Solve 1/frac{2{3}-4/5}=

$$\frac { 1 } { \frac { 2 } { 3 } - \frac { 4 } { 5 } } =$$

Evaluate

$$-\frac{15}{2}=-7.5$$

Solution Steps

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

$$\frac{1}{\frac{10}{15}-\frac{12}{15}}$$

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

$$\frac{1}{\frac{10-12}{15}}$$

Subtract 12 from 10 to get -2.

$$\frac{1}{-\frac{2}{15}}$$

Divide 1 by -\frac{2}{15} by multiplying 1 by the reciprocal of -\frac{2}{15}.

$$1\left(-\frac{15}{2}\right)$$

Multiply 1 and -\frac{15}{2} to get -\frac{15}{2}.

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

Factor

$$-\frac{15}{2} = -7\frac{1}{2} = -7.5$$