Solve 1/7*13/14+frac{4sqrt{3}}{7}*frac{4sqrt{3}}{14}

$$\frac { 1 } { 7 } \times \frac { 13 } { 14 } + \frac { 4 \sqrt { 3 } } { 7 } \times \frac { 4 \sqrt { 3 } } { 14 }$$

Evaluate

$$\frac{61}{98}\approx 0.62244898$$

Short Solution Steps

Multiply \frac{1}{7} times \frac{13}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 13}{7\times 14}+\frac{4\sqrt{3}}{7}\times \frac{4\sqrt{3}}{14}$$

Do the multiplications in the fraction \frac{1\times 13}{7\times 14}.

$$\frac{13}{98}+\frac{4\sqrt{3}}{7}\times \frac{4\sqrt{3}}{14}$$

Divide 4\sqrt{3} by 14 to get \frac{2}{7}\sqrt{3}.

$$\frac{13}{98}+\frac{4\sqrt{3}}{7}\times \frac{2}{7}\sqrt{3}$$

Multiply \frac{4\sqrt{3}}{7} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13}{98}+\frac{4\sqrt{3}\times 2}{7\times 7}\sqrt{3}$$

Express \frac{4\sqrt{3}\times 2}{7\times 7}\sqrt{3} as a single fraction.

$$\frac{13}{98}+\frac{4\sqrt{3}\times 2\sqrt{3}}{7\times 7}$$

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{4\sqrt{3}\times 2\sqrt{3}}{7\times 7} times \frac{2}{2}.

$$\frac{13}{98}+\frac{2\times 4\sqrt{3}\times 2\sqrt{3}}{98}$$

Since \frac{13}{98} and \frac{2\times 4\sqrt{3}\times 2\sqrt{3}}{98} have the same denominator, add them by adding their numerators.

$$\frac{13+2\times 4\sqrt{3}\times 2\sqrt{3}}{98}$$

Do the multiplications in 13+2\times 4\sqrt{3}\times 2\sqrt{3}.

$$\frac{13+48}{98}$$

Do the calculations in 13+48.

$$\frac{61}{98}$$

Factor

$$\frac{61}{2 \cdot 7 ^ {2}} = 0.6224489795918368$$