Solve (2/15+1,5):(12/3-24/5)

$$( \frac { 2 } { 15 } + 1,5 ) : ( 1 \frac { 2 } { 3 } - 2 \frac { 4 } { 5 } )$$

Evaluate

$$-\frac{49}{34}\approx -1,441176471$$

Solution Steps

Convert decimal number 1,5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{2}{15}+\frac{3}{2}}{\frac{1\times 3+2}{3}-\frac{2\times 5+4}{5}}$$

Least common multiple of 15 and 2 is 30. Convert \frac{2}{15} and \frac{3}{2} to fractions with denominator 30.

$$\frac{\frac{4}{30}+\frac{45}{30}}{\frac{1\times 3+2}{3}-\frac{2\times 5+4}{5}}$$

Since \frac{4}{30} and \frac{45}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4+45}{30}}{\frac{1\times 3+2}{3}-\frac{2\times 5+4}{5}}$$

Add 4 and 45 to get 49.

$$\frac{\frac{49}{30}}{\frac{1\times 3+2}{3}-\frac{2\times 5+4}{5}}$$

Multiply 1 and 3 to get 3.

$$\frac{\frac{49}{30}}{\frac{3+2}{3}-\frac{2\times 5+4}{5}}$$

Add 3 and 2 to get 5.

$$\frac{\frac{49}{30}}{\frac{5}{3}-\frac{2\times 5+4}{5}}$$

Multiply 2 and 5 to get 10.

$$\frac{\frac{49}{30}}{\frac{5}{3}-\frac{10+4}{5}}$$

Add 10 and 4 to get 14.

$$\frac{\frac{49}{30}}{\frac{5}{3}-\frac{14}{5}}$$

Least common multiple of 3 and 5 is 15. Convert \frac{5}{3} and \frac{14}{5} to fractions with denominator 15.

$$\frac{\frac{49}{30}}{\frac{25}{15}-\frac{42}{15}}$$

Since \frac{25}{15} and \frac{42}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{49}{30}}{\frac{25-42}{15}}$$

Subtract 42 from 25 to get -17.

$$\frac{\frac{49}{30}}{-\frac{17}{15}}$$

Divide \frac{49}{30} by -\frac{17}{15} by multiplying \frac{49}{30} by the reciprocal of -\frac{17}{15}.

$$\frac{49}{30}\left(-\frac{15}{17}\right)$$

Multiply \frac{49}{30} times -\frac{15}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{49\left(-15\right)}{30\times 17}$$

Do the multiplications in the fraction \frac{49\left(-15\right)}{30\times 17}.

$$\frac{-735}{510}$$

Reduce the fraction \frac{-735}{510} to lowest terms by extracting and canceling out 15.

$$-\frac{49}{34}$$

Factor

$$-\frac{49}{34} = -1\frac{15}{34} = -1.4411764705882353$$