Solve (-5/13)(-frac{sqrt{3}}{2})-(-12/13)(-1/2)

$$( - \frac { 5 } { 13 } ) ( - \frac { \sqrt { 3 } } { 2 } ) - ( - \frac { 12 } { 13 } ) ( - \frac { 1 } { 2 } )$$

Evaluate

$$\frac{5\sqrt{3}}{26}-\frac{6}{13}\approx -0.128451768$$

Short Solution Steps

Multiply -\frac{5}{13} and -1 to get \frac{5}{13}.

$$\frac{5}{13}\times \frac{\sqrt{3}}{2}-\left(-\frac{12}{13}\left(-\frac{1}{2}\right)\right)$$

Multiply -\frac{12}{13} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{13}\times \frac{\sqrt{3}}{2}-\frac{-12\left(-1\right)}{13\times 2}$$

Do the multiplications in the fraction \frac{-12\left(-1\right)}{13\times 2}.

$$\frac{5}{13}\times \frac{\sqrt{3}}{2}-\frac{12}{26}$$

Reduce the fraction \frac{12}{26} to lowest terms by extracting and canceling out 2.

$$\frac{5}{13}\times \frac{\sqrt{3}}{2}-\frac{6}{13}$$

Multiply \frac{5}{13} times \frac{\sqrt{3}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\sqrt{3}}{13\times 2}-\frac{6}{13}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 13\times 2 and 13 is 2\times 13. Multiply \frac{6}{13} times \frac{2}{2}.

$$\frac{5\sqrt{3}}{2\times 13}-\frac{6\times 2}{2\times 13}$$

Since \frac{5\sqrt{3}}{2\times 13} and \frac{6\times 2}{2\times 13} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\sqrt{3}-6\times 2}{2\times 13}$$

Do the multiplications in 5\sqrt{3}-6\times 2.

$$\frac{5\sqrt{3}-12}{2\times 13}$$

Expand 2\times 13.

$$\frac{5\sqrt{3}-12}{26}$$

Factor

$$\frac{5 \sqrt{3} - 12}{26} = -0.12845176777521594$$