Solve 15div(-3/2+5/6)

$$15 \div ( - \frac { 3 } { 2 } + \frac { 5 } { 6 } )$$

Evaluate

$$-\frac{45}{2}=-22.5$$

Solution Steps

Least common multiple of 2 and 6 is 6. Convert -\frac{3}{2} and \frac{5}{6} to fractions with denominator 6.

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

Since -\frac{9}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

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

Add -9 and 5 to get -4.

$$\frac{15}{\frac{-4}{6}}$$

Reduce the fraction \frac{-4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{15}{-\frac{2}{3}}$$

Divide 15 by -\frac{2}{3} by multiplying 15 by the reciprocal of -\frac{2}{3}.

$$15\left(-\frac{3}{2}\right)$$

Express 15\left(-\frac{3}{2}\right) as a single fraction.

$$\frac{15\left(-3\right)}{2}$$

Multiply 15 and -3 to get -45.

$$\frac{-45}{2}$$

Fraction \frac{-45}{2} can be rewritten as -\frac{45}{2} by extracting the negative sign.

$$-\frac{45}{2}$$

Factor

$$-\frac{45}{2} = -22\frac{1}{2} = -22.5$$