Solve {r}{2*1/2*1/2*1/3*1/3}{+2*frac{2}{3}*frac{1}{3}*frac{1}{2}*frac{1}{2}}

$$\left. \begin{array} { r } { 2 \times \frac { 1 } { 2 } \times \frac { 1 } { 2 } \times \frac { 1 } { 3 } \times \frac { 1 } { 3 } } \\ { + 2 \times \frac { 2 } { 3 } \times \frac { 1 } { 3 } \times \frac { 1 } { 2 } \times \frac { 1 } { 2 } } \end{array} \right.$$

Evaluate

$$\frac{1}{6}\approx 0.166666667$$

Solution Steps

Cancel out 2 and 2.

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

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

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

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

$$\frac{1}{6}\times \frac{1}{3}+2\times \frac{2}{3}\times \frac{1}{3}\times \frac{1}{2}\times \frac{1}{2}$$

Multiply \frac{1}{6} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{6\times 3}+2\times \frac{2}{3}\times \frac{1}{3}\times \frac{1}{2}\times \frac{1}{2}$$

Do the multiplications in the fraction \frac{1\times 1}{6\times 3}.

$$\frac{1}{18}+2\times \frac{2}{3}\times \frac{1}{3}\times \frac{1}{2}\times \frac{1}{2}$$

Express 2\times \frac{2}{3} as a single fraction.

$$\frac{1}{18}+\frac{2\times 2}{3}\times \frac{1}{3}\times \frac{1}{2}\times \frac{1}{2}$$

Multiply 2 and 2 to get 4.

$$\frac{1}{18}+\frac{4}{3}\times \frac{1}{3}\times \frac{1}{2}\times \frac{1}{2}$$

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

$$\frac{1}{18}+\frac{4\times 1}{3\times 3}\times \frac{1}{2}\times \frac{1}{2}$$

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

$$\frac{1}{18}+\frac{4}{9}\times \frac{1}{2}\times \frac{1}{2}$$

Multiply \frac{4}{9} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{18}+\frac{4\times 1}{9\times 2}\times \frac{1}{2}$$

Do the multiplications in the fraction \frac{4\times 1}{9\times 2}.

$$\frac{1}{18}+\frac{4}{18}\times \frac{1}{2}$$

Reduce the fraction \frac{4}{18} to lowest terms by extracting and canceling out 2.

$$\frac{1}{18}+\frac{2}{9}\times \frac{1}{2}$$

Multiply \frac{2}{9} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{18}+\frac{2\times 1}{9\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{1}{18}+\frac{1}{9}$$

Least common multiple of 18 and 9 is 18. Convert \frac{1}{18} and \frac{1}{9} to fractions with denominator 18.

$$\frac{1}{18}+\frac{2}{18}$$

Since \frac{1}{18} and \frac{2}{18} have the same denominator, add them by adding their numerators.

$$\frac{1+2}{18}$$

Add 1 and 2 to get 3.

$$\frac{3}{18}$$

Reduce the fraction \frac{3}{18} to lowest terms by extracting and canceling out 3.

$$\frac{1}{6}$$

Factor

$$\frac{1}{2 \cdot 3} = 0.16666666666666666$$