Solve 3/5*1/2-frac{4sqrt{5}}{25}*frac{sqrt{3}}{2}

$$\frac { 3 } { 5 } \times \frac { 1 } { 2 } - \frac { 4 \sqrt { 5 } } { 25 } \times \frac { \sqrt { 3 } } { 2 }$$

Evaluate

$$-\frac{2\sqrt{15}}{25}+\frac{3}{10}\approx -0.009838668$$

Short Solution Steps

Multiply \frac{3}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 1}{5\times 2}-\frac{4\sqrt{5}}{25}\times \frac{\sqrt{3}}{2}$$

Do the multiplications in the fraction \frac{3\times 1}{5\times 2}.

$$\frac{3}{10}-\frac{4\sqrt{5}}{25}\times \frac{\sqrt{3}}{2}$$

Multiply \frac{4\sqrt{5}}{25} times \frac{\sqrt{3}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{10}-\frac{4\sqrt{5}\sqrt{3}}{25\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3}{10}-\frac{2\sqrt{3}\sqrt{5}}{25}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{3}{10}-\frac{2\sqrt{15}}{25}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10 and 25 is 50. Multiply \frac{3}{10} times \frac{5}{5}. Multiply \frac{2\sqrt{15}}{25} times \frac{2}{2}.

$$\frac{3\times 5}{50}-\frac{2\times 2\sqrt{15}}{50}$$

Since \frac{3\times 5}{50} and \frac{2\times 2\sqrt{15}}{50} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 5-2\times 2\sqrt{15}}{50}$$

Do the multiplications in 3\times 5-2\times 2\sqrt{15}.

$$\frac{15-4\sqrt{15}}{50}$$

Factor

$$\frac{\sqrt{15} {(\sqrt{15} - 4)}}{50} = -0.009838667696593341$$