Solve frac{9sqrt{3}}{4}+1/4(9/4-9/2)

$$\frac { 9 \sqrt { 3 } } { 4 } + \frac { 1 } { 4 } ( \frac { 9 } { 4 } - \frac { 9 } { 2 } )$$

Evaluate

$$\frac{9\sqrt{3}}{4}-\frac{9}{16}\approx 3.334614317$$

Short Solution Steps

Least common multiple of 4 and 2 is 4. Convert \frac{9}{4} and \frac{9}{2} to fractions with denominator 4.

$$\frac{9\sqrt{3}}{4}+\frac{1}{4}\left(\frac{9}{4}-\frac{18}{4}\right)$$

Since \frac{9}{4} and \frac{18}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9\sqrt{3}}{4}+\frac{1}{4}\times \frac{9-18}{4}$$

Subtract 18 from 9 to get -9.

$$\frac{9\sqrt{3}}{4}+\frac{1}{4}\left(-\frac{9}{4}\right)$$

Multiply \frac{1}{4} times -\frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\sqrt{3}}{4}+\frac{1\left(-9\right)}{4\times 4}$$

Do the multiplications in the fraction \frac{1\left(-9\right)}{4\times 4}.

$$\frac{9\sqrt{3}}{4}+\frac{-9}{16}$$

Fraction \frac{-9}{16} can be rewritten as -\frac{9}{16} by extracting the negative sign.

$$\frac{9\sqrt{3}}{4}-\frac{9}{16}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 16 is 16. Multiply \frac{9\sqrt{3}}{4} times \frac{4}{4}.

$$\frac{4\times 9\sqrt{3}}{16}-\frac{9}{16}$$

Since \frac{4\times 9\sqrt{3}}{16} and \frac{9}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\times 9\sqrt{3}-9}{16}$$

Do the multiplications in 4\times 9\sqrt{3}-9.

$$\frac{36\sqrt{3}-9}{16}$$

Factor

$$\frac{9 {(4 \sqrt{3} - 1)}}{16} = 3.3346143170299736$$