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

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

Evaluate

$$\frac{7}{6}\approx 1.166666667$$

Short Solution Steps

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

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

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

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

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

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

Cancel out 2 in both numerator and denominator.

$$\frac{1}{6}+\frac{\sqrt{3}\sqrt{3}}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 3 is 6. Multiply \frac{\sqrt{3}\sqrt{3}}{3} times \frac{2}{2}.

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

Since \frac{1}{6} and \frac{2\sqrt{3}\sqrt{3}}{6} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 1+2\sqrt{3}\sqrt{3}.

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

Do the calculations in 1+6.

$$\frac{7}{6}$$

Factor

$$\frac{7}{2 \cdot 3} = 1\frac{1}{6} = 1.1666666666666667$$