Solve 5/24div(-1/5-3/10)sqrt{2+7/9}

$$\frac{ 5 }{ 24 } \div ( \frac{ -1 }{ 5 } - \frac{ 3 }{ 10 } ) \sqrt{ 2+ \frac{ 7 }{ 9 } }$$

Evaluate

$$-\frac{25}{36}\approx -0.694444444$$

Solution Steps

Fraction \frac{-1}{5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

$$\frac{\frac{5}{24}}{-\frac{1}{5}-\frac{3}{10}}\sqrt{2+\frac{7}{9}}$$

Least common multiple of 5 and 10 is 10. Convert -\frac{1}{5} and \frac{3}{10} to fractions with denominator 10.

$$\frac{\frac{5}{24}}{-\frac{2}{10}-\frac{3}{10}}\sqrt{2+\frac{7}{9}}$$

Since -\frac{2}{10} and \frac{3}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{24}}{\frac{-2-3}{10}}\sqrt{2+\frac{7}{9}}$$

Subtract 3 from -2 to get -5.

$$\frac{\frac{5}{24}}{\frac{-5}{10}}\sqrt{2+\frac{7}{9}}$$

Reduce the fraction \frac{-5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{5}{24}}{-\frac{1}{2}}\sqrt{2+\frac{7}{9}}$$

Divide \frac{5}{24} by -\frac{1}{2} by multiplying \frac{5}{24} by the reciprocal of -\frac{1}{2}.

$$\frac{5}{24}\left(-2\right)\sqrt{2+\frac{7}{9}}$$

Express \frac{5}{24}\left(-2\right) as a single fraction.

$$\frac{5\left(-2\right)}{24}\sqrt{2+\frac{7}{9}}$$

Multiply 5 and -2 to get -10.

$$\frac{-10}{24}\sqrt{2+\frac{7}{9}}$$

Reduce the fraction \frac{-10}{24} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{12}\sqrt{2+\frac{7}{9}}$$

Convert 2 to fraction \frac{18}{9}.

$$-\frac{5}{12}\sqrt{\frac{18}{9}+\frac{7}{9}}$$

Since \frac{18}{9} and \frac{7}{9} have the same denominator, add them by adding their numerators.

$$-\frac{5}{12}\sqrt{\frac{18+7}{9}}$$

Add 18 and 7 to get 25.

$$-\frac{5}{12}\sqrt{\frac{25}{9}}$$

Rewrite the square root of the division \frac{25}{9} as the division of square roots \frac{\sqrt{25}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$-\frac{5}{12}\times \frac{5}{3}$$

Multiply -\frac{5}{12} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5\times 5}{12\times 3}$$

Do the multiplications in the fraction \frac{-5\times 5}{12\times 3}.

$$\frac{-25}{36}$$

Fraction \frac{-25}{36} can be rewritten as -\frac{25}{36} by extracting the negative sign.

$$-\frac{25}{36}$$

Factor

$$-\frac{25}{36} = -0.6944444444444444$$