Solve 1/3-1/4/frac{1{5}-1/6}=

$$\frac { \frac { 1 } { 3 } - \frac { 1 } { 4 } } { \frac { 1 } { 5 } - \frac { 1 } { 6 } } =$$

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\frac{4}{12}-\frac{3}{12}}{\frac{1}{5}-\frac{1}{6}}$$

Since \frac{4}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4-3}{12}}{\frac{1}{5}-\frac{1}{6}}$$

Subtract 3 from 4 to get 1.

$$\frac{\frac{1}{12}}{\frac{1}{5}-\frac{1}{6}}$$

Least common multiple of 5 and 6 is 30. Convert \frac{1}{5} and \frac{1}{6} to fractions with denominator 30.

$$\frac{\frac{1}{12}}{\frac{6}{30}-\frac{5}{30}}$$

Since \frac{6}{30} and \frac{5}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{12}}{\frac{6-5}{30}}$$

Subtract 5 from 6 to get 1.

$$\frac{\frac{1}{12}}{\frac{1}{30}}$$

Divide \frac{1}{12} by \frac{1}{30} by multiplying \frac{1}{12} by the reciprocal of \frac{1}{30}.

$$\frac{1}{12}\times 30$$

Multiply \frac{1}{12} and 30 to get \frac{30}{12}.

$$\frac{30}{12}$$

Reduce the fraction \frac{30}{12} to lowest terms by extracting and canceling out 6.

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$