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

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

Evaluate

$$-\frac{4}{21}\approx -0.19047619$$

Solution Steps

Least common multiple of 4 and 6 is 12. Convert \frac{3}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{2}{3}-\frac{\frac{1}{2}}{\frac{9}{12}-\frac{2}{12}}$$

Since \frac{9}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{3}-\frac{\frac{1}{2}}{\frac{9-2}{12}}$$

Subtract 2 from 9 to get 7.

$$\frac{2}{3}-\frac{\frac{1}{2}}{\frac{7}{12}}$$

Divide \frac{1}{2} by \frac{7}{12} by multiplying \frac{1}{2} by the reciprocal of \frac{7}{12}.

$$\frac{2}{3}-\frac{1}{2}\times \frac{12}{7}$$

Multiply \frac{1}{2} times \frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}-\frac{1\times 12}{2\times 7}$$

Do the multiplications in the fraction \frac{1\times 12}{2\times 7}.

$$\frac{2}{3}-\frac{12}{14}$$

Reduce the fraction \frac{12}{14} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}-\frac{6}{7}$$

Least common multiple of 3 and 7 is 21. Convert \frac{2}{3} and \frac{6}{7} to fractions with denominator 21.

$$\frac{14}{21}-\frac{18}{21}$$

Since \frac{14}{21} and \frac{18}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14-18}{21}$$

Subtract 18 from 14 to get -4.

$$-\frac{4}{21}$$

Factor

$$-\frac{4}{21} = -0.19047619047619047$$