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

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

Evaluate

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

Solution Steps

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

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

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

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

Subtract 10 from 12 to get 2.

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

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

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

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

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

Factor

$$\frac{3 \cdot 5}{2} = 7\frac{1}{2} = 7.5$$