Solve (1/2+(1/2+(1/2+2/6):frac{10}{8})):(frac{3}{2})-(frac{1}{2}):(frac{1}{2})=

$$( \frac { 1 } { 2 } + ( \frac { 1 } { 2 } + ( \frac { 1 } { 2 } + \frac { 2 } { 6 } ) : \frac { 10 } { 8 } ) ) : ( \frac { 3 } { 2 } ) - ( \frac { 1 } { 2 } ) : ( \frac { 1 } { 2 } ) =$$

Evaluate

$$\frac{1}{9}\approx 0.111111111$$

Solution Steps

Divide \frac{1}{2} by \frac{1}{2} to get 1.

$$\frac{\frac{1}{2}+\frac{1}{2}+\frac{\frac{1}{2}+\frac{2}{6}}{\frac{10}{8}}}{\frac{3}{2}}-1$$

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

$$\frac{\frac{1+1}{2}+\frac{\frac{1}{2}+\frac{2}{6}}{\frac{10}{8}}}{\frac{3}{2}}-1$$

Add 1 and 1 to get 2.

$$\frac{\frac{2}{2}+\frac{\frac{1}{2}+\frac{2}{6}}{\frac{10}{8}}}{\frac{3}{2}}-1$$

Divide 2 by 2 to get 1.

$$\frac{1+\frac{\frac{1}{2}+\frac{2}{6}}{\frac{10}{8}}}{\frac{3}{2}}-1$$

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

$$\frac{1+\frac{\frac{1}{2}+\frac{1}{3}}{\frac{10}{8}}}{\frac{3}{2}}-1$$

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

$$\frac{1+\frac{\frac{3}{6}+\frac{2}{6}}{\frac{10}{8}}}{\frac{3}{2}}-1$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{1+\frac{\frac{3+2}{6}}{\frac{10}{8}}}{\frac{3}{2}}-1$$

Add 3 and 2 to get 5.

$$\frac{1+\frac{\frac{5}{6}}{\frac{10}{8}}}{\frac{3}{2}}-1$$

Reduce the fraction \frac{10}{8} to lowest terms by extracting and canceling out 2.

$$\frac{1+\frac{\frac{5}{6}}{\frac{5}{4}}}{\frac{3}{2}}-1$$

Divide \frac{5}{6} by \frac{5}{4} by multiplying \frac{5}{6} by the reciprocal of \frac{5}{4}.

$$\frac{1+\frac{5}{6}\times \frac{4}{5}}{\frac{3}{2}}-1$$

Multiply \frac{5}{6} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1+\frac{5\times 4}{6\times 5}}{\frac{3}{2}}-1$$

Cancel out 5 in both numerator and denominator.

$$\frac{1+\frac{4}{6}}{\frac{3}{2}}-1$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

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

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

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

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

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

Add 3 and 2 to get 5.

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

Divide \frac{5}{3} by \frac{3}{2} by multiplying \frac{5}{3} by the reciprocal of \frac{3}{2}.

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

Multiply \frac{5}{3} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{5\times 2}{3\times 3}.

$$\frac{10}{9}-1$$

Convert 1 to fraction \frac{9}{9}.

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

Since \frac{10}{9} and \frac{9}{9} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 9 from 10 to get 1.

$$\frac{1}{9}$$

Factor

$$\frac{1}{3 ^ {2}} = 0.1111111111111111$$