Solve 11/14*(1/7)+frac{5sqrt{3}}{14}*frac{4sqrt{3}}{7}

$$\frac{ 11 }{ 14 } \times ( \frac{ 1 }{ 7 } )+ \frac{ 5 \sqrt{ 3 } }{ 14 } \times \frac{ 4 \sqrt{ 3 } }{ 7 }$$

Evaluate

$$\frac{71}{98}\approx 0.724489796$$

Short Solution Steps

Multiply \frac{11}{14} times \frac{1}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 1}{14\times 7}+\frac{5\sqrt{3}}{14}\times \frac{4\sqrt{3}}{7}$$

Do the multiplications in the fraction \frac{11\times 1}{14\times 7}.

$$\frac{11}{98}+\frac{5\sqrt{3}}{14}\times \frac{4\sqrt{3}}{7}$$

Multiply \frac{5\sqrt{3}}{14} times \frac{4\sqrt{3}}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11}{98}+\frac{5\sqrt{3}\times 4\sqrt{3}}{14\times 7}$$

Cancel out 2 in both numerator and denominator.

$$\frac{11}{98}+\frac{2\times 5\sqrt{3}\sqrt{3}}{7\times 7}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 98 and 7\times 7 is 98. Multiply \frac{2\times 5\sqrt{3}\sqrt{3}}{7\times 7} times \frac{2}{2}.

$$\frac{11}{98}+\frac{2\times 2\times 5\sqrt{3}\sqrt{3}}{98}$$

Since \frac{11}{98} and \frac{2\times 2\times 5\sqrt{3}\sqrt{3}}{98} have the same denominator, add them by adding their numerators.

$$\frac{11+2\times 2\times 5\sqrt{3}\sqrt{3}}{98}$$

Do the multiplications in 11+2\times 2\times 5\sqrt{3}\sqrt{3}.

$$\frac{11+60}{98}$$

Do the calculations in 11+60.

$$\frac{71}{98}$$

Factor

$$\frac{71}{2 \cdot 7 ^ {2}} = 0.7244897959183674$$