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

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

Evaluate

$$\frac{2}{5}=0.4$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\frac{1}{6}}{\frac{8}{12}-\frac{3}{12}}$$

Since \frac{8}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{6}}{\frac{8-3}{12}}$$

Subtract 3 from 8 to get 5.

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

Divide \frac{1}{6} by \frac{5}{12} by multiplying \frac{1}{6} by the reciprocal of \frac{5}{12}.

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

Multiply \frac{1}{6} times \frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 12}{6\times 5}.

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

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

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

Factor

$$\frac{2}{5} = 0.4$$