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

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

Evaluate

$$\frac{10}{9}\approx 1.111111111$$

Solution Steps

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

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

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

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

Subtract 2 from 1 to get -1.

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

Anything divided by one gives itself.

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

The opposite of -\frac{1}{2} is \frac{1}{2}.

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

Convert 2 to fraction \frac{4}{2}.

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

Since \frac{4}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

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

Add 4 and 1 to get 5.

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

Express \frac{\frac{1}{2}}{2} as a single fraction.

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

Multiply 2 and 2 to get 4.

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

Convert 2 to fraction \frac{8}{4}.

$$\frac{\frac{5}{2}}{\frac{8}{4}+\frac{1}{4}}$$

Since \frac{8}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5}{2}}{\frac{8+1}{4}}$$

Add 8 and 1 to get 9.

$$\frac{\frac{5}{2}}{\frac{9}{4}}$$

Divide \frac{5}{2} by \frac{9}{4} by multiplying \frac{5}{2} by the reciprocal of \frac{9}{4}.

$$\frac{5}{2}\times \frac{4}{9}$$

Multiply \frac{5}{2} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 4}{2\times 9}$$

Do the multiplications in the fraction \frac{5\times 4}{2\times 9}.

$$\frac{20}{18}$$

Reduce the fraction \frac{20}{18} to lowest terms by extracting and canceling out 2.

$$\frac{10}{9}$$

Factor

$$\frac{2 \cdot 5}{3 ^ {2}} = 1\frac{1}{9} = 1.1111111111111112$$