Solve (-4/9+1/15):(-5/6-1/9)

$$( \frac { - 4 } { 9 } + \frac { 1 } { 15 } ) : ( \frac { - 5 } { 6 } - \frac { 1 } { 9 } )$$

Evaluate

$$\frac{2}{5}=0.4$$

Solution Steps

Fraction \frac{-4}{9} can be rewritten as -\frac{4}{9} by extracting the negative sign.

$$\frac{-\frac{4}{9}+\frac{1}{15}}{\frac{-5}{6}-\frac{1}{9}}$$

Least common multiple of 9 and 15 is 45. Convert -\frac{4}{9} and \frac{1}{15} to fractions with denominator 45.

$$\frac{-\frac{20}{45}+\frac{3}{45}}{\frac{-5}{6}-\frac{1}{9}}$$

Since -\frac{20}{45} and \frac{3}{45} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-20+3}{45}}{\frac{-5}{6}-\frac{1}{9}}$$

Add -20 and 3 to get -17.

$$\frac{-\frac{17}{45}}{\frac{-5}{6}-\frac{1}{9}}$$

Fraction \frac{-5}{6} can be rewritten as -\frac{5}{6} by extracting the negative sign.

$$\frac{-\frac{17}{45}}{-\frac{5}{6}-\frac{1}{9}}$$

Least common multiple of 6 and 9 is 18. Convert -\frac{5}{6} and \frac{1}{9} to fractions with denominator 18.

$$\frac{-\frac{17}{45}}{-\frac{15}{18}-\frac{2}{18}}$$

Since -\frac{15}{18} and \frac{2}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{17}{45}}{\frac{-15-2}{18}}$$

Subtract 2 from -15 to get -17.

$$\frac{-\frac{17}{45}}{-\frac{17}{18}}$$

Divide -\frac{17}{45} by -\frac{17}{18} by multiplying -\frac{17}{45} by the reciprocal of -\frac{17}{18}.

$$-\frac{17}{45}\left(-\frac{18}{17}\right)$$

Multiply -\frac{17}{45} times -\frac{18}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-17\left(-18\right)}{45\times 17}$$

Do the multiplications in the fraction \frac{-17\left(-18\right)}{45\times 17}.

$$\frac{306}{765}$$

Reduce the fraction \frac{306}{765} to lowest terms by extracting and canceling out 153.

$$\frac{2}{5}$$

Factor

$$\frac{2}{5} = 0.4$$