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

Divide 1 by \frac{2}{3} by multiplying 1 by the reciprocal of \frac{2}{3}.

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

Multiply 1 and \frac{3}{2} to get \frac{3}{2}.

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

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

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

Since \frac{2}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

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

Add 2 and 3 to get 5.

$$-\frac{\frac{5}{4}}{\frac{5}{2}}$$

Divide \frac{5}{4} by \frac{5}{2} by multiplying \frac{5}{4} by the reciprocal of \frac{5}{2}.

$$-\frac{5}{4}\times \frac{2}{5}$$

Multiply \frac{5}{4} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{5\times 2}{4\times 5}$$

Cancel out 5 in both numerator and denominator.

$$-\frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

Factor

$$-\frac{1}{2} = -0.5$$