Solve frac{3sqrt{13}}{13}*(-9*(frac{2sqrt{13}}{13}))+4(3/2)

$$\frac { 3 \sqrt { 13 } } { 13 } \cdot ( - 9 \cdot ( \frac { 2 \sqrt { 13 } } { 13 } ) ) + 4 ( \frac { 3 } { 2 } )$$

Evaluate

$$\frac{24}{13}\approx 1.846153846$$

Short Solution Steps

Express \frac{3\sqrt{13}}{13}\left(-9\right) as a single fraction.

$$\frac{-3\sqrt{13}\times 9}{13}\times \frac{2\sqrt{13}}{13}+4\times \frac{3}{2}$$

Multiply \frac{-3\sqrt{13}\times 9}{13} times \frac{2\sqrt{13}}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\sqrt{13}\times 9\times 2\sqrt{13}}{13\times 13}+4\times \frac{3}{2}$$

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

$$\frac{-3\sqrt{13}\times 9\times 2\sqrt{13}}{13\times 13}+\frac{4\times 3}{2}$$

Multiply 4 and 3 to get 12.

$$\frac{-3\sqrt{13}\times 9\times 2\sqrt{13}}{13\times 13}+\frac{12}{2}$$

Divide 12 by 2 to get 6.

$$\frac{-3\sqrt{13}\times 9\times 2\sqrt{13}}{13\times 13}+6$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{13\times 13}{13\times 13}.

$$\frac{-3\sqrt{13}\times 9\times 2\sqrt{13}}{13\times 13}+\frac{6\times 13\times 13}{13\times 13}$$

Since \frac{-3\sqrt{13}\times 9\times 2\sqrt{13}}{13\times 13} and \frac{6\times 13\times 13}{13\times 13} have the same denominator, add them by adding their numerators.

$$\frac{-3\sqrt{13}\times 9\times 2\sqrt{13}+6\times 13\times 13}{13\times 13}$$

Do the multiplications in -3\sqrt{13}\times 9\times 2\sqrt{13}+6\times 13\times 13.

$$\frac{-702+1014}{13\times 13}$$

Do the calculations in -702+1014.

$$\frac{312}{13\times 13}$$

Expand 13\times 13.

$$\frac{312}{169}$$

Reduce the fraction \frac{312}{169} to lowest terms by extracting and canceling out 13.

$$\frac{24}{13}$$

Factor

$$\frac{2 ^ {3} \cdot 3}{13} = 1\frac{11}{13} = 1.8461538461538463$$