Solve 2/3*1/3+3/4*1/3+frac{1}{2}*frac{1}{3}=

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

Evaluate

$$\frac{23}{36}\approx 0.638888889$$

Solution Steps

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

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

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

$$\frac{2}{9}+\frac{3}{4}\times \frac{1}{3}+\frac{1}{2}\times \frac{1}{3}$$

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

$$\frac{2}{9}+\frac{3\times 1}{4\times 3}+\frac{1}{2}\times \frac{1}{3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{2}{9}+\frac{1}{4}+\frac{1}{2}\times \frac{1}{3}$$

Least common multiple of 9 and 4 is 36. Convert \frac{2}{9} and \frac{1}{4} to fractions with denominator 36.

$$\frac{8}{36}+\frac{9}{36}+\frac{1}{2}\times \frac{1}{3}$$

Since \frac{8}{36} and \frac{9}{36} have the same denominator, add them by adding their numerators.

$$\frac{8+9}{36}+\frac{1}{2}\times \frac{1}{3}$$

Add 8 and 9 to get 17.

$$\frac{17}{36}+\frac{1}{2}\times \frac{1}{3}$$

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

$$\frac{17}{36}+\frac{1\times 1}{2\times 3}$$

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

$$\frac{17}{36}+\frac{1}{6}$$

Least common multiple of 36 and 6 is 36. Convert \frac{17}{36} and \frac{1}{6} to fractions with denominator 36.

$$\frac{17}{36}+\frac{6}{36}$$

Since \frac{17}{36} and \frac{6}{36} have the same denominator, add them by adding their numerators.

$$\frac{17+6}{36}$$

Add 17 and 6 to get 23.

$$\frac{23}{36}$$

Factor

$$\frac{23}{2 ^ {2} \cdot 3 ^ {2}} = 0.6388888888888888$$