Solve (1/2-1/3):(1/4-1/6)

$$( \frac { 1 } { 2 } - \frac { 1 } { 3 } ) : ( \frac { 1 } { 4 } - \frac { 1 } { 6 } )$$

Evaluate

$$2$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{\frac{3}{6}-\frac{2}{6}}{\frac{1}{4}-\frac{1}{6}}$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3-2}{6}}{\frac{1}{4}-\frac{1}{6}}$$

Subtract 2 from 3 to get 1.

$$\frac{\frac{1}{6}}{\frac{1}{4}-\frac{1}{6}}$$

Least common multiple of 4 and 6 is 12. Convert \frac{1}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{\frac{1}{6}}{\frac{3}{12}-\frac{2}{12}}$$

Since \frac{3}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{6}}{\frac{3-2}{12}}$$

Subtract 2 from 3 to get 1.

$$\frac{\frac{1}{6}}{\frac{1}{12}}$$

Divide \frac{1}{6} by \frac{1}{12} by multiplying \frac{1}{6} by the reciprocal of \frac{1}{12}.

$$\frac{1}{6}\times 12$$

Multiply \frac{1}{6} and 12 to get \frac{12}{6}.

$$\frac{12}{6}$$

Divide 12 by 6 to get 2.

$$2$$

Factor

$$2$$