Solve (1/2-sqrt{25/4})*1/3-sqrt{16/25}=

$$( \frac { 1 } { 2 } - \sqrt { \frac { 25 } { 4 } } ) \cdot \frac { 1 } { 3 } - \sqrt { \frac { 16 } { 25 } } =$$

Evaluate

$$-\frac{22}{15}\approx -1.466666667$$

Solution Steps

Rewrite the square root of the division \frac{25}{4} as the division of square roots \frac{\sqrt{25}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\left(\frac{1}{2}-\frac{5}{2}\right)\times \frac{1}{3}-\sqrt{\frac{16}{25}}$$

Since \frac{1}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-5}{2}\times \frac{1}{3}-\sqrt{\frac{16}{25}}$$

Subtract 5 from 1 to get -4.

$$\frac{-4}{2}\times \frac{1}{3}-\sqrt{\frac{16}{25}}$$

Divide -4 by 2 to get -2.

$$-2\times \frac{1}{3}-\sqrt{\frac{16}{25}}$$

Multiply -2 and \frac{1}{3} to get \frac{-2}{3}.

$$\frac{-2}{3}-\sqrt{\frac{16}{25}}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$-\frac{2}{3}-\sqrt{\frac{16}{25}}$$

Rewrite the square root of the division \frac{16}{25} as the division of square roots \frac{\sqrt{16}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$-\frac{2}{3}-\frac{4}{5}$$

Least common multiple of 3 and 5 is 15. Convert -\frac{2}{3} and \frac{4}{5} to fractions with denominator 15.

$$-\frac{10}{15}-\frac{12}{15}$$

Since -\frac{10}{15} and \frac{12}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-10-12}{15}$$

Subtract 12 from -10 to get -22.

$$-\frac{22}{15}$$

Factor

$$-\frac{22}{15} = -1\frac{7}{15} = -1.4666666666666666$$