Solve (5/6-5/12):5/18

$$( \frac { 5 } { 6 } - \frac { 5 } { 12 } ) : \frac { 5 } { 18 }$$

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Least common multiple of 6 and 12 is 12. Convert \frac{5}{6} and \frac{5}{12} to fractions with denominator 12.

$$\frac{\frac{10}{12}-\frac{5}{12}}{\frac{5}{18}}$$

Since \frac{10}{12} and \frac{5}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{10-5}{12}}{\frac{5}{18}}$$

Subtract 5 from 10 to get 5.

$$\frac{\frac{5}{12}}{\frac{5}{18}}$$

Divide \frac{5}{12} by \frac{5}{18} by multiplying \frac{5}{12} by the reciprocal of \frac{5}{18}.

$$\frac{5}{12}\times \frac{18}{5}$$

Multiply \frac{5}{12} times \frac{18}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 18}{12\times 5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{18}{12}$$

Reduce the fraction \frac{18}{12} to lowest terms by extracting and canceling out 6.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$