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

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

Evaluate

$$\frac{5}{3}\approx 1.666666667$$

Solution Steps

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

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

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

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

Subtract 3 from 4 to get 1.

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

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{1}{5} to fractions with denominator 20.

$$\frac{\frac{1}{12}}{\frac{5}{20}-\frac{4}{20}}$$

Since \frac{5}{20} and \frac{4}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{12}}{\frac{5-4}{20}}$$

Subtract 4 from 5 to get 1.

$$\frac{\frac{1}{12}}{\frac{1}{20}}$$

Divide \frac{1}{12} by \frac{1}{20} by multiplying \frac{1}{12} by the reciprocal of \frac{1}{20}.

$$\frac{1}{12}\times 20$$

Multiply \frac{1}{12} and 20 to get \frac{20}{12}.

$$\frac{20}{12}$$

Reduce the fraction \frac{20}{12} to lowest terms by extracting and canceling out 4.

$$\frac{5}{3}$$

Factor

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$